Class 8 Maths Sample Paper

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PGRMS Education
SAMPLE PAPER (01)
CLASS: 8 MAX. MARKS :30
SUBJECT: MATHEMATICS TIME: 1:30 HOUR
CH: 2 (Linear Equations in One Variable)
General Instructions:
I. All questions are compulsory.
II. This question paper contains 14 questions divided into four
Sections A, B, C and D.
III. Section A has 5 questions of 1 mark each. Section B has 4
questions 2 marks each. Section C has 3 questions of 3 marks
each. and Section D has 2 questions of 4 marks each.
IV. Use of Calculators is not permitted.
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Section – A
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In Questions 1 to 10, there are four options, out of which one is
correct. Write the correct answer.
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1. If 3x – 4 (64 – x) = 10, then the value of x is.
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(a) –266 (b) 133 (c) 66.5 (d) 38

2. The number of solutions which a linear equation in one variable has,
A. 0 B. 1 C. 2 D. infinite
3. The value of x for which the expressions 3x – 4 and 2x + 1 become
equal is.
(a) –3 (b) 0 (c) 5 (d) 1
4. Power of a variable in a linear equation is ...........
A. zero B. one
C. two D. three
5. A linear equation in one variable has.
(a) Only one solution (b) Two solutions
(c) More than two solutions (d) No solution
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Section – B
6. state whether the statements are true (T) or false (F).
(a) 3 years ago, the age of a boy was y years. His age 2 years ago was
(y – 2) years.
(b) Shikha’s present age is p years. Reemu’s present age is 4 times the
present age of Shikha. After 5 years Reemu’s age will be 15p years.
7. fill in the blanks to make each statement true.
(a) In a linear equation, the _________ power of the variable appearing
in the equation is one.
(b) The solution of the equation 3x – 4 = 1 – 2 x is _________.
8. Solve the following equations.
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(b) x – 2 = 7
(b) y + 3 = 10
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9. The perimeter of a rectangular swimming pool is 154 m. Its length is
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2 m more than twice its breadth. What are the length and the breadth
of the pool?
Section – C
10. Solve the following equations and check your results.
(a) 3x = 2x + 18
(b) 5t – 3 = 3t – 5
11. The organisers of an essay competition decide that a winner in the
competition gets a prize of Rs. 100 and a participant who does not win
gets a prize of Rs. 25. The total prize money distributed is Rs. 3,000. Find
the number of winners, if the total number of participants is 63.

12. Half of a herd of deer are grazing in the field and three fourths of the
remaining are playing nearby. The rest 9 are drinking water from the
pond. Find the number of deer in the herd.
Section – D
13. Solve the following:
14. (a) The ages of Hari and Harry are in the ratio 5:7. Four years from
now the ratio of their ages will be 3:4. Find their present ages.
(b) A lady went to a bank with Rs. 1,00,000. She asked the cashier to give
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her Rs. 500 and Rs. 1,000 currency notes in return. She got 175 currency
notes in all. Find the number of each kind of currency notes.
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PGRMS Education
SAMPLE PAPER (03)
II. This question paper contains 14 questions divided into four
Sections A, B, C and D.
III. Section A has 5 questions of 1 mark each. Section B has 4
questions 2 marks each. Section C has 3 questions of 3 marks
each. and Section D has 2 questions of 4 marks each.
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Section – A
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1. The solution of which of the following equations is neither a fraction
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nor an integer.
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(a) 3x + 2 = 5x + 2 (b) 4x – 18 = 2
(c) 4x + 7 = x + 2 (d) 5x – 8 = x + 4
2. If a and b are positive integers, then the solution of the equation
ax = b has to be always.
(a) positive (b) negative
(c) one (d) zero
3. Power of variable in a simple equation.
(a) Three (b) Two
(c) One (d) None of these
4. Power of a variable in a linear equation is _______ .
(a) 0 (b) One (c) Two (d) Three

5. The digit in the tens place of a two digit number is 3 more than the
digit in the units place. Let the digit at units place be b. Then the number
is.
(a)11b + 30 (b) 10b + 30
(c) 11b + 3 (d) 10b + 3
Section – B
(a) In a 2 digit number, the units place digit is x. If the sum of digits be 9,
then the number is (10x – 9).
(b) Sum of the ages of Anju and her mother is 65 years. If Anju’s present
age is y years then her mother’s age before 5 years is (60 – y) years.
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7. (a) Two numbers are in the ratio 5:3. If they differ by 18, what are the
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numbers?
(b) Three consecutive integers add up to 51. What are these integers?
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(a) Any value of the variable which makes both sides of an equation
equal is known as a _________ of the equation.
(b) 9x – _________ = –21 has the solution (–2)
9. Solve the following equations.
(a) 14y – 8 = 13
(b) 17 + 6p = 9
Section – C
(a) 3(5z – 7) – 2(9z – 11) = 4(8z – 13) – 17
(b) 0.25(4f – 3) = 0.05(10f – 9)

11. Solve the following equations and check your results.
(a) 5x + 9 = 5 + 3x (b) 4z + 3 = 6 + 2z
12. (a) I have a total of Rs. 300 in coins of denomination ₹ 1, ₹ 2 and ₹ 5
The number of 2 ₹ coins is 3 times the number of 5 ₹ coins. The total
number of coins is 160. How many coins of each denomination are with
me?
(b) There is a narrow rectangular plot, reserved for a school, in Rampur
village. The length and breadth of the plot are in the ratio 11:4. At the
rate ₹ 100 per metre it will cost the village panchayat ₹ 75000 to fence
the plot. What are the dimensions of the plot?
Section – D
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(a)
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(b)
14. (a) The denominator of a rational number is greater than its

numerator by 8. If the numerator is increased by 17 and the
denominator is decreased by 1, the number obtained is 3/2 . Find the
rational number.
(b) Kusum buys some chocolates at the rate of Rs. 10 per chocolate. She
also buys an equal number of candies at the rate of Rs. 5 per candy. She
makes a 20% profit on chocolates and 8% profit on candies. At the end
of the day, all chocolates and candies are sold out and her profit is Rs.
240. Find the number of chocolates purchased.

PGRMS Education
SAMPLE PAPER (04)
II. This question paper contains 14 questions divided into four Sections A,
B, C and D.
III. Section A has 5 questions of 1 mark each. Section B has 4 questions
2 marks each. Section C has 3 questions of 3 marks each. and Section D
has 2 questions of 4 marks each.
Section – A
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1.The shifting of a number from one side of an equation to other is
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Called.
(a) Transposition (b) Distributivity
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(c) Commutativity (d) Associativity

2. Equation for the statement:
thrice the length of a room is 340 metres.
(a) 3l = 430 (b) 3l = 340
(c) 3+l = 340 (d) None of these
3. Which of the following is a linear expression:
(a) x2 + 1 (b) y + y2 (c) 4 (d) 1 + z
4. The sum of three consecutive multiples of 7 is 357. Find the smallest
multiple.
(a) 112 (b) 126
(c) 119 (d) 116

5. What is a linear equation is one variable?
(a) An equation containing one variable raised to the power 11.
(b) An equation in which all variables are of power 11.
(c) An expression containing one variable.
(d) None of these.
Section – B
(a) The number of boys and girls in a class are in the ratio 5:4. If the
number of boys is 9 more than the number of girls, then number of
boys is 9.
(b) Ram and Mohan are together 90 years old. Five years ago Ram was
thrice as old as Mohan was. Hence, the ages of A and B five years back
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would be (x – 5) years and (85 – x) years respectively.
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(a) A term of an equation can be transposed to the other side by
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changing its _________.
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(b)On subtracting 8 from x, the result is 2. The value of x is _________.

8. Solve the following equations. 4. 4z + 3 = 6 + 2z 5. 2x – 1 = 14 – x
9. The ages of Rahul and Haroon are in the ratio 5:7. Four years later
the sum of their ages will be 56 years. What are their present ages? 10.
The number of boys and girls in a class are in the ratio 7:5. The number
of boys is 8 more than the number of girls. What is the total class
strength?
Section – C
10.Solve the following:
(a)8x – 7 – 3x = 6x – 2x – 3
(b)10x – 5 – 7x = 5x + 15 – 8

11. Baichung’s father is 26 years younger than Baichung’s grandfather
and 29 years older than Baichung. The sum of the ages of all the three
is 135 years. What is the age of each one of them?
12. One of the two digits of a two digit number is three times the other
digit. If you interchange the digits of this two-digit number and add the
resulting number to the original number, you get 88. What is the
original number?
Section – D
13. Sum of the digits of a two-digit number is 11. The given number is
less than the number obtained by interchanging the digits by 9.
Find the number.
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14. Distance between two places A and B is 210 km. Two cars start
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simultaneously from A and B in opposite direction and distance
between them after 3 hours is 54 km. If speed of one car is less than
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that of other by 8 km/hr, find the speed of each.
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PGRMS Education
SAMPLE PAPER (1)
CH: 9 (Algebraic Expressions and Identities)
II. This question paper contains 14 questions divided into four Sections
A, B, C and D.
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Section – A
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In Questions 1 to 10, there are four options, out of which one is correct.
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Write the correct answer.
1. Which is the like term as 24a2bc?
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(a) 13 × 8a × 2b × c × a
(b) 8 × 3 × a × b × c
(c) 3 × 8 × a × b × c × c
(d) 3 × 8 × a × b × b × c
2. In a polynomial, the exponents of the variables are always
(a) integers (b) positive integers
(c) non-negative integers (d) non-positive integers
3. Like term as 4m3n2 is
(a) 4m2n2 (b) – 6m3n2
(c) 6pm3n2 (d) 4m3n
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4. Area of a rectangle with length 4ab and breadth 6b2 is
(a) 24a2b2 (b) 24ab3
(c) 24ab2 (d) 24ab
5. Which of the following are like terms?
(a) 5xyz2, – 3xy2z (b) – 5xyz2, 7xyz2
(c) 5xyz2, 5x2yz (d) 5xyz2, x2y2z2
Section – B
6. Identify the terms, their coefficients for each of the following
expressions.
(i) 5xyz2 – 3zy
(ii) 1 + x + x
7. (a) Add ab – bc, bc – ca, ca – ab S
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(b) Subtract 4a – 7ab + 3b + 12 from 12a – 9ab + 5b – 3
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8. Obtain the volume of rectangular boxes with the following
length, breadth and height respectively.
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(i) 5a, 3a2, 7a4

(ii) (a2) × (2a22) × (4a26)
9. (a) Simplify 3x (4x – 5) + 3 and find its values for
(i) x = 3
(ii) x =12.
Section – C
10. Find the product.
(i) (2x + 5) and (4x – 3)
(i) (x2– 5) (x + 5) + 25
(iii) (t + s2) (t2 – s)

11. Simplify.
(a) (a + b) (c – d) + (a – b) (c + d) + 2 (ac + bd)
(b) (x + y)(x2– xy + y2)
12. Use a suitable identity to get each of the following products.
(a) (x + 3) (x + 3)
(b) (xyz – 4) (xyz – 2)
(c) (2y + 5) (2y + 5)
Section – D
13. Simplify.
(a) (ab + bc)2– 2ab2c
(b) (3x + 7)2 – 84x = (3x – 7)2
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(c) 103 × 98
(d) 1022
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14. (a) If m – n = 16 and m2 + n2 = 400, then find mn.
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(b) The base of a parallelogram is (2x + 3 units) and the

corresponding height is (2x – 3 units). Find the area of the
parallelogram in terms of x. What will be the area of parallelogram
of x = 30 units?

PGRMS Education
SAMPLE PAPER (2)
A, B, C and D.
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Section – A
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1. Which of the following is an identity?
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(a) (p + q)2 = p2 + q2 (b) p2 – q2 = (p – q)2

(c) p2 – q2 = p2 + 2pq – q2 (d) (p + q)2 = p2 + 2pq + q2
2. Which of the following is correct?
(a) (a – b)2 = a2 + 2ab – b2
(b) (a – b)2 = a2 – 2ab + b2
(c) (a – b)2 = a2 – b2 (d) (a + b)2 = a2 + 2ab – b2
3. Which of the following is a binomial?
(a) 7 × a + a (b) 6a2 + 7b + 2c
(c) 4a × 3b × 2c (d) 6 (a2 + b)
4. Volume of a rectangular box (cuboid) with length = 2ab,
breadth = 3ac and height = 2ac is
(a) 12a3bc2 (b) 12a3bc
(c) 12a2bc (d) 2ab +3ac + 2ac
5. a2 – b2 is equal to
(a) (a – b)2 (b) (a – b) (a – b)
(c) (a + b) (a – b) (d) (a + b) (a + b)
Section – B
expressions.
(i) x/2 + y/2− xy
(ii) 0.3a – 0.6ab + 0.5b
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7. (a) Add (i) a – b + ab, b – c + bc, c – a + ac
(b) Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz
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8. Obtain the product of
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(i) xy, yz, zx
(ii) a, – a2, a3
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9. Simplify a (a2+ a + 1) + 5 and find its value for (i) a = 0,

(ii) a = 1
(iii) a = – 1.
Section – C
(a) (y – 8) and (3y – 4)
(b) (a2+ 5) (b3+ 3) + 5
(c) (a2+ b) (a + b2)
11. Simplify.
(a) (x + y)(2x + y) + (x + 2y)(x – y)

(b) (1.5x – 4y)(1.5x + 4y + 3) – 4.5x + 12y
(a) (1.1m – 0.4) (1.1m + 0.4)
(b) (4x + 5) (4x + 1)
(c) (2x + 5y) (2x + 3y)
Section – D
13. Simplify.
(a) (9p – 5q)2 + 180pq = (9p + 5q)2
(b) (m2 – n2m)2 + 2m3n2
(c) 9.7 × 9.8
(d) 9982
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14. (a) If a + b = 25 and a2 + b2 = 225, then find ab.
(b) What should be added to 4c (– a + b + c) to obtain 3a (a + b +
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c) – 2b(a – b + c)?
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PGRMS Education
SAMPLE PAPER (2)
A, B, C and D.
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Section – A
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1. a ( b + c) = ab + ac is
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(a)commutative property (b) distributive property

(c) associative property (d) closure property
2. The sum of –7pq and 2pq is
(a) –9pq (b) 9pq
(c) 5pq (d) – 5pq
3. Sum of a – b + ab, b + c – bc and c – a – ac is
(a) 2c + ab – ac – bc (b) 2c – ab – ac – bc
(c) 2c + ab + ac + bc (d) 2c – ab + ac + bc
4. Product of 6a2 – 7b + 5ab and 2ab is
(a) 12a3b – 14ab2 + 10ab (b) 12a3b – 14ab2 + 10a2b2

(c) 6a2 – 7b + 7ab (d) 12a2b – 7ab2 + 10ab
5. Square of 9x – 7xy is
(a) 81x2 + 49x2y2 (b) 81x2 – 49x2y2
(c) 81x2 + 49x2y2 –126x2y (d) 81x2 + 49x2y2 – 63x2y
Section – B
expressions.
(i) 4x2y2 – 4x2y2z2+ z2
(ii) 3 – pq + qr – rp
7. (a) Add (iii) 2p2q2– 3pq + 4, 5 + 7pq – 3p2q2
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(c) Subtract 4p2q – 3pq + 5pq2 – 8p + 7q – 10 from 18 – 3p – 11q
+ 5pq2 pq2+ 5p2q
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8. Obtain the volume of rectangular boxes with the following
length, breadth and height respectively.
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(iii) xy, 2x2y, 2xy2
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(iv) x × x2× x3× x4

9. (a) Simplify 3x (4x – 5) + 3 and find its values for
(i) x = 4
(ii) x =10.
Section – C
(a) (2.5l – 0.5m) and (2.5l + 0.5m)
(b) (p2 – q2) (2p + q)
(c) (a + 3b) and (x + 5)
11. Simplify.

(a) (a + b + c)(a + b – c)
(b) (a + b) (2a – 3b + c) – (2a – 3b)
(c) (m + n) (m2 – mn + n2) = m3 + n3
(a) (a2+ b2) (– a2 + b2)
(b) (2a2 + 9) (2a2 + 5)
(c) (6x – 7) (6x + 7)
Section – D
13. Simplify.
(a) (4pq + 3q)2 – (4pq – 3q)2 = 48pq2
(b) (2.5p – 1.5q)2– (1.5p – 2.5q)2
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(c) 103 × 104
(d) 992
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14 (a) If a2 + b2 = 74 and ab = 35, then find a + b.
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(b) The height of a triangle is x4 + y4 and its base is 14xy. Find the
area of the triangle.

PGRMS Education
SAMPLE PAPER (4)
A, B, C and D.
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Section – A
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1. The product of a monomial and a binomial is a
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(a) monomial (b) binomial

(c) trinomial (d) none of these
2. If we subtract –3x2y2 from x2y2, then we get
(a) – 4x2y2 (b) – 2x2y2
(c) 2x2y2 (d) 4x2y2
3. Product of the following monomials 4p, – 7q3, –7pq is
(a) 196 p2q4 (b) 196 pq4
(c) – 196 p2q4 (d) 196 p2q3
4. Square of 3x – 4y is
(a) 9x2 – 16y2 (b) 6x2 – 8y2

(c) 9x2 + 16y2 + 24xy (d) 9x2 + 16y2 – 24xy
5. Coefficient of y in the term 3/−y is
(a) – 1 (b) – 3
(c) -1/3 (d)1/3
Section – B
6. Classify the following polynomials as monomials, binomials,
trinomials. Which polynomials do not fit in any of these three
categories?
x + y, 1000, x + x2 + x3+ x4, 7 + y + 5x, 2y – 3y2, 2y – 3y2 + 4y3,
5x – 4y + 3xy, 4z – 15z2,
7. Add (a) l2+ m2, m2 + n2, n2 + l2, 2lm + 2mn + 2nl
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(b) Subtract 5x2– 4y2+ 6y – 3 from 7x2– 4xy + 8y2+ 5x 3y.
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8. Obtain the product of
(a) 2, 4y, 8y2, 16y3
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(b) pq + qr + rp, 0
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9. Simplify a (a2 + a + 1) + 5 and find its value for

(i) a = 0,
(ii) a = 5
Section – C
(a) (2pq + 3q2) and (3pq – 2q2)
(b) (a + 7) and (b – 5)
(c) (a2+ 2b2) and (5a – 3b)
11. Simplify
(a) (2.5m + 1.5q)2 + (2.5m – 1.5q)

(b) (x2 – 4) (x2 + 4) + 16
(a) (7a – 9b) (7a – 9b)
(b) (4x + 5) (4x + 1)
(c) (– a + c) (– a + c)
Section – D
13. Simplify.
(a) (a – b) (a + b) + (b – c) (b + c) + (c – a) (c + a) = 0
(b) (4m + 5n)2+ (5m + 4n)2
(c) 5.1 × 5.2
(d) 712
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14. (a) The cost of a chocolate is Rs (x + y) and Rohit bought (x +
y) chocolates. Find the total amount paid by him in terms of x. If x
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= 10, find the amount paid by him.
(b) Subtract b (b2 + b – 7) + 5 from 3b2 – 8 and find the value of
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expression obtained for b = – 3.

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(a) –266 (b) 133 (c) 66.5 (d) 38

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8. fill in the blanks to make each statement true.

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14. (a) The denominator of a rational number is greater than its

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(c) Commutativity (d) Associativity

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(b)On subtracting 8 from x, the result is 2. The value of x is _________.

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(i) 5a, 3a2, 7a4

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(b) The base of a parallelogram is (2x + 3 units) and the

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(a) (p + q)2 = p2 + q2 (b) p2 – q2 = (p – q)2

9. Simplify a (a2+ a + 1) + 5 and find its value for (i) a = 0,

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(a)commutative property (b) distributive property

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(iv) x × x2× x3× x4

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(a) monomial (b) binomial

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9. Simplify a (a2 + a + 1) + 5 and find its value for

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expression obtained for b = – 3.

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