Revision Questions on Integers,Algebraic expressions,linear equations
INTEGERS
1. Evaluate the following:
(i) 22 – (–87) (ii) 198 + (–12) (iii) –16.87 – 30 (iv) – 19 + 34 – 34
2. Evaluate using properties:
(i) 89 – 58 + 28 – (–32) (ii) 193 + 208 – {29 – (367)}
(iii) 56 – 34 + 235 – (123) (iv) (84 – 34) × (84 + 45)
3. Write ‘true’ or ‘false’ for the following:
(i) Zero is the smallest integer.
(ii) –10 is smaller than –7.
(iii) 1 is the smallest positive integer.
(iv) –1 is the smallest negative integer.
(v) Sum of two negative integers is a positive integer.
4. Evaluate:
(i) (–4) × (–15) × (–33) (ii) (–1) × (–1) × (–1) × … 100 times (iii) (–7) × (–4) × 5
5. In a class test containing 20 questions, 5 marks are awarded for each correct answer and 2 marks is
deducted for each wrong answer. If Riya get 15 correct answers out of all the questions attempted.
What is her total score?
6. What number should be added to the sum of 345 and 67 to make it equal to the smallest 3-digit
number?
ALGEBRAIC EXPRESSIONS
1. Identify the monomials, binomials, trinomials and quadrinomials from the following expressions:
(i) a2 (ii) a2 − b2 (iii) x3 + y3 + z3 (iv) x3 + y3 + z3 + 3xyz (v) 7 + 5 (vi) a b c + 1
(vii) 3x – 2 + 5 (viii) 2x – 3y + 4 (ix) x y + y z + z x (x) ax3 + bx2 + cx + d
2. Write all the terms of each of the following algebraic expressions:
(i) 3x (ii) 2x – 3 (iii) 2x2 – 7 (iv) 2x2 + y2 − 3xy + 4
3. Write the coefficient of x in the following:
(i) –12x (ii) –7xy (iii) xyz (iv) –7ax
4. Evaluate each of the following algebraic expressions for x = 1, y = -1, z = 2, a = -2, b = 1, c = -2:
(i) ax + by + cz ii) ax2 + by2 – cz (iii) axy + byz + cxy
5. Add the following:
(i) 7abc, -5abc, 9abc, -8abc (ii) 2x2y, – 4x2y, 6x2y, -5x2y
6. Add the following expressions:
(i) x3 -2x2y + 3xy2– y3, 2x3– 5xy2 + 3x2y – 4y3
(ii) a4 – 2a3b + 3ab3 + 4a2b2 + 3b4, – 2a4 – 5ab3 + 7a3b – 6a2b2 + b4
7. Add x2 + 2xy + y2 to the sum of x2 – 3y2and 2x2 – y2 + 9.
8. Subtract:
(i) 6x3 −7x2 + 5x − 3 from 4 − 5x + 6x2 − 8x3
(ii) − x2 −3z from 5x2 – y + z + 7
(iii) x3 + 2x2y + 6xy2 − y3 from y3−3xy2−4x2y
9. Subtract the sum of 13x – 4y + 7z and – 6z + 6x + 3y from the sum of 6x – 4y – 4z and 2x + 4y – 7.
10. What should be added to xy – 3yz + 4zx to get 4xy – 3zx + 4yz + 7?
11. If P = 7x2 + 5xy − 9y2, Q = 4y2 − 3x2 − 6xy and R = −4x2 + xy + 5y2, show that P + Q + R = 0.
12. Simplify: -2(x2 – y2 + xy) – 3(x2 +y2 – xy)
LINEAR EQUATIONS
1. Verify by substitution that:
(i) x = 4 is the root of 3x – 5 = 7 (ii) x = 3 is the root of 5 + 3x = 14
(iii) x = 2 is the root of 3x – 2 = 8x – 12
2. Solve each of the following equations by trial – and – error method:
(i) x + 3 =12 (ii) x -7 = 10 (iii) 4x = 28
3. Solve the following
i) 6 (1 – 4x) + 7 (2 + 5x) = 53 ii)8 (2x – 5) – 6(3x – 7) = 1 iii)3 (x – 3) = 5 (2x + 1)
6𝑥 – 2 3𝑥 + 5 1 𝑚–1 𝑚–2 5𝑥 – 1 2𝑥 – 2
iv) + = v) 𝑚 – = 1– vi) – = 1
9 18 3 2 3 3 3
4. If a number is tripled and the result is increased by 5, we get 50. Find the number
5. Shikha is 3 years younger to her brother Ravish. If the sum of their ages 37 years, what are their
present age?
6. A man 4 times as old as his son. After 16 years, he will be only twice as old as his son. Find their
present ages.
7. A bag contains 25 paise and 50 paise coins whose total value is Rs 30. If the number of 25 paise coins
is four times that of 50 paise coins, find the number of each type of coins.
8. The length of a rectangular field is twice its breadth. If the perimeter of the field is 228 meters, find the
dimensions of the field.
