Dreaming to solve Pipes and Cisterns related problems in no time? Get the complete preparation kit of shortcuts and tricks here. These are another model of Time and Work problems. If you are perfect with the Time & Work Problems, then you can easily solve Pipes & Cisterns Problems and score well in them. Check for the sample solved questions here. Follow the below sections to know the full details regarding shortcuts, solved examples, easy steps to solve problems, formulae, important points etc.

Pipes and Cisterns – Important Points

Most of the students lose their marks in quantitative aptitude because of lack of time. If you have good practice over the problems, you can solve them in a very less time. Therefore check for the shortcuts and tricks to solve problems in a very less time. Once you know the important formulae, shortcuts and tips, focus on your practice. As said, practice makes a man perfect, practice more and more to get grip on the subject and learn it perfectly.

If you practice Cisterns and Pipes problems more, then you can know a few shortcuts by yourself. As every single minute is important in the competitive exam. These shortcuts help you in saving every minute and solve questions quickly.

Basic Terms:

Inlet:  A pipe that is used to fill the tank, reservoir or cistern is commonly known as “Inlet”. This kind of nature designates “positive type” or “plus” of work done.

Outlet: A pipe that is used to empty tank, reservoir or cistern is commonly known as “Outlet”. This kind of nature designates “negative type” or “negative” of work done.

Important Formulae

1. Suppose an inlet is attached to a tank fills in A hours, then part of that tank filled in one hour = 1/A
2. Suppose an outlet is attached to a tank empties in B hours, then part of that tank emptied in one hour = 1/B
3. An inlet fills a tank in A hours and outlet empties the same tank in B hours. If both pipes are opened at a similar time and B>A, the complete part of the tank filled in one hour can be calculated as (1/A – 1/B)
4. When two pipes are open at the same time, the time taken to fill the complete tank is (AB/B-A) Hours
5. If A is greater than B, water flowing into the tank is less than water flowing out of the tank. The net part of the tank that is emptied in one hour is calculated as (1/B – 1/A)
6. Hence, To empty the full tank when both pipes are open is calculated as (BA/A-B) Hours
7. Suppose an inlet can fill the tank in A hours and other inlets can fill the same tank in B hours. The net portion of the tank that is filled in one hour of both the inlets are opened at a similar time is calculated a (1/A+1/B)
8. Hence, the time required to fill the complete tank is calculated as (AB/A+B) Hours
9. As in an above-mentioned way, Suppose an outlet can empty the tank in A hours and other outlets can empty the same tank in B hours. The net portion of the tank that is emptied in one hour of both pipes start working together at a similar time is calculated as (1/A + 1/B)
10. Hence, the time required to empty the complete tank is calculated as (AB/A+B) Hours

Tricks and Tips to Solve Pipes & Cisterns

As mentioned above, time management is an important factor to crack a competitive exam. Look for the shortcuts which help you better in solving the problems quickly. Here are the important tips to solve all the problems with ease.

• Be familiar with all the terms like an outlet, inlet, filling a tank, emptying a tank, leak and all the related formulas. If you are perfect with these terms and formulas then only you can solve the problems easily.
• Don’t spend too much time on a single question, jump to the next one in this case. It kills so much of your time, instead get back to that question at the last stage of the exam.
• Memorize formulae and tricks as many times as possible, to score better marks in the exam.

Sample Questions on Pipes and Cisterns

Question 1:

X and Y are two outlet pipes which are connected to a full tank.  Pipe X can alone empty the tank in 10 minutes and pipe Y can alone empty the tank in 30 minutes. How much time does it take to empty the tank completely when both the pipes are opened?

Solution:

Suppose the capacity of the tank be LCM(10,30) = 30 units

• Proficiency of pipe X = 30/10 = 3 units/minute
• Proficiency of pipe Y= 30/30 = 1 unit/minute
• Combined proficiency of pipe X and Y = 4 units/minute

Therefore, the total time required to empty the tank if both pipes work together = 30/4 = 7 minutes 30 seconds

Question 2:

One large pump and 3 other small pumps are filling a tank. Each of the small pumps works at 2/3rd of the large pump rate. Suppose all the pumps work at the similar time, they should fill the full tank in what portion of the time that it would have taken the large pump alone?

Solution:

According to the question, Volume of two large pumps = Volume of three small pumps

To express the volume of one large pump + three small pumps with reference to the large pump, you should add a large pump on either side of the above equation.

Then the final equation will be as

One large pump + Three small pumps = Three large pumps

Hence, if all the pumps are open at the same time, they would fill the complete tank in 1/3rd of the time that large pump takes alone.

Question 3:

A water tank consists of three taps X, Y and Z. X tank fills 4 buckets in 24 minutes. Y tank fills 8 buckets in 1 hour. Z fills 2 buckets in 20 minutes. The tank will be emptied in 2 hours if all the taps are opened. How much is the capacity of the tank if a bucket can hold 5 litres of water?

Solution:

In 1 Hour

X tank fills 4 buckets in 24 minutes, Hence X fills 1 bucket in 6 minutes(24/4)

In the same way, Y tank fills 8 buckets in 1 hour. Hence Y fills 1 bucket in 60/8 minutes

In the same way, Z tank fills one bucket in 10 minutes (20/2)

In 2 hours

No. of buckets filled by X tank will be = 20 buckets (120/6)

Number of buckets filled by Y tank will be = 16 buckets ((120*8)/60))

No of buckets filled by Z tank will be =12 buckets (120/10)

Total no of buckets filled = 48 buckets (20+16+12)

The capacity of the tank i.e., total water coming out of the tank = 240 litres (48 * 5 litres)

Most of the questions asked in the competitive exams are of the same pattern mentioned above. Be perfect with the models and also practice various questions to know the patterns of questions asked. Practice all the questions beforehand and score better marks in the exam. Moreover, you can check various details of other competitive, inter, bank, police exams etc on our site. Get the latest updates on complete information of all the exams.

The post Quantitative Aptitude Pipes & Cisterns Problems with Solutions – Concept, Tricks appeared first on Learn CBSE.

Cube and Cube Root of numbers can be found easily using the simplest and quickest methods. Check the complete details of the How to Find the Cube and Cube Root of a Number? We have covered everything like the definition of cube and Cubes Relation with Cube Numbers, Perfect Cube, etc. For better understanding, we even jotted the solved examples explained in detail.

Cube

The cube of a number is calculated by multiplying a number itself by 3 times. If you consider a number n, then the cube of a number n is n. Here, n is the natural number.

Example:

1, 8, 27 are the cube number of the numbers 1, 2, and 3 respectively.

Cube of 9 = 9 × 9 × 9 = 729
Cube of 8 = 8 × 8 × 8 = 512
Cube of 6 = 6 × 6 × 6 = 216

Cubes Relation with Cube Numbers

In mathematics, a cube is defined as a solid figure where all edges are of the same sizes and each edge is perpendicular to other edges.

Example:

If you take cubes of 4 units, then you can form a bigger cube of 64 units. Or else, if you take cubes of 3 units, then you can form a bigger cube of 27 units.

Perfect Cube Cube Numbers

The product of the three same numbers will give you a cube of a number (perfect cube).

Example:

The cube of a number 2 is 2 × 2 × 2 = 8.
8 is a perfect cube.

Properties of Cube Numbers

1. The cube of an even number is always an even number.

Example:
(i) Find the cube of a number 2?
2 × 2 × 2 = 8
8 is an even number.
(ii) Find the cube of a number 4?
4 × 4 × 4 = 64
64 is an even number.
(iii) Find the cube of a number 6?
6 × 6 × 6 = 216

2. The cube of an odd number is always an odd number.

Example:
(i) Find the cube of a number 3?
3 × 3 × 3 = 27
27 is an odd number.
(ii) Find the cube of a number 5?
5 × 5 × 5 = 125
125 is an odd number.
(ii) Find the cube of a number 7?
7 × 7 × 7 = 343
343 is an odd number.

Units Digits in Cube Numbers

If a number is even or odd, its cube is even or odd respective to the given number. The cube of a unit’s digit always shows the below results.

(i) Cube of 1 = 1 × 1 × 1 = 1;
The Units Digits of Cube of 1 is 1.
(ii) Cube of 2 = 2 × 2 × 2 = 8
The Units Digits of Cube of 2 is 8.
(iii) Cube of 3 = 3 × 3 × 3 = 27
The Units Digits of Cube of 3 is 7.
(iv) Cube of 4 = 4 × 4 × 4 = 64
The Units Digits of Cube of 4 is 4.
(v) Cube of 5 = 5 × 5 × 5 = 125
The Units Digits of Cube of 5 is 5.
(vi) Cube of 6 = 6 × 6 × 6 = 216
The Units Digits of Cube of 6 is 6.
(vii) Cube of 7 = 7 × 7 × 7 = 343
The Units Digits of Cube of 7 is 3.
(viii) Cube of 8 = 8 × 8 × 8 = 512
The Units Digits of Cube of 8 is 2.
(ix) Cube of 9 = 9 × 9 × 9 = 729
The Units Digits of Cube of 9 is 9.

Cube roots

Cube Root of a Number is the inverse of finding the cube of a number. If the cube of a number 3 is 27, then the cube root of 27 is 3.

How to Find the Cube Root of a Number by Prime Factorisation Method?

The Prime Factorisation of any Number Cube Root can be calculated by grouping the triplets of the same numbers. Multiply the numbers by taking each one from each triplet to provide you the Cube Root of a Number.

Example:
Cube Root of 216 = 2 × 2 × 2 × 3 × 3 × 3 = 2 × 3 = 6
6 is the cube root of 216.

FAQs on Cube and Cube Roots

1. Find the cube of 3.4?
The cube of a number can be calculated by multiplying it three times.
Cube of 3.4 = 3.4 x 3.4 x 3.4 = 39.304

2. Is 288 a perfect cube? If not, find the smallest natural number by which 288 should be multiplied so that the product is a perfect cube.
The prime factorization of 288 is
288 = 2 x 2 x 2 x 6 x 6
Since we can see number 6 cannot be paired in a group of three. Therefore, 288 is not a perfect cube.
To make it a perfect cube, we have to multiply the 6 by the original number.
Thus, 2 x 2 x 2 x 6 x 6 x 6 = 1728, which is a perfect cube.
Hence, the smallest natural number which should be multiplied to 288 to make a perfect cube is 6.

3: Find the smallest number by which 256 must be divided to obtain a perfect cube.
The prime factorization of 256 is
256 = 2×2×2×2×2×2×4
Now, if we group the factors in triplets of equal factors,
256 = (2×2×2)×(2×2×2)×4
Here, 4 cannot be grouped into triples of equal factors.
Therefore, we will divide 256 by 4 to get a perfect cube.

4. Michael makes a cuboid of plasticine of sides 3 cm, 2 cm, 3 cm. How many such cuboids will he need to form a cube?
Given that the sides of the cube are 3 cm, 2 cm, and 3 cm.
Therefore, volume of cube = 3×2×3 = 18
The prime factorization of 18 = 3×2×3
Here, 2, 3, and 3 cannot be grouped into triplets of equal factors.
Therefore, we will multiply 18 by 2×2×3 = 12 to get a perfect square.
Hence, 12 cuboids are needed.

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In Set Theory we usually perform different operations on sets such as intersection, union, complement. The Difference of Sets is also a similar kind of operation which we perform on sets. You will understand the difference between intersection and difference of sets clearly after going through this article. Check out Set Theory to be clear with the concepts of Sets Operations.

How to find the Difference of Sets?

In general, the Difference between the Two Sets is the Set of elements present in A but not in B. It is represented as A – B. You can see the difference in the orange shaded region of the below Venn diagram. In the same way, the region shaded in violet indicates the difference between B and A.

Identities Involving Difference of Sets

• If Set A and B are equal then A-B = A-A = ϕ
• If you subtract an empty set from a Set then the result is the Set itself i.e. A – ϕ = A.
• In the Similar Way, if you subtract a Set from an Empty Set then the result is an Empty Set i.e. ϕ – A = ϕ
• If you subtract a Superset from Subset the result is an empty set i.e. A – B = ϕ if A ⊂ B
• If Two Sets A and B are disjoint then A – B = A, B – A = B

Solved Examples for finding Difference of Sets

1. If A = {4, 5, 6} and B = {7, 8, 9}. Find the Difference between Sets A and B and B and A?

Solution:

Given A = { 4, 5, 6}

B = {7, 8, 9}

A-B = {4, 5, 6} – { 7, 8, 9}

= { 4, 5, 6}

B-A = {7, 8, 9} – {4, 5, 6}

= {7, 8, 9}

Since two sets A, B are disjoint the difference between A and B yields A and difference between B and A gives B.

2. Let A = {c, d, e, f, g, h, i} and B = {b, d, f, g, i, h} find A-B and B-A?

Solution:

Given A = {c, d, e, f, g, h, i}

B = {b, d, f, g, i, h}

A-B = {c, d, e, f, g, h, i} – {b, d, f, g, i, h}

= { c, e}

The elements c, e belong to Set A but not B

B-A = {b, d, f, g, i, h} – {c, d, e, f, g, h, i}

= {b}

Thus, the element b belongs to Set B but not A.

3. Given Sets A = {3 , 4 , 8 , 9 , 11 , 12 } B = {3 , 4 , 8 , 9 , 11 , 12 }. Find the difference between them i.e. A-B?

Solution:

A = {3 , 4 , 8 , 9 , 11 , 12 }

B = {3 , 4 , 8 , 9 , 11 , 12 }

A-B = A- A( since both the sets are equal)

= ϕ or {}

When you subtract two equal sets the difference between them will be an Empty Set.

4. Given three sets P, Q and R such that:

P = {x : x is a natural number between 12 and 18},

Q = {y : y is a even number between 14 and 20} and

R = {5, 9, 10, 12, 18, 20}

(i) Find the difference between two sets P and Q

(ii) Find Q – R

(iii) Find R – P

(iv) Find Q – P

Solution:

Given P = {x : x is a natural number between 12 and 18}

P = { 13, 14, 15, 16, 17}

Q = {y : y is a even number between 14 and 20}

Q = { 16, 18}

R = {5, 9, 10, 12, 18, 20}

(i) Difference between two sets P and Q i.e. P-Q

P-Q = { 13, 14, 15, 16, 17} – { 16, 18}

= {13, 14, 15, 17}

Elements 13, 14, 15, 17 are there in P but not in Q.

(ii)Q – R

Q = { 16, 18}

R = {5, 9, 10, 12, 18, 20}

Q – R = { 16, 18} – {5, 9, 10, 12, 18, 20}

= {16}

16 is the element that is present in Q but not in R.

(iii) R – P

R = {5, 9, 10, 12, 18, 20}

P = {13, 14, 15, 16, 17}

R – P = {5, 9, 10, 12, 18, 20} – {13, 14, 15, 16, 17}

= { 5, 9, 10, 12, 18, 20}

(iv) Q – P

Q = { 16, 18}

P = {13, 14, 15, 16, 17}

Q – P = { 16, 18} – {13, 14, 15, 16, 17}

= { 18}

18 is the element that is present in Q but not in P.

The post Difference of Two Sets | What is Difference of Two Sets in Set Theory? appeared first on Learn CBSE.

Let’s learn about Sets before diving deep into the article Complement of a Set. Check out the Definition of Complement of a Set, its Representation, Venn Diagram of the Complement of the Set. Refer to Solved Examples for finding the Complement of a Set. To learn more about the Operations of Sets you can have a look at the Set Theory and clarify all your concerns easily.

Sets Definition

A Well Defined Collection of Objects or Elements is called Sets. Any set containing all the objects or elements related to a particular context is known as a Universal Set and is represented by U.

For any Set A that is a subset of the Universal Set U, the Complement of the Set A contains the elements that are members of Universal Set but not from Set A. The Complement of Set A is denoted by A′.

Complement of a Set

If U is a Universal Set and A is a Subset of U then the Complement of A is the set of all the elements in the Universal Set but not aren’t elements of Set A.

A′ = {x : x ∈ U and x ∉ A}

In Other Words, we can say that the Complement of A is nothing but the difference between the Universal Set and the Sub Set A.

Venn Diagram for Complement of a Set

The Venn Diagram representing the Complement of a Set is given by

Solved Examples on Complement of a Set

1.  Let U be a Universal Set that consists of natural numbers greater than 10 and less than 20. A, B are Subsets of U and given by

A ={x:x ∈ U and x is a perfect square}

B = {8, 9, 11, 12, 13}

Find the complement of sets A and B?

Solution:

U = {11,12,13,14,15,16,17,18,19}

A = {x:x ∈ U and x is a perfect square}

= {16}

B = {8, 9, 11, 12, 13}

A′ = U – A

{11,12,13,14,15,16,17,18,19} – {16}

= { 11, 12, 13, 14, 15, 17, 18, 19}

B′ = U – B

= {11,12,13,14,15,16,17,18,19} – {8, 9, 11, 12, 13}

= { 12, 14, 15, 16, 17, 18, 19}

2. If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = { 1, 3, 5, 7}. Find the Complement of A?

Solution:

Given U = {1, 2, 3, 4, 5, 6, 7, 8,, 9, 10}

A = {1, 3, 5, 7}

A′ = U – A

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} – {1, 3, 5, 7}

= { 2, 4, 6, 8, 9, 10}

3. If U = {3, 5, 7, 9, 11, 13, 15, 17, 19}, A = {6, 10, 4, 16}. Find the Complement of A?

Solution:

U = {3, 5, 7, 9, 11, 13, 15, 17, 19}

A = {6, 10, 4, 16}

A′ = U – A

= {3, 5, 7, 9, 11, 13, 15, 17, 19} – {6, 10, 4, 16}

= {3, 5, 7, 9, 11, 13, 15, 17, 19}

The post Complement of a Set Definition | How to find Complement of a Set? appeared first on Learn CBSE.

In this article, you will learn how to find the Complement of a Set. Check out the below sections to get an idea of how to find the Complement of a Set. Refer to Questions on Complement of a Set along with Answers explained in detail and get a grip on the concept. To learn completely about various operations on sets have a glance at the Set Theory and get a good hold of all the underlying topics.

Solved Example Questions on Complement of a Set

1. If U = {2, 4, 6, 8, 10, 12, 14} and A = {1, 3, 5}. Find the Complement of A?

Solution:

A^c or A^‘ = U – A

= {2, 3, 4, 5, 6, 8, 10, 12, 14} – {1, 3, 5}

= { 2, 4, 6, 8, 10, 12, 14}

The Complement of A is the Elements that are in the Universal Set and not in the Set A.

2. Given Sets B = {1 Orange, 1 Pineapple, 1 Guava, 1 Pomegranate} and U = {1 Guava, 1 Orange, 1 Apricot, 1 Pomegranate, 1 Custard Apple, 1 Banana, 1 Mango, 1 Apple, 1 Kiwifruit }. Find the Complement of B?

Solution:

B = {1 Orange, 1 Pineapple, 1 Guava, 1 Pomegranate}

U = {1 Guava, 1 Orange, 1 Apricot, 1 Pomegranate, 1 Custard Apple, 1 Banana, 1 Mango, 1 Apple, 1 Kiwifruit }

B^c or B^‘ = U – B

= {1 Guava, 1 Orange, 1 Apricot, 1 Pomegranate, 1 Custard Apple, 1 Banana, 1 Mango, 1 Apple, 1 Kiwifruit } – {1 Orange, 1 Pineapple, 1 Guava, 1 Pomegranate}

= { 1 Apricot, 1 Custard Apple, 1 Banana, 1 Mango, 1 Apple, 1 Kiwifruit}

3. Find the Complement of B if the Sets are B = {1, 3, 4, 5} U = {1, 2, 3, 4, 5, 6, 7, 8, 9 }?

Solution:

Given Sets are

U = {1, 2, 3, 4, 5, 6, 7, 8, 9}

B = {1, 3, 4, 5}

B^c or B^‘ = U – B

= {1, 2, 3, 4, 5, 6, 7, 8, 9} – {1, 3, 4, 5}

= {2, 6, 7, 8, 9}

4. Find the Complement of A

A = { x / x is a number bigger than 6 and smaller than 10}

U = { x / x is a positive number smaller than 10}

Solution:

Given

A = { x / x is a number bigger than 6 and smaller than 10}

= { 7, 8, 9}

U = { x / x is a positive number smaller than 10}

= { 1, 2, 3, 4, 5, 6, 7, 8, 9 }

A^c or A^‘ = U – A

= { 1, 2, 3, 4, 5, 6, 7, 8, 9 } – { 7, 8, 9}

= {1, 2, 3, 4, 5, 6}

5. Let U = {x : x is an integer, –7 ≤ x ≤ 4}, P = {-4, -2, 0, 7, 8, 9, 6}. Find the Complement of P?

Solution:

P = {-4, -2, 0, 7, 8, 9, 6}

U = {x : x is an integer, –7 ≤ x ≤ 4}

U = {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4}

P^c or P^‘ = U – P

= {-7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4} – {-4, -2, 0, 7, 8, 9, 6}

= { -7, -6, -5, -3, -1, 1, 2, 3, 4}

The post Problems on Complement of a Set | Complement of a Set Questions and Answers appeared first on Learn CBSE.

Generally, a cube is defined as a solid figure that has all sides equal. In other words, a Cube is a solid three-dimensional figure that consists of 6 square faces, 8 vertices, and 12 edges. When six identical square face together along with their edges form a cube. Also, the three edges of a cube join at each corner to form a vertex. The cube in a Cube and Cube Roots chapter is the first and basic concept that will let you know about the perfect cubes or cube numbers.

In mathematical terms, a cube of a number is explained as the multiplication of a number by three times. The cube of a number represents as a superscript 3 or 3 is written a little up to the right of the numbers.

Representation of a cube of a number: m³, where 3 is the power of m and read as “m cubed”.

Cube of a Number

A number is multiplied by itself 3 times to find the cube of that number.
cube of m = m × m × m
cube of m = m³

Examples:

(i) Find the cube of a number 3?

Solution:
cube of 3 = 3³
The cube of 3 = 3³ = 3 × 3 × 3
cube of 3 = 3³ = 27

The cube of 3 is 27

(ii) Find the cube of a number 2?

Solution:
Cube of 2 = 2³
The cube of 2 = 2³ = 2 × 2 × 2
cube of 2 = 2³ = 8

The cube of 2 is 8

(iii) Find the cube of a number 4?

Solution:
cube of 4 = 4³
The cube of 4 = 4³ = 4 × 4 × 4
cube of 4 = 4³ = 64

The cube of 4 is 64

(iii) Find the cube of a number 5?

Solution:
Cube of 5 = 5³
The cube of 5 = 5³ = 5 × 5 × 5
cube of 5 = 5³ = 125

The cube of 5 is 125

(iv) Find the cube of a number 6?

Solution:
cube of 6 = 6³
The cube of 6 = 6³ = 6 × 6 × 6
cube of 6 = 6³ = 216

The cube of 6 is 216

(v) Find the cube of a number 7?

Solution:
cube of 7 = 7³
The cube of 7 = 7³ = 7 × 7 × 7
cube of 7 = 7³ = 343

The cube of 7 is 343

Perfect Cubes and Cube Roots

A perfect cube is defined as a number that is the cube of an integer or the cube of some natural number.

Examples:
Cube of 1 = 1³ = 1 × 1 × 1 = 1
Cube of 2 = 2³ = 2 × 2 × 2 = 8
The Cube of 3 = 3³ = 3 × 3 × 3 = 27
Cube of 4 = 4³ = 4 × 4 × 4 = 64
The Cube of 5 = 5³ = 5 × 5 × 5 = 125

Cube of Negative Numbers

Cubing the number is nothing but raising the number to its 3rd power. The Cube of a negative number is always a negative number. If -m is a number, then the cube of -m is (-m)³ = -m × -m × -m

Examples:

(i) Find the cube of -1?

Answer:
cube of -1 = (-1)³ = -1 × -1 × -1 = -1

The cube of -1 is -1

(ii) Find the cube of -2?

Answer:
cube of -2 = (-2)³ = -2 × -2 × -2 = -8

The cube of -2 is -8

(iii) Find the cube of -3?

Answer:
cube of -3 = (-3)³ = -3 × -3 × -3 = -27

The cube of -3 is -27

(iv) Find the cube of -4?

Answer:
cube of -4 = (-4)³ = -4 × -4 × -4 = -64

The cube of -4 is -64

(v) Find the cube of -5?

Answer:
cube of -5 = (-5)³ = -5 × -5 × -5 = -125

The cube of -5 is -125

Cube of a Rational Number

Finding the cube of a rational number is represents as the (a/b)³ that is also eqaul to the a/b × a/b × a/b = (a × a × a)/(b × b × b) = a³/b³
Therefore, (a/b)³ = a³/b³

Examples:

(i) Find the cube of (1/2)³?

Answer:

cube of 1/2 = (1/2)³
The cube of 1/2 = (1/2)³ = (1/2) × (1/2) × (1/2)
cube of 1/2 = 1³/2³
cube of 1/2 = (1/2)³ = 1³/2³ = (1 × 1 × 1)/(2 × 2 × 2)
The cube of 1/2 = (1/2)³ = 1³/2³ = 1/8

The cube of (1/2) is 1/8

(i) Find the cube of (-4/3)³?

Answer:
cube of (-4/3) = (-4/3)³
The cube of (-4/3) = (-4/3)³ = (-4/3) × (-4/3) × (-4/3)
cube of (-4/3) = (-4)³/3³
cube of (-4/3) = (-4/3)³ = (-4)³/3³ = (-4 × -4 × -4)/(3 × 3 × 3)
The cube of (-4/3) = (-4/3)³ = (-4)³/3³ = -64/27

The cube of (-4/3) is -64/27

Cube number Properties:

(i) The cube of even integers is always even.
(ii) The cube of odd integers is always odd.

Perfect Cube Solved examples

1. Is 189 a perfect cube?

Answer:
Separate 189 into different prime factors
The prime factors for 189 are 3, 3, 3, 7
189 = 3 × 3 × 3 × 7
189 = 3 × 7
Divide 189 with 7 to make it a perfect cube.
So, 189 is not a perfect cube.

2. Find the number 216 is a perfect cube?

Answer:

Firstly, find the prime factors of 216
The prime factors of 216 are 2, 2, 2, 3, 3, 3
So, 216 = 2 × 2 × 2 × 3 × 3 × 3
216 = (2 × 3) × (2 × 3) × (2 × 3)
216 = 6 × 6 × 6
The 216 = 6³ = cube of 6
216 is a perfect cube as it is the cube of 6.

216 is a perfect cube

3. Find the smallest number that makes the 3087 a perfect cube?

Answer:
To know the smallest number that makes the 3087 a perfect cube, first, we need to find the prime factors of 3087.
The 3087 prime factors are 3, 3, 7, 7, 7
3087 = 3 × 3 × 7 × 7 × 7
If the product of prime factors is multiplied by the number 3, then 3087 becomes a perfect cube.

The required number is 3

4. Which number needs to divide from 392 to make it a perfect cube?

Answer:
To find the number that makes 392 a perfect cube, we need to find the prime factors of 392
The prime factors of 392 are 2, 2, 2, 7, 7
392 = 2 × 2 × 2 × 7 × 7
The 392 will becomes a perfect cube if 7 × 7 is divided from the product of prime factors.

The required number is 7 × 7

5. Find the cube of each of the following?
(i) 8 (ii) (2/5) (iii) 0.2 (iv) 2 3/4 (v) -5

Solutions:

(i) 8
cube of 8 = 8³
The cube of 8 = 8³ = 8 × 8 × 8
cube of 8 = 8³ = 512

The cube of 8 is 512

(i)(2/5)
cube of (2/5) = (2/5)³
The cube of (2/5) = (2/5)³ = (2/5) × (2/5) × (2/5)
cube of (2/5) = (2/5)³ = 2³/5³ = (2 × 2 × 2)/(5 × 5 × 5) = 8/125

The cube of (2/5) is 8/125

(iii) 0.2
cube of 0.2 = 0.2³
The cube of 0.2 = 0.2³ = (0.2) × 0.2 × 0.2
cube of 0.2 = (0.2)³ = 0.008

The cube of (0.2) is 0.008

(iv) 2 3/4
2 3/4 = 11/4
cube of 11/4 = (11/4)³
The cube of (11/4) = (11/4)³ = (11/4) × (11/4) × (11/4)
cube of (11/4) = (11/4)³ = (11 × 11 × 11)/(4 × 4 × 4) = 1331/64

The cube of (2 3/4) is 1331/64

(i) -5
cube of -5 = -5³
The cube of -5 = -5³ = -5 × -5 × -5
cube of -5 = -5³ = -125

The cube of (-5) is -125

The cube of a number is clearly explained along with examples and explanations.

The post Cube | Cube of a Number | Perfect Cube | Cube of a Negative Integer appeared first on Learn CBSE.

A perfect cube is the prime factors of a number that are arranged in triplets of equal factors. Check more about the perfect cubes and How to find if the given number is a perfect cube or not from the Cube and Cube Roots Chapter.

How to Find if the Given Number is a Perfect Cube?

To Find if the Given Number is a Perfect Cube, we need to find the prime factors of that number. If the prime factors are grouped together with the triplets, then the number is considered as the perfect cube. If not, the number is not a perfect cube. If you see the prime factor is a single factor or it is a double factor, then that particular number is not treated as a perfect cube.

Let’s find whether the given numbers are perfect cubes or not.

1. Find the below Numbers are Perfect Cubes?
(i) 18 (ii) 27,000 (iii) 120

Answer:

(i) 18
First, find the prime factors of the given number.
The prime factors of the given number 18 are 2, 3, 3
Therefore, 18 = 2 × 3 × 3
The prime factors 2 and 3 are single and double factors. There is no triple factor available in the prime factors of the given number. So, the given number is not a perfect cube.

The given number 18 is not a perfect cube.

(ii) 27,000

First, find the prime factors of the given number.
The prime factors of the given number 27,000 are 30, 30, 30
Therefore, 27,000 = 30 × 30 × 30
The prime factor 30 is grouped in triples. There is no other prime factor is left as single and double factors. So, the given number is a perfect cube.

The given number 27,000 is a perfect cube.

(i) 120
First, find the prime factors of the given number.
The prime factors of the given number 120 are 2, 2, 2, 3, 5
Therefore, 120 = 2 × 2 × 2 × 3 × 5
The prime factors 3 and 5 are single factors. There is one prime factor grouped in triples. As the single prime factors available in the product of prime factors of the given number, it is is not a perfect cube.

The given number 120 is not a perfect cube.

Smallest Multiple that is a Perfect Cube

The smallest multiple that make a number perfect cube can be calculated by following the step by step method product of prime factors of a number. A clear explanation is given To Find if the Given Number is a Perfect Cube and what is the smallest multiple that needs to make it a perfect cube. Check the below examples for a better understanding.

2. Find the smallest number by which 1372 must be multiplied so that the product is a perfect cube?

To find the smallest number by which 1372 must be multiplied so that the product is a perfect cube, you need to find the prime factors of the given number.
The prime factors of the given number 1372 are 7, 7, 7, 2, 2
1372 = 7 × 7 × 7 × 2 × 2
1372 = 7³ × 2 × 2
From above, by multiplying 2 the number 1372 becomes the perfect cube.
Therefore, the smallest number is 2.

3. Find the smallest number by which 2000 must be multiplied so that the product is a perfect cube?

To find the smallest number by which 2000 must be multiplied so that the product is a perfect cube, you need to find the prime factors of the given number.
The prime factors of the given number 2000 are 5, 5, 5, 4, 4
2000 = 5 × 5 × 5 × 4 × 4
2000 = 5³ × 4 × 4
From above, by multiplying 4 the number 2000 becomes the perfect cube.
Therefore, the smallest number is 4.

The post To Find if the Given Number is a Perfect Cube appeared first on Learn CBSE.

Cube Root of a number can be obtained by doing the inverse operation of calculating cube. In general terms, the cube root of a number is identified by a number that multiplied by itself thrice gives you the cube root of that number. The cube root of any number is denoted with the symbol ∛. Look at the Cube and Cube Roots solved examples and their explanations to learn them easily.

For example, the cube root of a number x is represented as ∛x.

How to Find the Cube Root of a Number?

Simply, Note down the product of primes a number. Then, form the groups in triplets using the product of primes a number. After that take one number from each triplet. The selected single number is the required cube root of the given number.

Note: If you find a group of prime factors that cannot form a group in triplets they remain the same and their cube root cannot be found.

Cube Root of a Number Solved Examples

(i) Find the Cube Root of a number 64?

Answer:
Write the product of primes of a given number 64 those form groups in triplets.
Cube Root of 64 = ∛64 = ∛(4 × 4 × 4)
Take one number from a group of triplets to find the cube root of 64.
Therefore, 4 is the cube root of a given number 64.

4 is the cube root of a given number 64.

(ii) Find the Cube Root of a number 8?

Answer:
Write the product of primes of a given number 8 those form groups in triplets.
Cube Root of 8= ∛8= ∛(2 × 2 × 2)
Take one number from a group of triplets to find the cube root of 8.
Therefore, 2 is the cube root of a given number 8.

2 is the cube root of a given number 8.

(iii) Find the Cube Root of a number 125?

Answer:
Write the product of primes of a given number 125 those form groups in triplets.
Cube Root of 125= ∛125= ∛(5 × 5 × 5)
Take one number from a group of triplets to find the cube root of 125.
Therefore, 5 is the cube root of a given number 125.

5 is the cube root of a given number 125.

(iv) Find the Cube Root of a number 27?

Answer:
Write the product of primes of a given number 27 those form groups in triplets.
Cube Root of 27 = ∛27 = ∛(3 × 3 × 3)
Take one number from a group of triplets to find the cube root of 27.
Therefore, 3 is the cube root of a given number 27.

3 is the cube root of a given number 27.

(iv) Find the Cube Root of a number 216?

Answer:
Write the product of primes of a given number 216 those form groups in triplets.
Cube Root of 216 = ∛216 = ∛(6 × 6 × 6)
Take one number from a group of triplets to find the cube root of 216.
Therefore, 6 is the cube root of a given number 216.

6 is the cube root of a given number 216.

Finding Cube Root by Prime Factorisation Method

Find the cube root of a number using the Prime Factorisation Method with the help of the below steps.

Step 1: Firstly, take the given number.
Step 2: Find the prime factors of the given number.
Step 3: Group the prime factors into each triplet.
Step 4: Collect each one factor from each group.
Step 5: Finally, find the product of each one factor from each group.
Step 6: The resultant is the cube root of a given number.

Cube Root of a Number by Prime Factorisation Method Solved Examples

(i) Find the Cube Root of 216 by Prime Factorisation Method?

Answer:
Firstly, find the prime factors of the given number.
216 = 2 × 2 × 2 × 3 × 3 × 3
Group the prime factors into each triplet.
216 = (2 × 2 × 2) × (3 × 3 × 3)
Collect each one factor from each group.
2 and 3
Finally, find the product of each one factor from each group.
∛216 = 2 × 3 = 6
6 is the cube root of 216.

(ii) Find the Cube Root of 343 by Prime Factorisation Method?

Answer: 
Firstly, find the prime factors of the given number.
343 = 7 × 7 × 7
Group the prime factors into each triplet.
343 = (7 × 7 × 7)
Collect each one factor from each group.
7
Finally, find the product of each one factor from each group.
∛343 = 7
7 is the cube root of 343.

(iii) Find the Cube Root of 2744 by Prime Factorisation Method?

Answer:
Firstly, find the prime factors of the given number.
2744 = 2 × 2 × 2 × 7 × 7 × 7
Group the prime factors into each triplet.
2744 = (2 × 2 × 2) × (7 × 7 × 7).
Collect each one factor from each group.
2 and 7
Finally, find the product of each one factor from each group.
∛2744 = 2 × 7 = 14
14 is the cube root of 2744.

Cube Roots of Negative Numbers

Cube Root of a negative number is always negative. If -m be a negative number. Then, (-m)³ = -m³.
Therefore, ∛-m³ = -m.
cube root of (-m³) = -(cube root of m³).
∛-m = – ∛m

Solved Examples of Cube Root of a Negative Numbers

(i) Find the Cube Root of (-1000)

Answer:
Firstly, find the prime factors of the number 1000.
1000 = 2 × 2 × 2 × 5 × 5 × 5
Group the prime factors into each triplet.
1000 = (2 × 2 × 2) × (5 × 5 × 5).
Collect each one factor from each group.
2 and 5
Finally, find the product of each one factor from each group.
∛1000 = 2 × 5 = 10
∛-m = – ∛m
∛-1000 = – ∛1000 = -10
-10 is the cube root of (-1000).

(ii) Find the Cube Root of (-216)

Answer:
Firstly, find the prime factors of the number 216.
216 = 2 × 2 × 2 × 3 × 3 × 3
Group the prime factors into each triplet.
216 = (2 × 2 × 2) × (3 × 3 × 3)
Collect each one factor from each group.
2 and 3
Finally, find the product of each one factor from each group.
∛216 = 2 × 3 = 6
∛-216 = – ∛216
∛-216= – ∛216= -6
-6 is the cube root of -216.

How to Find Cube Root of Product of Integers?

Cube Root of Product of Integers can be solved by using ∛ab = (∛a × ∛b)

Solved Examples:

(i) Find ∛(125 × 64)?

Answer:
Firstly, apply the cube root to both integers.
∛ab = (∛a × ∛b)
∛(125 × 64) = ∛125 × ∛64
Then, find the prime factors for each integer separately.
[∛{5 × 5 × 5}] × [∛{4 × 4 × 4}]
Take each integer from the group in triplets and multiply them to get the cube root of a given number.
(5 × 4) = 20
20 is the cube root of ∛(125 × 64).

(ii) Find ∛(27 × 64)?

Answer:
Firstly, apply the cube root to both integers.
∛ab = (∛a × ∛b)
∛(27 × 64) = ∛27 × ∛64
Then, find the prime factors for each integer separately.
[∛{3 × 3 × 3}] × [∛{4 × 4 × 4}]
Take each integer from the group in triplets and multiply them to get the cube root of a given number.
(3 × 4) = 12
12 is the cube root of ∛(27 × 64).

(iii) Find ∛[216 × (-343)]?

Answer:
Firstly, apply the cube root to both integers.
∛ab = (∛a × ∛b)
∛[216 × (-343)] = ∛216 × ∛-343
Then, find the prime factors for each integer separately.
[∛{6 × 6 × 6}] × [∛{(-7) × (-7) × (-7)}]
Take each integer from the group in triplets and multiply them to get the cube root of a given number.
[6 × (-7)] = -42
-42 is the cube root of ∛[216 × (-343)].

Cube Root of a Rational Number

The Cube Root of a Rational Number can be calculated with the help of ∛(a/b) = (∛a)/(∛b). Apply the Cube Root separately to each integer available on the numerator and the denominator to find the cube root of a rational number.

Solved Examples of Cube Root of a Rational Number

(i) Find ∛(216/2197)

Answer:
Firstly, apply the cube root to both integers.
∛(a/b) = (∛a)/(∛b)
∛(216/2197) = ∛216/∛2197
Then, find the prime factors for each integer separately.
[∛(6 × 6 × 6)]/[ ∛(13 × 13 × 13)]
Take each integer from the group in triplets to get the cube root of a given number.
6/13
6/13 is the cube root of ∛(216/2197).

(ii) Find ∛(27/8)

Answer:
Firstly, apply the cube root to both integers.
∛(a/b) = (∛a)/(∛b)
∛(27/8) = ∛27/∛8.
Then, find the prime factors for each integer separately.
[∛(3 × 3 × 3)]/[ ∛(2 × 2 × 2)]
Take each integer from the group in triplets to get the cube root of a given number.
3/2
3/2 is the cube root of ∛(27/8).

How to Find the Cube Root of Decimals?

The Cube Root of Decimals can easily be solved by converting them into fractions. After converting the decimal number into a fraction apply the cube root to the numerator and denominator separately. Then, convert the resultant value to decimal.

Cube Root of Decimals Solved Examples

(i) Find the cube root of 5.832.

Answer:
Conver the given decimal 5.832 into a fraction.
5.832 = 5832/1000
Now, apply the cube root to the fraction.
∛5832/1000
Apply the cube root to both integers.
∛(a/b) = (∛a)/(∛b)
∛5832/1000 = ∛5832/∛1000.
Then, find the prime factors for each integer separately.
∛(2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3)/∛(2 × 2 × 2 × 5 × 5 × 5)
Take each integer from the group in triplets to get the cube root of a given number.
(2 × 3 × 3)/(2 × 5) = 18/10
Convert the fraction into a decimal
18/10 = 1.8
1.8 is the cube root of 5.832.

The post Cube Root appeared first on Learn CBSE.

Learn the fast and easy Method for Finding the Cube of a Two-Digit Number that makes the Cube and Cube Root calculation more simple. The easy way to find the Cube of a Two-Digit Number is by using (a + b)³ = a³ + 3a²b + 3ab² + b³.

Solving Cube of a Two-Digit Number is easier after you identify the step by step process. Have a look at the simplest way to find the cube of all two-digit numbers. Also, learn more about Cube and Cube Roots of a Number with more tips and tricks.

What is the Short Cut Method for Finding The Cubes Of a Two-Digit Number?

The cube of a two-digit number can be found with the help of tens digit = a and also with the units digit b. We can make four columns using a³, (3a² × b), (3a × b²), and b³.

The remaining process is the same as the squaring a number by the column method. a³, 3a², 3ab², and b³ are simplified as

a² × a = a³;
a² × 3b = 3a²b;
b² × 3a = 3ab²;
b² × b = b³;

Cubes Of a Two-Digit Number Solved Examples

1. Find the value of (29)³ by the short-cut method?

Answer:
Let a = 2 and b = 9
Now, find the values of a³, 3a², 3ab², and b³.

Therefore, Cube of 29 = (29)³ = 24389

Cube of 29 is 24389

2. Find the value of (71)³ by the short-cut method?

Answer:

Let a = 7 and b = 1
Now, find the values of a³, 3a², 3ab², and b³.

Therefore, Cube of 71 = (71)³ = 357911

Find the easy and short cut method to learn the cube of a two-digit number. Begin your practice now with the help of the solved examples. Cube and Cube Root of a Numbers are clearly explained here.

The post Method for Finding the Cube of a Two-Digit Number appeared first on Learn CBSE.

Table of Cube Roots helps you to solve the cube of a number in an easy way. The approximate value of a cube root can be found easily with the help of the Table of Cube Roots.

If the given number is not a perfect cube, then one can find the number that has a cube which is nearly equal to the given number. The below table will give a clear idea of the approximate value of the cube roots of different numbers. Also, get complete knowledge on Cube and Cube Roots Concept by referring to our concepts.

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In the life of most teenagers, a significant part of their school life circles around their favorite subjects. With this, naturally comes the desire to score the most marks in a paper that you like, in addition to learning it in great detail. Particularly if we are talking about board exams like the one in class 10th, full marks are what most students aspire to score in Maths.

To know all about the class 10 Maths paper, tips and tricks on mark distribution, and best ways to score full marks, keep reading!

Syllabus- Class 10 Maths

One of the most important things to master in any examination is to be thoroughly versed in the prescribed syllabus. For all the doubts that a student has regarding the syllabus, here’s everything that you need to study for the class 10 Maths examination: 

• NUMBER SYSTEMS – 06 Marks 

Real Numbers  

Fundamental Theorem of Arithmetic – statements after reviewing the work done earlier and after illustrating and motivating through examples; Proofs of the irrationality of. The decimal representation of rational numbers in terms of terminating/non-terminating recurring decimals.

• ALGEBRA – 20 Marks 

1. Polynomials 

Zeros of a polynomial. Relationship between zeros and coefficients of quadratic polynomials.

2. Pair of Linear Equations in Two Variables

Pair of linear equations in two variables and graphical methods of their solution, consistency/ inconsistency.

Algebraic conditions for a number of solutions. The solution of a pair of linear equations in two variables algebraically – by substitution, by elimination. Simple situational problems. Simple problems on equations reducible to linear equations.

3. Quadratic Equations 

Standard form of a quadratic equation ax2 + bx + c = 0, (a ≠ 0). Solutions of quadratic equations (only real roots) by factorization and by using the quadratic formula. Relationship between discriminant and nature of roots.

4. Arithmetic Progressions 

The motivation for studying Arithmetic Progression Derivation of the nth term and sum of the first n terms of an A.P.

• COORDINATE GEOMETRY – 06 Marks 

1. Lines (In two-dimensions)
   

Review: Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula (internal division).

• GEOMETRY – 15 Marks

a. Triangles

Definitions, examples, counterexamples of similar triangles.

1. (Prove) If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
2. (Motivate) If a line divides two sides of a triangle in the same ratio, the line is parallel to the third side.
3. (Motivate) If the corresponding angles are equal in two triangles, their corresponding sides are proportional, and the triangles are similar.
4. (Motivate) If the corresponding sides of two triangles are proportional, their corresponding angles are equal, and the two triangles are similar.
5. (Motivate) If one angle of a triangle is equal to one angle of another triangle and the sides, including these angles, are proportional, and the two triangles are similar.
6. (Motivate) If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse, the triangles on each side of the perpendicular are similar to the whole triangle and to each other.
7. (Prove) In a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.

b. Circles 

Tangent to a circle at the point of contact.

1. (Prove) The tangent at any point of a circle is perpendicular to the radius through the point of contact.
2. (Prove) The lengths of tangents drawn from an external point to a circle are equal.

c. Constructions 

1. Division of a line segment in a given ratio (internally).
2. 2. Tangents to a circle from a point outside it.

• TRIGONOMETRY – 12 Marks 

a. Introduction to Trigonometry 

Trigonometric ratios of an acute angle of a right-angled triangle. Proof of their existence (well defined). Values (with proofs) of the trigonometric ratios of 30o, 45o, and 60o. Relationships between the ratios.

b. Trigonometric Identities 

Proof and applications of the identity sin2A + cos2A = 1. Only simple identities to be given.

c. Heights and Distances: Angle of elevation, Angle of Depression

Simple problems on heights and distances. Problems should not involve more than two right triangles. Angles of elevation/depression should be only 30o, 45o, 60o.

• MENSURATION – 10 Marks

a. Areas Related to Circles 

Motivate the area of a circle; area of sectors and segments of a circle. Problems based on areas and perimeter/circumference of the above-said plane figures. (In calculating the area of a segment of a circle, problems should be restricted to the central angle of 60°, 90° only. Plane figures involving triangles, simple quadrilaterals, and circles should be taken.)

b. Surface Areas and Volumes 

1. Surface areas and volumes of combinations of any two of the following: cubes, cuboids, spheres, hemispheres, and right circular cylinders/cones.
2. 2. Problems involving converting one type of metallic solid into another and other mixed problems. (Problems with combinations of not more than two different solids can be taken).

• STATISTICS AND PROBABILITY – 11 Marks

a. Statistic

Mean, median, and mode of grouped data (bimodal situation to be avoided).

b. Probability

The classical definition of probability. Simple problems on finding the probability of an event.

Class 10 Maths – Paper Pattern, Tips, and Tricks

The question paper pattern for this exam is:

• Section A: Objective Type Questions that are 20 in a number containing 1 mark each.
• Section B: Short Answer Type Questions – I, 6 questions of marks each.
• Section C: Short Answer Type Questions – II, 8 questions of 3 marks each.
• Section D: Long Answer Type Questions, 6 questions containing 4 marks each.

Some tips and tricks during preparation and exam time to score full marks would be to understand each unit and solve sums by yourself, find your strengths and weaknesses, complete the syllabus on time and start a thorough revision. During the exam, start with the section that you are most familiar with, keep your paper as clean as possible, solve in steps as step marking is essential and draw as many diagrams and graphs as time permits.

FAQs on How To Score Full Marks In Class 10 Maths

1. What are the total marks in the written examination for class 10 Maths?

Answer. There are 80 marks in total, along with an internal evaluation that contains 20 marks (making 100).

2. Which is the most difficult section in the paper?

Answer. Section C is reportedly the most challenging section as it tests more of your understanding than practice.

3. How many mock tests should one take to be completely ready?

Answer. Solving more and more questions will always help to grasp the concepts better, but this can vary depending on individual needs. Around 8-10 tests would be great.

The post How To Score Full Marks in Class 10 Maths? appeared first on Learn CBSE.

Maths is a subject that is available in both streams whether it is science or commerce. It is a very technical and formula based subject in which a student takes the most time for preparation. The Class 10 Maths Board Exam is very difficult and students have to be systematic while attempting this exam because it is very time-consuming and lengthy. Many students fail to complete the entire exam because they fail to manage time.

Maths is a subject that resolves around formulas. Students have to remember all the formulas and take the correct steps in sequence to solve the equation.

Maths Board Exam Class 10- Exam pattern

Class 10th maths exams consist of 4 sections i.e. section A, section B, section C, and section D. The student has to solve 40 questions which are divided into 4 sections. The passing marks in boards are 33 out of 80 marks.

Maths Board Exam Class 10- Subjects

To get a good score in the maths board exam, CBSE recommends that a student must prepare the following topics properly as these topics contain the highest value. The list of topics are as follows:

• Trigonometry
• Statistics
• Probability
• Real numbers
• Surface areas
• Constructions

Preparing for the above-mentioned topics will help you score good marks. Students have to keep in mind that they have to prepare in a given time. Spending too much time on one topic may result in failure to cover the entire syllabus.

Maths Board Exam Class 10- Reference Books

Here is the list of some reference books which students can go through if they want to score good marks or top the exam. Since NCERT is considered the best resource for the preparation of the board exams if a student understands the concepts of NCERT, then they can score 95% very easily. But for the remaining 5%, you can go through these reference books listed below.

• Mathematics for class 10 by RD Sharma
• Secondary School Mathematics by RS Aggarwal
• All in One by Arihant
• Class 10th maths Xam Idea

Maths Board Exam Class 10- Tips and tricks

1. One thing you should definitely do is to practice solving the question paper in 3 hours and increase your speed. If you want to score good marks then you have to attempt all the questions given in the question paper.
2. It is advised to attempt the exam from section D which consists of the questions with the highest marks. This is the trick that is suggested by many teachers so that students can attempt all high marking questions with ample time in their hands. If the student starts the exam from section A, then there might be a chance that they will leave section D or might attempt the high marking questions in a haste.
3. Practice all the examples and questions given at the end of the chapters and in between the chapters as most of the questions will be from the example section.
4. Prepare a strategy before the exam. Decided how much time you want to give to each section and also analyze which section needs most of the time.
5. Read the question paper carefully in the allotted 15 minutes for reading, you will analyze all the formulas and solve the questions in your mind which gives you confidence while attempting the exam.

Maths Board Exam Class 10- Marking scheme

Maths Board Exam Class 10 is divided into 4 sections i.e. section A which consists of 20 questions of 1 mark each, section B which consist of 6 questions having 2 marks each, section C which consists of 8 questions having 3 marks each and last is section D consists of 4 questions having 6 marks each.

FAQs on Maths Board Exam Class 10

Q 1. How many chapters are there in the syllabus of Maths Board Exam Class 10?

Answer. There are 15 chapters that you need to prepare for class 10th board exam, which is divided into 2 parts.

Q 2. Is NCERT enough to get 90% marks in the board exam?

Answer. Yes, if you understand the core concepts of NCERT, then you can easily score 95% in the examination.

Q 3. How many chapters are there in part 1 of the NCERT book for Mathematics?

Answer. There are 8 chapters in part 1 and 7 chapters in part 2. One needs to prepare both parts to pass the exam with a high score.

The post How to Prepare for Maths Board Exam Class 10? appeared first on Learn CBSE.

Maths is one of those subjects which is either a dream or a nightmare. For some students, there exists a world within the world where only calculations, heights and distances speak. On the other hand, there are others who live through a battle as long as their maths board exam class 10 Board exams aren’t over. In either case, what is of utmost importance is to make the best use of the time, technique and resources available to you.

While time and technique may vary depending upon the preparation of individual students, resources in the form of books, previous year papers and study materials are what can be common between all maths board exam class 10 aspirants. The basic textbook prescribed by any Board remains a must but there are reference books for every subject – the right choice of which can greatly affect the outcome of your exams.

To answer all queries regarding the best reference books for class 10, this article will be instrumental.

Why are reference books a must for class 10 Maths?

In the case of most other subjects pertaining to the class 10 syllabus, the NCERT textbooks are more than sufficient. Both in terms of quantity and quality, the textbook is essential for any student. The same is the case while preparing for your maths board exam class 10. With all the concepts explained in detail with clarity and topics covered within the syllabus range, the Maths NCERT is indeed most of what you need to go through.

But from the point of view of your exams and inching closer to scoring full marks in this paper, a student might need to take a step ahead. The textbook indeed has enough questions from easy, intermediate to advanced level for students to practice. But that will cover 95% of your question paper. To bridge the gap between 95 and 100, reference books are a must. If you desire to be able to attempt and solve every question on the paper correctly, there will be some extra question solving needed – the questions for which you will need the reference books.

Additionally, the more conceptual questions you practice for your class 10th, the stronger will be your foundation. This in turn will bring a large-scale impact if you wish to pursue Maths further and sit for any entrance exams.

Class 10 Maths – Reference Books

So, the key to scoring the best in any board exam is to go through the length and breadth of your NCERT textbook. Additionally, to be able to solve any HOTS or tricky question in the paper, the reference books that have given desired assistance and outputs, time and again for maths board exam class 10 are by authors RD Sharma and RS Aggarwal. Throughout India and the world, students are seen to use these as the key reference books all through the years.

Class 10 Maths- Preparation Tips

The important thing is to solve all your NCERT examples and exercise questions first and then move ahead on the reference book questions. The best thing about books by RD Sharma and RS Aggarwal is the fact that they constantly update their versions as per the question paper trends. Every question in the book will be marked with the year beside if it has been asked in any Board exam. This helps to better prioritize which questions will give you the most benefit.

All you need is knowledge in the right amount in the right manner and proper practice. If you are someone who has covered the textbook and solved the most important reference book questions thoroughly, most of your job is done. Time management and paper solving bundled with confidence will prepare you in the best possible way no matter how easy or difficult the level of the paper.

With the right books by your side, you are certain to get the best out of your maths board exam class 10!

FAQs on  class 10 Maths examination

Q 1.What is the pattern of the class 10 maths exam?

A.The paper is divided into 4 sections with 1, 2, 3, 4 marks per question and a varying number and difficulty of questions in each section.

Q 2. Is it possible to score full marks in maths?

A.With the right strategy and dedication, it is very much possible and many students secure full marks every year.

Q3. Is there a fixed difficulty level for the paper?

A.The level of questions may change for every batch but a basic standard is maintained for all students.

The post Which Is The Best Reference Book For Class 10 Maths? appeared first on Learn CBSE.

Class 10th plays a very important role in building the student’s future. It is the foundation of the future of the student. It is also important because, based on class 10th percentage, the student will decide which stream they want to take. One of the toughest streams of class 10th is a science that contains three parts, i.e., Physics, Chemistry, and Biology. Central Board of Secondary Education (CBSE), which conducts the examination of class 10th and class 12th boards, advises the students to follow some tricks and tips to score good marks in these technical subjects.

So, let us find out.

Science Board Exam Class 10- Overview

Class 10th science exam takes place in 2 parts i.e.

•         One is the theory part, which consists of 80 marks written exams.
•         The second is based on the internal assessment, which consists of 20 marks. The internal assessment consists of journal submission, practical file submission, and viva.

Science Board Exam Class 10- Subjects

To prepare for Class 10 Science Board Exam, you need to focus on the important topics. Here are the lists of topics which you need to focus on:

For Physics

•         Human eye
•         Rays of light
•         Formula based questions
•         AC and DC generators

For Chemistry

•         Chemical reactions
•         Periodic table
•         The cleansing action of soap
•         Concepts of acid and bases

For Biology

•         Reproduction
•         Diagrams of organs
•         One line definition of biology terms
•         Mendel’s Experiments

Science Board Exam Class 10- Reference Books

Here are the lists of the best books you can buy to prepare for the science exam. You can also purchase these books online. The names of the books are as follows:

• Physics class 10th  by Lakhwinder Singh and Manjit Kaur
• Principles of Physics S. Chand Book- N.k Chowdhry
• Fundamentals of Physics- Pradeep Publications
• Chemistry class 10th  by  Lakhwinder Singh and Manjit Kaur
• Biology class 10th by Lakhwinder Singh and Manjit Kaur

Science Board Exam Class 10- Tips and Tricks

1.       Prepare a proper timetable, plan your schedule according to the number of chapters, and analyze which topic needs more preparation.
2.       Note down the important notes or highlight them so that you can focus on those points at the time of the revision.
3.       Sleep at least 7-8 hours before the day of your exam.
4.       On the day of the exam, do not study new topics. Focus on those topics which you studies already and only need revision.
5.       Attempt your exam in sequence and make proper diagrams with the proper labeling of parts.
6.       Try to score more in internal assessments that will help you in the final theory exams.
7.       Write all the formulas and the periodic table in a separate notebook or in a chart and paste it near your study table so that you can learn it every day.
8.       Before going through any reference book, first completely revise the NCERT book of the subject as NCERT is known as the bible of the board exams, and those who understand the concept of NCERT can easily score more than 95%.
9.       Read all the examples and extra questions present at the end of every chapter.
10.   While attempting the exam, carefully read the question paper before you attempt the answers.

Science Board Exam Class 10- Marking system

The question paper consists of 30 questions divided into three sections A, B, and C. Section A contains MCQs and one line answer questions, and section B contains short answer type questions having three marks each. Lastly, section C contains five marks long answer type questions. Physics, Chemistry, and Biology have equal weightage in the exam.

FAQs on Science Board Exam Class 10

Q1. How much percentage a does a student need to score to get a science stream in +1?

Answer. To opt for the science stream in +1, a student must score 75% to 80% in science subjects in the 10th board.

Q 2. What are the passing marks in class 10th board exams?

Answer. The passing marks in the board exams is equivalent to 33%. If a student fails in one subject, then the result would be a compartment, and if a student fails in more than two subjects, then the student will have to reappear for the examination.

Q 3. What will be the marking scheme of the science exam?

Answer. The science theory exam has three sections. Section A consists of 14 marks, Section B consists of 36 marks, and section C consists of 30 marks.

The post How to Prepare for Science Board Exam Class 10? appeared first on Learn CBSE.

In school life, the prescribed syllabus often finds us in the midst of a troublesome situation. There are subjects or parts of subjects that we absolutely love and then there is the part that we don’t. Social science or some aspects of this subject usually come under this group. It’s manageable in all other classes, but in class 10, with your Board Exams, things get difficult. You have to study a subject and score marks even if you don’t really find it in your list of interests.

If you are someone stuck in the same situation, the article here will help you. Scroll down for details, the syllabus, weightage ad tips on how to study social science for your class 10.

Social Science in class 10 – Overview and Paper Pattern

The class 10 social science paper includes brief concepts from History, Geography, Civics, and Economics. To have a better grasp of the subject, it is imperative to know the pattern of the paper and an overview of the questions that can be asked. The paper is divided into three sections with a total of 35 questions to be answered by a student. The total marks are 80 along with the internal assessment components.

Section A consists of multiple-choice, short answers, match the columns, or picture-based questions that are of a total of 20 marks.

Section B has 8 questions of the short answer type to be written within 80 words by the students.

Section C has long answer type questions that have to be answered in about 120 words.

The last part is a map-based question that tests the History and Civics knowledge of students. The paper has no overall choice but the individual questions may have an internal choice between topics of a chapter.

Social Science in Class 10 – Syllabus

The next thing to know before we go on to the details of how to study Class 10 Social science in class 10 is to understand the exact syllabus. This is as follows:

1. India and the Contemporary World – II – 20 marks 

Section 1: Events and Processes:

a. The Rise of Nationalism in Europe:

• The French Revolution and the Idea of the Nation
• The Making of Nationalism in Europe
• The Age of Revolutions: 1830-1848
• The Making of Germany and Italy
• Visualizing the Nation
• Nationalism and Imperialism

b. Nationalism in India:

• The First World War, Khilafat and Non – Cooperation
• Differing Strands within the Movement
• Towards Civil Disobedience
• The Sense of Collective Belonging

Section 2: Livelihoods, Economies and Societies: Anyone theme of the following. The theme selected should be assessed in the Periodic Tests only and will not be evaluated in the Board Examination.

c. The Making of a Global World:

• The Pre-modern world
• The Nineteenth Century global economy, colonialism)
• The Interwar Economy (Great Depression)
• Rebuilding the World Economy

d. The Age of Industrialization:

• Before the Industrial Revolution
• Hand Labour and Steam Power
• Industrialization in the colonies
• Factories Come Up
• The Peculiarities of Industrial Growth
• Market for Goods

2. Contemporary India – II – 20 marks

a. Resources and Development:

• Types of Resources
• Development of Resources
• Resource Planning in India
• Land Resources
• Land Utilization
• Land Use Pattern in India
• Land Degradation and Conservation Measures
• Soil as a Resource
• Classification of Soils
• Soil Erosion and Soil Conservation

b. Water Resources:

Note: The theoretical aspect of this chapter will not be assessed in Periodic Tests and Board Examination. Only Map Items as given in the Map List from this chapter will be evaluated in Board Examination.

c. Agriculture:

• Types of farming
• Cropping Pattern
• Major Crops
• Technological and Institutional Reforms
• Impact of Globalization on Agriculture

d. Minerals :

Note: The theoretical aspect of this chapter will not be assessed in Periodic Tests and Board Examination. Only Map items as given in the map list from this chapter will be evaluated in the Board Examination.

e. Manufacturing Industries:

• Importance of manufacturing
• Contribution of Industry to National Economy
• Industrial Location
• Classification of Industries
• Spatial distribution
• Industrial pollution and environmental degradation
• Control of Environmental Degradation

g. Life Lines of National Economy:

• Transport – Roadways, Railways, Pipelines, Waterways, Airways
• Communication
• International Trade
• Tourism as a Trade

3. Democratic Politics – II – 20 marks

a. Power Sharing:

• Case Studies of Belgium and Sri Lanka
• Why power sharing is desirable?
• Forms of Power Sharing

b. Federalism

• What is Federalism?
• What makes India a Federal Country?
• How is Federalism practiced?
• Decentralization in India

c. Political Parties:

• Why do we need Political Parties?
• How many Parties should we have?
• National Political Parties
• State Parties
• Challenges to Political Parties
• How can Parties be reformed?

d. Outcomes of Democracy:

• How do we assess democracy’s outcomes?
• Accountable, responsive and legitimate government
• Economic growth and development
• Reduction of inequality and poverty
• Accommodation of social diversity
• Dignity and freedom of the citizens

4. Understanding of Economic Development 

1. Development:

• What Development Promises – Different people different goals
• Income and other goals
• National Development
• How to compare different countries or states?
• Income and other criteria
• Public Facilities
• Sustainability of development

2. Sectors of the Indian Economy:

• Sectors of Economic Activities
• Comparing the three sectors
• Primary, Secondary and Tertiary Sectors in India
• Division of sectors as organized and unorganized
• Sectors in terms of ownership: Public and Private Sectors

3. Money and Credit:

• Money as a medium of exchange
• Modern forms of money
• Loan activities of Banks
• Two different credit situations
• Terms of credit
• Formal sector credit in India
• Self Help Groups for the Poor

4. Globalization and the Indian Economy:

• Production across countries
• Interlinking production across countries
• Foreign Trade and the integration of markets
• What is globalization?
• Factors that have enabled Globalisation
• World Trade Organisation
• Impact of Globalization on India
• The Struggle for a Fair Globalisation

Social Science in Class 10 – Tips & Tricks

After knowing the syllabus and paper pattern, all you need is to get used to NCERT textbooks and other interesting study material, write more and more answers, understand the ideas, revise thoroughly and practice as many papers as you can. More importance should be given to understanding and going through the sample and previous year’s papers. Practice Map work and also focus on formatting. It is wise to underline important components in long answers to make it easier for the examiner to grasp your idea and knowledge on the specific topic.

FAQs on Social Science in Class 10

1. Is there any guidebook for the preparation of social science in class 10?

Answer. The NCERT book and previous year’s papers is the best way to study social science without the need for guidebooks.

2. Is it a scoring subject class 10 social science?

Answer. The scores will depend on your answers. To the point answers will be rewarded with more marks. However, since it a theory-based exam, there is a high possibility to score more marks as everything is from the textbook itself.

3. Is there a specific question pattern?

Answer. There is a common pattern comprising 3 sections as mentioned above but that can be changed with the commencement of each year.

The post How to Study Social Science In Class 10? appeared first on Learn CBSE.

CBSE Class 10 helps the students decide the stream for the higher class. Class 10th board is also important because it is the first time when a student gives an exam which is prepared by a third party.

SST or Social Science is a very scoring subject for a student because it is all theory based exam and also the questions asked by the examiner are simple and straightforward. Unlike the other subjects, the student does not need to learn the formulas and solve equations. Apart from the straight question answer, students get a chance to score good marks in the map section where they only have to mark the location in maps.

CBSE Class 10 Social Science- Exam pattern

Class 10 Social Science exam consists of 3 sections i.e. section A, section B, section C. Section A consists of objective type questions like match the following and one-line questions. Section B consists of short type answers in which students have to answer each question within 80 words. Section C consists of long answers in which students have to answer each question within 120 words. The last question of the social science exam is a map question in which students have to mark the locations in the map as per the question. The location can be of state, river, or any national park.

CBSE Class 10 Social Science- Subjects

Most of the students find this subject boring because of its vast syllabus and long and boring topics. But if prepared properly, one can score more than 90% in this subject easily. Here is the list of some important topics students can prepare to score good marks in this exam. Social science consists of 3 subjects i.e. History, Geography, and Political Science (Civics).

For History

• The Rise of Nationalism in Europe
• Nationalism in India
• Print Culture and the Modern World

For Geography

• Water Resources
• Forest and wildlife resources
• Resources and Development

For Political Science (Civics)

• Power Sharing
• Federalism
• Democracy and Diversity
• Outcome of Democracy

For Economics

• Sectors of the Indian economy
• Money and credit
• Consumer rights
• Globalization

CBSE Class 10 Social Science- Reference books

To score good marks in the board exam, one needs to understand the concepts of NCERT as the majority of questions are from this book only. You can score more than 90% if you remember the concepts of NCERT. Apart from NCERT, the following are the reference books best for the social science board examination:

• All in One SST by Arihant
• S. Chand for social science
• Exam idea for Social Science by Editorial board

CBSE Class 10 Social Science- Tips and tricks

1. Management of time is very important. Give enough time to each section and revise all the chapters properly.
2.  Never start a new chapter on the day of the exam. This leads to confusion which results in a loss of confidence.
3. Highlight the important lines and sentences or write them separately so that you can revise them easily.
4. Before writing the exam, use the first 15 minutes in reading the question paper. With this, you can remember all the answers and you can write them without any confusion.
5.  Go through the sample paper or previous year’s question paper. With this, you can know the level of questions that will be asked in the board exam.

CBSE Class 10 Social Science- Marking scheme

CBSE Class 10 Social Science board exam consists of 3 sections i.e. section A which consists of 20 marks having one-liner, MCQ, and fill in the blanks as questions. Section B consists of 8 short answer type questions having a weightage of 3 marks each and last section C consists of 6 long answer type questions having a weightage of 5 marks each including the map question.

 FAQs on Class 10 Social Science Board Examination

Q 1. What is the passing percentage for the class 10 social science examination?

Answer. To pass the board exam, students have to score 33% both internally and in the main exam.

Q 2. Do students get choices in questions in class 10 social science board exam?

Answer. Yes, students have limited choices in question in board exams as they can choose which question they want to attempt. 

Q 3. How many chapters do students need to prepare for the Board exam?

Answer. Students need to prepare 4 chapters of History, 7 chapters of Geography, and 5 chapters of political science in total.

The post Which is the Best Reference Book for CBSE Class 10 Social Science? appeared first on Learn CBSE.

One of the most challenging subjects for class 10 students is social science. However, it is a subject that doesn’t require hard efforts to learn formulas and theories.  If you’re preparing for this subject well in advance so there is a high possibility to score good marks. Social science is an interesting and easy to score subjects that can help you gain good marks.

Class 10 Social Science- Overview

The subject is divided into four parts i.e. History, Geography, Civics and Economics. You are required to remember important dates and names of leaders across centuries for short answers type questions and it is advised to make full-fledged notes for attempting lengthy questions and increase your chances to score full marks for your answer. This post will give you the best idea on how to prepare for the social science exam as we wish you the best of luck for your board examinations.

Class 10 Social Science- Exam pattern

The exam pattern set by CBSE for the social scient examination is as follows:

The exam consists of 80 marks-divided into 3 sections.

• Section A consists of the one-liner, MCQ, and fills in the blanks type questions.
• Section B consists of short answer type questions in which students have to answer the question in 80-90 words.
• Section C consists of long answer type questions having a word limit of 120-130 words.
• In section C, you will find a map question in which you have to mark the location on the map. It is one of the most scoring questions for every student.

Class 10th social science board exam is divided into 3 sections and also one or two map questions. Section A consists of 20 questions of 1 mark each, Section B consists of 8 questions of 3 marks each and Section C consists of 6 questions of 5 marks each and a map question with a weightage of 5 marks.

Class 10 Social Science– Subjects

Social science is divided into 4 parts i.e. history, geography, economics and political science. Each part contains 6-7 chapters and that’s why students find it difficult to cover the entire syllabus if they decide to study at the last minute. Here is the list of the important chapters which help the students score good marks in the final examination. Since social science is a theory-based subject, it is important to understand the topics and concepts from the core.

History

• Nationalism in India
• Print culture
• Novel chapter in History

Geography

• Mineral and energy resources
• Agriculture
• Manufacturing industries

Political Science

• Challenges to Democracy
• Popular struggles and parties
• Gender, religion, and caste

Economics

• Development
• Sectors of the economy
• Money and credit
• Consumer rights
• Globalization and the Indian economy

Class 10 Social Science– Reference books

NCERT is the book that guides students to understand the topics from their core essence. But if the student finds it difficult to understand the concept of NCERT books then these are a few reference books that help students to score good marks.

• Exam idea by Editorial board
• Golden guide for SST by Sudha Rastogi, J.P. Singhal
• S. Chand of social science
• NCERT Economics

Tips To Score Good Marks In Class 10 Social Science Examination

If you want to score good marks in the class 10 social science board exam, then these tricks and tips will help you score good marks. Here is a list of some tips for the preparation for the social science board exam:

1. Go through the heading of the answer. It is very difficult for a student to cramp up the entire answer, so to ease the pressure, always try to remember the headings.
2. Always make the time table according to the topics. If you are good at geography, then try to give more time to history or economics or vice-e-versa.
3. Do not start with a new chapter on the day of the exam. Try to avoid this because this will lead to confusion, thus poor performance in the examination.

FAQs on Class 10 Social Science examination

Q 1. How to prepare for the map question?

Answer. The map question can be asked from the history topics or mostly it comes from the geography chapters such as the name of the wildlife or name of the river, or location of an important war.

Q 2. Which part is more scoring in social science subject?

Answer. Social science consists of different parts. Each part has equal weightage in the exam. However, the subject which interests the student the most remains the most beneficial.

Q 3. Are reference books necessary for the preparation of the examination?

Answer. Reference books are recommended only when the student can’t understand the concept of NCERT and if the student wants to practice previous year’s question papers.

The post How to Score Good Marks in Class 10 Social Science? appeared first on Learn CBSE.

In recent times, English is considered the most important subject and language that students cannot overlook under any circumstances. If you really want to stand out from the crowd you must have command over the English language. In class 10 students miss out on focusing on grammar, but they must not forget that it is the most scoring section that has the potential to score full marks in the board examination. If you want to perform your best in the board exams this year, find our useful tips and tricks to score high in the English exam.

Class 10 English- Exam Pattern

The English exam is divided into four sections and each carries 20 marks.

• Section A includes comprehension, an unseen passage where students need to answer the questions correctly. This section is included to test the comprehension skills of the student.
• Section B includes writing skills where students are requested to write on different genres such as letter, notice, article, essay, etc.
• Section C includes the grammar test where students need to answer for tenses, punctuation, synonyms, translation, etc.
• Section D includes Literature and poems where students have to answer the questions.

Class 10 English- Subjects

Class 10 English examination is based on different parts such as literature, supplementary, grammar and writing skills. In the literature and supplementary section, students have to learn questions and answers whereas in the Grammar and writing section students have to learn the basics of grammartical rules and vocabulary.

 Comprehension

• Conceptual understanding
• Decoding
• Inferring
• Interpreting and vocabulary

Grammar & writing skills

• Determiners
• Modals
• Tenses
• Voice
• Reported speech
• Creative writing
• Fluency
• Style and tone
• Conventions

Literature & supplementary 

• Recalling
• Reasoning
• Understanding the writer’s message
• Questions/answers
• Phrases
• Understanding theme
• Central idea

Class 10 English- Reference books

NCERT offers the best book for the most helpful study material that any student must not ignore. Here are the subjects, topics and chapters that one needs to cover:

NCERT Literature

• A letter to god
• Nelson Mandela: Long walk to freedom
• Two stories about flying
• The hundred dresses-I
• The hundred dresses-II
• Glimpses of India
• Mijbil the other
• The sermon at Benares
• Madam rides the bus
• The proposal

NCERT Supplementary

• The necklace
• The making of a scientist
• The midnight visitor
• The thief’s story
• A triumph of surgery
• Footprints without feet
• The hack driver
• Bholi
• The book that saved the earth

NCERT Grammar

• Determiners
• Idioms
• Phrases
• Voice
• Narration
• Tenses
• Essay
• Notice
• Creative writing
• Letter writing

Tips and tricks to score well in class 10 English examination

• Regularly practice writing essays and answers to reduce grammatical errors.
• Read one chapter a day and make notes on the topics that you find the most important.
• Read the chapter aloud to improve your speech and vocabulary.
• Prepare notes or cards to remember the name of poets and authors.
• Read the stories again and again to understand the details.
• Attempt NCERT books for the preparation of the examination as most of the questions are based on the same reference.
• Set your time for studying each section and do not start a new chapter on the day of the exam.

Class 10 English Examination- Marking Scheme

Class 10 English marking scheme can be very beneficial for students as it is structured in such a way that it makes scoring high very easy. As per the CBSE guidelines, the following is the marking pattern that will be followed by the examiners.

• Section A- 15 marks
• Reading- 20 marks
• Grammar- 15 marks
• Literature + supplementary- 20 marks
• Listening and speaking- 10 marks
• Assessment- 20 marks

FAQs on Class 10 English Examination

Q1. How many books of English are there in Class 10?

Answer. Class 10 English NCERT syllabus is divided into three books as follows:

• English literature
• Supplementary
• Grammar

Q2. How to get full marks in English?

The following tips can be very helpful in order to score a high score in class 10 English examination:

• Read previous exam papers and solve them.
• Schedule your hours for studying each topic.
• Focus on the scoring sections.

Q3. Which part is more scoring in English?

Answer. English grammar and vocabulary is the most scoring section as it gives you an opportunity to score full marks on each correct answer.

The post How to Score Good Marks in Class 10 English? appeared first on Learn CBSE.

English Paper Class 10: Central Board of Secondary Education conducts Class 10 board examination every year in March. Class 10 English Paper is one of the core subjects. Preparation for board examination can be very hectic. With competition getting tougher in other subjects namely mathematics and science, pupils generally leave English for the end. However, it is where students generally make mistakes. Last-minute preparation leaves them with no strategies to score well and therefore they end up making blunders in the easiest questions.

Overview- English Paper Class 10

English Paper Class 10 is of 80 marks stretching for 3 hours. 20 marks are awarded for internal assessment. The entire paper is divided into three sections:

Section A which tests your reading skills. (20 marks)

Section B that tests your writing skills with grammar.  (30 marks)

Section C wherein questions are raised from literature textbooks and include the supplementary reading test. (30 marks)

Before we discuss a few tips to score better in English Paper for Class 10, let us first see what subjects or topics are covered in the English Board Examination:

Subjects, Topics and Pattern in Detail

Section A (Reading skills)

Section A includes multiple-choice questions from a philosophical passage in general which is 10 marks.

It also includes another passage-based on facts and figures and is of 10 marks in total.

The reading skills also cover extracts from prose or drama based on your prescribed textbook. Another extract is based on poetry. Both are questions that carry five marks each.

The portion is not devoid of grammar; questions carrying 10 marks in total are put up covering tenses, modals, subject-verb concord, statements, commands and requests, questions, determiners and reported speech.

A few topics have been reduced from the syllabus for board examination 2021. Initially, the paper also touched on questions covering passive voice, nouns, adverbs, relatives (clauses) as well as prepositions.

Sections B (Writing skills)

Section B consists of two questions carrying 5 marks each. One question includes a formal letter not exceeding 100-120 words.

The other question includes penning down an analytical paragraph based on the given data, chart, clue, or outline. The word limit should not exceed 100-120 words.

Section C (Literature) 

The literature portion includes short and long answer questions. There are six short answer questions wherein one has to answer 4 questions in total. Each answer should not exceed 30-40 words. Questions are asked from the prescribed textbooks from CBSE.

There are another set of six short answer questions that must be answered within a word limit of 40-50 words. These questions again are put up from the prescribed textbooks. Students need to answer just 4 questions out of 6.

Long answer type questions carry five marks each and are to be answered within 100-120 words. These questions are put up from the prescribed textbooks.

Books prescribed for English in Class X

CBSE has prescribed the following books:

1. First Flight
2. Footprints without Feet

Tips to score better in English Board Exam 2021:

•         Start prepping up at least a month before for English instead of studying at the 11th hour to avoid confusion.
•         Focus on reading skills, read at least two paragraphs daily to improve comprehension skills.
•         Set a time limit for reading, start with 15 minutes and reduce to 10 the next week.
•         Write answers on your own, instead of mere copying. Also, pen down a few lines on topics that you find relevant.
•         The regular habit of writing will enhance your speed and will develop a flow.
•         Learn 5 new words daily including their synonyms to improve your vocabulary and quality of answers.
•         Prepare a chart of letters, compositions and all the important topics so that you don’t forget the correct format.
•         Read your textbooks thoroughly. Remember the names of chapters and their authors/poets with correct spellings.
•         Don’t forget underlining important keywords in your answer sheets while attempting the questions.
•         Attempt all the questions in a proper sequence- section a, section b and section c.
•         Go for regular mock tests, these will help you analyze your performance before boards.

Reference books for English Paper for Class X

Following are the reference books that may prove helpful for your preparation:

•         English Language and Literature – Togetherwith
•         All in One English Language and Literature CBSE class 10-Arihant
•         English Communicative- Oswaal
•         High School English Grammar and Composition Book- Wren and Martin
•         Xam Idea Complete Course English for CBSE Class 10- VK Global

Frequently Asked Questions on English Paper Class 10

1. Will CBSE Board Exams of Class X 2021 be conducted online?

Answer. No, board exams of all the subjects will be conducted offline.

2. Which is the best book for practice for English Board Exam?

Answer. You can download the previous years’ question paper for practice and can also seek the help of Xam Idea Complete Course English CBSE Class 10 by VK Global Publication.

3. What about the remaining 20 marks if the paper is of 80 marks in total?

Answer. The rest 20 marks are based on school or internal assessment. It depends on the school if it assesses students in terms of unit tests or viva voice or projects.

The post How to Attempt English Paper Class 10? appeared first on Learn CBSE.

We all are story weavers, we all possess the talent of ‘cooking stories in our minds,’ isn’t it? But when it comes to expressing these notions on paper, not all can write them with flair. 

English Exam Class 10: Story writing is also a part of the syllabus of English Class 10 and therefore it is very important to understand its concepts, essentials, and techniques. We have mastered story making in our own ways pertaining to our own circumstances and situations be it making excuses for submitting incomplete homework or evading project work or assignments. Yet, when it comes to penning our thoughts down in a structured format with all the given rules of grammar, we need to learn the correct art to score well.

Overview- English Exam Class 10

A story is a set of thoughts, situations or circumstances in a proper structured format. It has a central character, a theme, an antagonist that may be a person or a situation and a central theme as well as a message.

When weaving a story we need to keep the above points in mind. The length of the story may vary, depending upon its types- a story exceeding the 12000-word limit can take the form of a novel or a novella.

However, in-class 10 board examination you are asked to attempt a short story with the clues given in your question paper. The question carries 10 marks, 6 marks are allotted for reading skills, 2 marks for accuracy, and 2 marks for accuracy. Therefore, it is important to attempt questions with utmost care.

Format of writing story

When attempting a story you may adhere to the following format for your ease:

• Start with a phrase: For example, once upon a time, once there lived, keeping the context in mind.
• Introduce your characters: Write how your character looked, what qualities did it/ he/ she posses— you can do it using conversations or dialogues.
• Plot: Circumstance, situation, event or any happening.
• The climax of the story: The story’s heightened crises, and the end.

Tips for writing a story creatively

• Plotting: Note down the points and ideas that come up to your mind on a rough sheet. Arrange them accordingly or in a serial order.
• Include these three situations: 

Situation–  What is the event that a protagonist or a central character is going through?

Crises- What problem is the character stuck into?

Solution- How does a character find the solution.

• Include more dialogues: Inclusion of dialogues or conversation makes the story what it is different from an essay or an article as well as a debate. Include catchy dialogues.
• Mind your vocabulary: Since you get very little word limit to spin a tale, you need to learn some good words to impress the reader. However, avoid using grandiloquent language.
• Express through words: Story isn’t limited to telling, it is rather based on a concept – ‘show don’t tell.’ Write exactly how you feel, write in a way a reader is able to visualize. For instance-

Instead of writing, ‘Ron was scared to death when he saw himself in the mirror,’ you can rephrase it this way, ‘Ron hair at the back stood, his face turned white and teeth jittered as he saw his reflection in the mirror! ‘

• Include a message: Not all stories carry a message. Some are just for the purpose of entertainment. However, when you are writing a story for your exam, it must carry some meaningful message. Try figuring out what the clues say or may lead to. Figure out what moral lesson the story brings home.
• Read: Another important thing that you must for almost daily is to read short stories regularly. It will give you an idea of what to write and how to develop the plot of the story. The more you read, the more learned you become.
• Practice: Practice makes a man perfect, and it ain’t a joke! If not daily, pen your thoughts down and weave them into meaningful stories at least thrice a week. This will help you get a good grasp of the genre. Also, you would enjoy spinning a tale on your own, once you have mastered it.

Frequently Asked Questions on English Exam Class 10

1. What are the key elements of a story? 

Answer. A story has these basic elements:

• Plot
• Protagonist/hero/central character
• Antagonist – villain (a person or a situation)
  
• Theme
  
• Message 

2. Are there any reference books for writing stories? 

Answer. You can go for Xam Idea Complete Course English for CBSE by VK Global Publication. It covers all the grammatical portions of class X syllabus.

3. How many marks does a story writing question carry? 

Answer. Story writing comes under section B. It carries 10 marks and therefore is an important topic.

The post How to Write A Story in English Exam Class 10? appeared first on Learn CBSE.