CBSE Class 8 - Maths Periodic Assessment-1 (2017-18) (#cbseNotes)

CBSE Class 8 - Maths Periodic Assessment-1 (2017-18) 

Questions asked in the Q. Paper are from the following chapters:

1. Rational Numbers

CBSE Class 8 - Unit Test Paper Mathematics - Rational Numbers (#cbseNotes)

CBSE Class 8 - Unit Test Paper Mathematics - Rational Numbers

CBSE Class 8 - Maths - Squares and Square Roots (Assignment) (#cbsenotes)

CBSE Class 8 - Maths - Squares and Square Roots (Assignment)

CBSE Class 8 - Maths - Squares - Properties of A Perfect Square (#cbsenotes)

Properties of A Perfect Square

Please look at the table of some squares given below. You will see interesting patterns here.

Square of number 0 = 0

Number	Square	Number	Square	Number	Square
1	1	11	121	21	441
2	4	12	144	22	484
3	9	13	169	23	529
4	16	14	196	24	576
5	25	15	225	25	625
6	36	16	256	26	676
7	49	17	289	27	729
8	64	18	324	28	784
9	81	19	361	29	841
10	100	20	400	30	900

PROPERTY 1:
Look at the table above. Observe that none of the column of squares ends with 2, 3, 7, or 8. Therefore we can say that a number endings with 2, 3, 7, 8 can never be a perfect square.
Thus 228257 , 132457 , 189678 , 84453 are not perfect squares.

PROPERTY 2:
Look at the last row of the table shown above. We notice that all the perfect squares are ending with an even number or 0. In the first line  e.g. 10² = 100 , 20² = 400, 30² =900,
Similarly 80²  = 6400, 50² = 2500.

We can prime factorise and see that 10, 20, 30,  etc . are not perfect squares. Thus a number ending with odd  number of zeros can never be a perfect square.

CBSE Class 8 - Maths SA2 Sample Question Paper (2016-17)(#cbsepapers)

CBSE Class 8 - Maths SA2 Sample Question Paper (2016-17)

CBSE Class 8 - SA2 Maths Sample Question Paper (2016-17) (#cbsepapers)

CBSE Class 8 - SA2 Maths Sample Question Paper (2016-17)

CBSE Class 8 - Maths - CH3 - Understanding Quadrilaterals (Worksheet) (#cbsenotes)

Understanding Quadrilaterals

(Worksheet)

The worksheet helps you identify a specific quadrilateral based on its properties.

☛Directions: Fill in the blanks

① A simple closed curve made up of only line segments is called a ________.
 


② A _________ of a polygon is a line segment connecting two non- consecutive vertices.
 


③ A _______ _______ is a polygon in which no portion of its any diagonal is in its exterior.
 


④ A quadrilateral is a polygon having only ________ sides.
 

Class 8/ Class 9 - Properties Of Quadrilateral Figures (Worksheet) (#CBSEClass8Maths) (#CBSEClass9Maths)

Properties Of Quadrilateral Figures

(Worksheet)

Question. Fill in the blanks (True or False) for the properties of the following figures:

Property	Parallelogram	Rhombus	Rectangle	Square
1. Both pairs of opposite sides are parallel and equal.	?	?	?	?
2. Both pairs of opposite angles are equal.	?	?	?	?
3. Diagonals bisect each other.	?	?	?	?
4. Diagonals are equal.	?	?	?	?
5. Each angle is 90°	?	?	?	?
6. Diagonals intersect at right angles.	?	?	?	?
7. All sides are equal.	?	?	?	?

CBSE Class 8 - Maths - Comparing Quantities (Worksheet) (#CBSENotes)

Comparing Quantities

Worksheet

Class 8  NCERT Exemplar Chapter Answers

In the following questions, fill in the blanks to make the statements true.

1. _________ is a reduction on the marked price of the article.

2. Increase of a number from 150 to 162 is equal to increase of _________ per cent.

3. 15% increase in price of an article, which is Rs 1,620, is the increase of Rs _________.

4. Discount = _________ – _________.

5. Discount = Discount % of _________.

6. _________ is charged on the sale of an item by the government and is added to the bill amount.

CBSE Class 8 - Mathematics - Direct and Inverse Proportions

Direct and Inverse Proportions

CBSE Class 8 - Mathematics

NCERT Exemplar Problems and Solutions


Q1: If x and y are directly proportional and when x = 13, y = 39, which of the following is not a possible pair of corresponding values of x and y ?

(a) 1 and 3
(b) 17 and 51
(c) 30 and 10
(d) 6 and 18

Answer: (c) 30 and 10
For direct variation,

x1	=	x2
y1		y2

Thus x/y = 13/39 = 1/3. Options (a), (b) and (d) have the same ratio while option (c) does not.


Q2: Which of the following is in direct proportion?

(a) One side of a cuboid and its volume.
(b) Speed of a vehicle and the distance travelled in a fixed time interval.
(c) Change in weight and height among individuals.
(d) Number of pipes to fill a tank and the time required to fill the same tank.

Answer: (b) Speed of a vehicle and the distance travelled in a fixed time interval.
∵ Speed / distance = fixed ratio.


Q3: Both u and v vary directly with each other. When u is 10, v is 15, which of the following is not a possible pair of corresponding values of u and v?

(a) 2 and 3
(b) 8 and 12
(c) 15 and 20
(d) 25 and 37.5


Answer: (c) 15 and 20
u/v = 2/3
Option (C) does not maintain the same ratio.

Class 8 Mathematics - Rotational Symmetry

Rotational Symmetry

Swastika has a rotational symmetry (order:4)
image credits: wikipedia

Class 8 Mathematics 

A figure has rotational symmetry if the object can be rotated about a fixed point without changing the overall shape.

e.g. Consider the following equilateral triangle, if you rotate by 120°, you get the same figure.
Order of Rotational Symmetry
The order of rotational symmetry is the number of times the shape maps onto itself during a rotation of 360°.

CBSE Class 8 Maths - Linear Equations In One Variable (Q and A) (#eduvictors)(#class8Maths)

Linear Equations In One Variable

Class 8 Maths

Q & A based on Class 8 NCERT Chapter 

Q1(MCQ): If 3x – 4 (64 – x) = 10, then the value of x is

(a) –266
(b) 133
(c) 66.5
(d) 38



Answer: (d)38
  3x - 256 + 4x =10
  7x = 10 + 256 = 266
  x = 266/7 = 38


Q2: Three consecutive even numbers whose sum is 156 are 51, 52 and 53.
State if the above statement is True or False

Answer: False

Let the three consecutive even numbers be x, x+2, x+4
∴ x + x+ 2 + x+4 = 156
⇒ 3x + 6 = 156
⇒ 3x = 156 - 6 = 150
⇒ x = 150 /  3 = 50
Thus numbers are 50, 51, 52


Q3: Fifteen added to thrice a whole number gives 93. The number is __________.

Answer: 26



Q4: x = –12 is the solution of the linear equation 5x –3(2x + 1) = 21+x (True or False)

CBSE Class 8 - Mathematics - Factorisation - NCERT Exercise (14.2)

Factorisation

NCERT Exercise 14.2

Q1: Factorise the following expressions.

(i) a² + 8a + 16

(ii) p² − 10p + 25

(iii) 25m² + 30m + 9

(iv) 49y² + 84yz + 36z²

(v) 4x² − 8x + 4

(vi) 121b² − 88bc + 16c²

(vii) (l + m)² − 4lm (Hint: Expand (l + m)² first)

(viii) a⁴ + 2a²b² + b⁴


Answer:

(i) a² + 8a + 16 = (a)² + 2 ☓ a ☓ 4 + (4)²

= (a + 4)² [(x + y)² = x² + 2xy + y²]


(ii) p² − 10p + 25 = (p)² − 2 ☓ p ☓ 5 + (5)²

= (p − 5)² [(a − b)² = a² − 2ab + b²]


(iii) 25m² + 30m + 9 = (5m)² + 2 ☓ 5m ☓ 3 + (3)²

= (5m + 3)² [(a + b)² = a² + 2ab + b²]

(iv) 49y² + 84yz + 36z² = (7y)² + 2 ☓ (7y) ☓ (6z) + (6z)²

= (7y + 6z)² [(a + b)² = a² + 2ab + b²]

(v) 4x² − 8x + 4 = (2x)² − 2 (2x) (2) + (2)²

= (2x − 2)² [(a − b)² = a² − 2ab + b²]

= [(2) (x − 1)]² = 4(x − 1)²

(vi) 121b² − 88bc + 16c² = (11b)² − 2 (11b) (4c) + (4c)²

= (11b − 4c)² [(a − b)² = a² − 2ab + b²]

(vii) (l + m)² − 4lm = l² + 2lm + m² − 4lm

= l² − 2lm + m²

= (l − m)² [(a − b)² = a² − 2ab + b²]

(viii) a⁴ + 2a²b² + b⁴ = (a²)² + 2 (a²) (b²) + (b²)²

= (a² + b²)² [(a + b)² = a² + 2ab + b²]

CBSE Class8 - Mathematics - Ch 14 - Factorisation (NCERT Ex 14.1)

Factorisation

NCERT Exercise 14.1 Solutions

Q1: Find the common factors of the terms

(i)   12x, 36

(ii)  2y, 22xy

(iii)  14pq, 28p²q²

(iv) 2x, 3x², 4

(v) 6abc, 24ab², 12a²b

(vi) 16x³, −4x², 32x

(vii) 10pq, 20qr, 30rp

(viii) 3x²y³, 10x³y², 6x²y²z

Answer:

(i) 12x = 2 ☓ 2 ☓ 3 ☓ x

36 = 2 ☓ 2 ☓ 3 ☓ 3

The common factors are 2, 2, 3.

And, 2 ☓ 2 ☓ 3 = 12

(ii) 2y = 2 ☓ y

22xy = 2 ☓ 11 ☓ x ☓ y

The common factors are 2, y.

And, 2 ☓ y = 2y

(iii) 14pq = 2 ☓ 7 ☓ p ☓ q

28p²q² = 2 ☓ 2 ☓ 7 ☓ p ☓ p ☓ q ☓ q

The common factors are 2, 7, p, q.

And, 2 ☓ 7 ☓ p ☓ q = 14pq

(iv) 2x = 2 ☓ x

3x² = 3 ☓ x ☓ x

4 = 2 ☓ 2

The common factor is 1.

CBSE - Class 6-12 - Mathematics - Important Formulas

Mathematics - Important  Formulas 

eduvictors.com has added a new section "Mathematics" and has compiled important formulas on different topics.

Here is the list of Mathematics formulas:

1. Algebra Formulas

⓵ Polynomials
⓶ Fractions
⓷ Algebraic Identities
⓸ Exponents
⓹ Roots

Class 8 - Maths - Algebraic Expressions and Identities (NCERT Ex 9.2 Answers)

Algebraic Expressions and Identities 

(NCERT Ex 9.2 Answers)

Q1: Find the product of following pair of monomials.

(i) 4 , 7p

Answer:

4   ☓   7p = 4  ☓ 7   ☓ p = 28p

(ii) -4p , 7p

Answer:

-4p   ☓   7p = -4 ☓ p ☓ 7  ☓ p = (-4☓7)☓ (p☓ p) = -28p²

(iii) 4p , 7pq

Answer:

-4p  &#9747 7p = -4 ☓ p ☓7  ☓ p  ☓ q = (-4☓ 7)☓ (p☓ p☓ q) = -28p²q

(iv) 4p³ , -3p

Answer:

4p³  ☓  -3p = 4  ☓(-3)   ☓ p ☓ p☓ p☓ p = -12p⁴

(v) 4p , 0

Answer:

4p ☓ 0 = 4☓ p☓ 0 = 0


Q2: Find the areas of rectangles with the following pairs of monomials as their lengths
and breadths respectively.

(p , q);(10m , 5n);(20x² , 5y²);(4x , 3x²);(3mn ,4np)

Answer:

We know that,

Area of rectangle = Length ☓ Breadth

Area of 1^st rectangle = p ☓ q = pq

Area of 2^nd rectangle = 10m ☓ 5n = 10☓ 5 ☓ m ☓ n = 50mn

Area of 3^rd rectangle = 20x² ☓ 5y² = 20☓ 5 ☓ x² ☓ y² = 100x²y²

Area of 4^th rectangle = 4x ☓ 3x² = 4☓3 ☓ x ☓ x² = 12x³

Area of 5^th rectangle = 3mn ☓4np = 3☓ 4 ☓ m ☓ n ☓ n ☓ p = 12mn²p


Q3: Complete the table of products.

First Monomial (⇨) Second Monomial(⇩)

2x

-5y

3x2

-4xy

7x2y

-9x2y2

2x	4x2	...	...	...	...	...
-5y	...	...	-15x2y	...	...	...
3x2	...	...	...	...	...	...
-4xy	...	...	...	...	...	...
7x2y	...	...	...	...	...	...
-9x2y2	...	...	...	...	...	...

Answer:

CBSE Class 8 - Maths - CH 6 - Square and Square Roots (Ex 6.4)

Square and Square roots

Exercise 6.4

Q1: Find the square root of each of the following numbers by division method.

(i)2304  (ii) 4489  (iii)3481  (iv) 529   (v)3249 (vi) 1369

(vii)5776 (viii) 7921  (ix)576 (x) 1024 (xi)3136 (xii) 900

Answer:

(i)The square root of 2304 is calculated as follows.

	48
4	23 04 -16
88	704 704
	0

∴√ 2304  = 48

(ii)The square root of 4489 is calculated as follows.

	67
6	44 89 -36
127	889 889
	0

∴√ 4489  = 67

(iii)The square root of 3481 is calculated as follows.

	59
5	34 81 -25
109	981 981
	0

∴√ 3481  = 59

(iv)The square root of 529 is calculated as follows.

	23
5	5 29 -4
43	129 129
	0

∴√ 529  = 23

(v)The square root of 3249 is calculated as follows.

	57
5	32 49 -25
107	749 749
	0

∴√ 3249  = 57

(vi)The square root of 1369 is calculated as follows.

	37
3	13 69 -9
67	469 469
	0

∴√ 1369  = 37

(vii)The square root of 5776 is calculated as follows.

	76
7	57 76 -49
146	876 876
	0

∴√ 5776  = 76

CBSE Class 8 - Maths - Cube and Cube Roots (Ex 7.1)

Cube and Cube Roots 

(NCERT Ex 7.1)

Q1: Which of the following numbers are not perfect cubes?
(i)  216
(ii) 128
(iii) 1000
(iv) 100
(v) 46656

Answer:

(i) The prime factorisation of 216 is as follows:

2	216
2	108
2	54
3	27
3	9
3	3
	1

∴ 216 = 2 ☓ 2 ☓ 2 ☓ 3 ☓ 3 ☓ 3 = 2³ ☓ 3³

Here, each prime factor appears as many times as a perfect multiple of 3, therefore, 216 is a
perfect cube.

(ii) The prime factorisation of 128 is as follows:

2	128
2	64
2	32
2	16
2	8
2	4
2	2
	1

∴  128 = 2 ☓ 2 ☓ 2 ☓ 2 ☓ 2 ☓ 2 ☓ 2

Here, each prime factor does not appear as many times as a perfect multiple of 3. Therefore, 128 is not a perfect cube.

(iii)The prime factorisation of 1000 is as follows.

2	1000
2	500
2	250
5	125
5	25
5	5
	1

∴ 1000 = 2 ☓ 2 ☓ 2 ☓ 5 ☓ 5 ☓ 5 =  2³ ☓ 5³

Here, as each prime factor appears as many times as a perfect multiple of 3, therefore, 1000 is a perfect cube.

(iv)The prime factorisation of 100 is as follows.

2	100
2	50
5	25
5	5
	1

∴ 100 = 2 ☓ 2 ☓ 5 ☓ 5

Here, each prime factor does not form triplet group(s). Therefore, 100 is not a perfect cube.

(iv) The prime factorisation of 46656 is as follows.

2	46656
2	23328
2	11664
2	5832
2	2916
2	1458
3	729
3	243
3	81
3	27
3	9
3	3
	1

46656 = 2 ☓ 2 ☓ 2 ☓ 2 ☓ 2 ☓ 2 ☓ 3 ☓ 3 ☓ 3 ☓ 3 ☓ 3 ☓ 3
 = 2³ ☓ 2³ ☓ 3³ ☓ 3³
Here, each prime factor appears as many times as a perfect multiple of 3,
∴ 46656 is a perfect cube.

Q2: Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.

CBSE Class 8 - Maths - Comparing Quantities (Ex 8.2)

Comparing Quantities 

NCERT Chapter (Ex 8.2)

Q1:A man got a 10% increase in his salary.If his new salary is 1,54,000,find his original salary.
Answer:

Let original salary be x. Given that new salary is 1,54,000.

Original salary + increment= New salary

But it is given that increment is 10% of the original salary.

Therefore,







Thus,the original salary was Rs 1,40,000.

Q2: On Sunday 845 people went to the zoo.On Monday only 169 people went.What is the percent decrease in the people visiting zoo on Monday?

Answer:

Given that on Sunday,845 people went to the zoo and on Monday,169 people went.

Decrease in number of people = 845-169=676

Percentage Decrease

CBSE Class 8 - Maths - Comparing Quantities (Ex 8.1)

Comparing Quantities 

NCERT Chapter (Ex 8.1)

Q1: Find the ratio of the following:

(a)Speed of cycle 15 km per hour to speed of scooter 30 km per hour

Answer:
Ratio of speed of cycle to speed of scooter

(b) 5m to 10 km

Answer:

Since 1 Km = 1000 m,

Required Ratio

(c) 50 paise to Rs 5

Answer:

Since Re 1 = 100 paise ,

Required Ratio

Q2: Convert the following ratios to percentages.

(a)3:4