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CLASS VIICHAPTER – ALGEBRIC EXPRESSION

Q.1. Identify the variables, terms with factor x, coefficient of x and coefficient

of y :

(i) 3x – 4y (ii) 2x + 3y – 9

(iii) y2x – 3y (iv) + +Q.2. Identify the numerical coefficient of terms (other than constants) in the

following expressions :

(i) 5 – 3t2 (ii) x + 2xy + 3y (iii) – p2q2 + 7pq

Q.3. Classify into monomial, binomial and trinomial.

(i) 2x – 3y (ii) 3y2 (iii) x + y – xy

(iv) – 13p2q2r4 (v) 4p2q – 4pq2 (vi) z2 – 3z + 8


of y :

(i) 6x + 7y (ii) 5x – 8y + 8

(iii) 3xy2 – 2y (iv) + +Q.5. Identify the numerical coefficient of terms (other than constants) in the


(i) 5 – 3t2 (ii) x + 2xy + 3y (iii) – p2q2 + 7 pq

Q.6. Classify into monomial, binomial and trinomial.

(i) 2x – 3y (ii) 3y2 (iii) x + y – xy

(iv) – 13p2q2r4 (v) 4p2q – 4pq2 (vi) z2 – 3z + 8




of y :

(i) 6x + 7y (ii) 5x – 8y + 8

(iii) 3xy2 – 2y (iv) – + +Q.8. Identify the numerical coefficient of terms (other than constant) in the


(a)(i) 100m + 1000n (ii) 1.2a + 0.8b (iii) 3.14r2

(b)(i) 0.1y + 0.01y2 (ii) 2(l + b) (iii) 1 + t + t2 + t3

Q.9. Identify the terms and their factors in the following expressions. Show

the terms and factors by tree diagrams :

(a)(i) 5xy2 + 7x2y (ii) x + x2 (iii) – 4x + 5y

(b)(i) xy + 2x2y2 (ii) 5y + 3y2 (iii) 3p2q – 3pq2

Q.10. Identify like terms in the following :

(a) – 11x2 , - 100x, - 11yx , - xy2, - 4yx2 , 8x2,

2xy2 , 7y, 20x2y, - 6x2 , y, 2xy, 3x.

(b) 12p2q2, - 5p2, 41, 2405p, 10pq, 7p, 8q, - p2q2

78pq, 701p2, - 7qp, - 100q, - 23.

Q.11. Classify into monomial, binomial and trinomial :

(i) z2 + z (ii) y2 (iii) ab – a – b

(iv) 1 + x + x2 (v) 5 – 3t (vi) pq + pq2 + qp2

Q.12. State whether a given pair of terms is of like or unlike terms :

(i) 1,100 (ii) – 7x, (iii) – 29x, - 29y

(iv) 14xy, 42yx (v) 4m2p, 4mp2 (vi) 12xz , 12x2z2



Q.13. Add :

(i) 3mn, - 5mn, 8mn, - 4mn

(ii) a + b – 3, b – a + 3, a – b + 3

(iii) 3p2 q2 – 4pq + 5, - 10p2q2, 15 + 9pq + 7p2q2

Q.14. Add the following expressions :

3x2 + 2 + 4x – 5x2 , 6x2 – 8 – 9x, 4x – 2x2 + 4x3 , 4x3 – 3x – x2 and x – x2 – x3 – 8

Q.15. From the sum of 4 + 3x and 5 – 4x + 2x2 subtract the sum of 3x2 – 5x and

– x2 + 2x + 5.

Q.16. If A = a2 + 4b2 – 5ab, B = - 2a2 + b2 – ab + a and C = a2 – 2ab + b2 . Find A +

B – C.

Q.17. Simplify combining like terms :

(i) p – (p – q) – q – (q – p) (ii) – 6(a – b) + 3 (2a – b) + 4a – 7

Q.18. Simplify :

(i) 8x + 3y – { − ( − )}(ii) p – [2q – { − ( − )}]

Q.19. Add :

(a) (i) 5xy, - 4xy, 9xy, - 7xy

(ii) t – 8tz, 3tz – z, z – t

(iii) 5m – 7n, 3n – 4m + 2, 2m – 3mn – 5

(b) (i) – 7mn + 5, 12mn + 2, 9mn – 8, - 2mn – 3

(ii) 14x + 10y – 12xy – 13, 18 – 7x – 10y + 8xy, 4xy

Q.20. Add the following expression.

(a) – 6z + 6x + 3y, - 4y – 4z, 2x + 4y – 7 and 13x – 4y + 7z

(b) 5x4 – 3x3 – 7x + 4, - 3x4 – 5x2 + 2x, 4x3 + 4x – 3 and 4x4 – 3x3 + 6x2



Q.21. Subtract :

(i) 3y2 from – 8y2 (ii) –x2 + 10x – 5 from 5x – 10

Q.22. (a) What should be taken away from 3x2 – 4y2 + 5xy + 20 to obtain – x2

– y2+ 6xy + 20?

Q.23. What should be added to x2 + xy + y2 to obtain 2x2 + 3xy?

Q.24. (a) What should be taken away from 3x2 – 4y2 + 5xy + 20 to obtain – x2

– y2 + 6xy + 20 ?

(b) What should be added to x2 + xy + y2 to obtain 2x2 + 3xy?

Q.25. (a) From the sum of 3x – y + 11 and – y – 11, subtract 3x – y – 11.

(b) From the sum of 2y2 + 3yz, - y2 – yz – z2 and yz + 2z2 , subtract the sum of

3y2 – z2 and – y2 + yz + z2.

Q.26. (a) If A = - 5x2 – 8x + 9, B = 3x2 – 5x + 2 and C = 4x2 – 7x + 9, find A + B –

C.

(b) If A = 4x4 – 3x3 + 6x2 , B = 4x3 + 4x – 3, C = - 3x4 – 5x2 + 2x and D = 5x4 – 7x3 –

3x + 4. Find A + B + C – D.

Q.27. Simplify combining like terms :

(a) (i) – z2 + (13z2 – 5z) – (15z – 7z3) (ii) (3y2 + 5y – 4) – (8y – y2 – 4)

(b) (i) 3a – 2b – ab – (a – b + ab) = 3ab + b – a

(ii) 5x2y – (5x2 – 3yx2 + 3y2) + (x2 – y2) + 8xy2 – 3y2

Q.28. Simplify :

(a) (i) 8a – { − ( − ) + } (ii) 4x – [ − { − ( − )}](iii) 12x - [ + − { − ( − − ) − } − ]Q.29. Add :

(i) + − , + − , + −



(ii) − − , − − , − −Q.30. If A = + − , = − + − + − + , =− + , = + E = − . Find A – B + C + D + E.Q.31. Simplify : 9 + [a – { − ( + − ) + } − { − ( − )}]Q.32. Find the value of expressions, when x = - 1(i) – x + 2 (ii) 9 – 5x (iii) + + (iv) − −Q.33. If a = 2 and b = -2, find the value of(i) + (ii) − + (iii) 2 + −Q.34. Simplify these expressions and find their values if = , = − and b= − .(i) 4( − ) + + (ii) 2a – 2b – 4 – 5 + a (iii) 2(x – 1) – (a + 2)+ 2(b – 3) + 11Q.35. What should be the value of if the value of + − equals to 5,when = ?Q.36. If = and = − , then verify(i) ( − ) = − + (ii) + = ( + )( − + )Q.37. (a) Find the value of expressions, when = .(i) + (ii) − (iii) 19 - (iv) 100 -(b) Find the value of expressions, when m = 2.(i) m – 2 (ii) 3m – 5 (iii) 9 – 5m (iv) 3m2 – 2m – 7Q.38. (a) If a = 2 and b = - 2, find the value of(i) + (ii) + + (iii) −(b) Find the value of the following expressions for a = 3 , b = 2(i) a + b (ii) 7a – 4b (iii) + +



Q.39. Simplify these expressions and find their values if = 3, a = -1, b = -2(a) (i) − − + (ii) 2 - ( − ) + (iii) 5a – ( − + )Q.40. What should be the value of if(a) the value of 2a + b + 1 equals to 25, when b = 0?(b) the value of 3ab + 2b2 – 3a + 6 equals to – 18, when b = 0?Q.41. (a) If = and = , then verify :(i) ( + ) = + + (ii) − = ( − )( + + )(b) If = - 2, y = 1 and Z = 3, then verify(i) ( + ) = + + + (ii) ( + + ) = + ++ + +Q.42. If = , = = , then verify :+ + − = ( + + )( + + − − − )Q.43. Write the following statements in the form of equation.(i) The sum of numbers and 4 is 9.(ii) If you subtract 5 from 6 times a number, you get 7.(iii) One – fourth of a number x minus 4 gives 4.(iv) If you add 3 to one – third of z, you get 30.(v) Raju’s father’s age is 5 years more than three times Raju’s age. Raju’sfather is 44 years old. Set up an equation to find Raju’s age.(vi) The teacher tells the class that the highest marks obtained by a studentin her class is twice the lowest marks plus 7. The highest score is 87.Q.44. Convert the following equations in statement form:(i) p + 4 = 15 (ii) 3p + 4 = 25 (iii) − = (iv)+ = +Q.45. Concert the following equations in statement form :



(i) − = (ii) + = (iii) + = (iv) + = +Q.46. Solve each of the following equations by systematic method :(i) − = − (ii) + =(iii) = (iv) 20t = - 30Q.47. Solve each of the following equations by systematic method and verifythe result.(i) 10p + 10 = 100 (ii) 14 = −Q.48. Solve the following equations.(i) 6z + 10 = -2 (ii) 2y + =(iii) 3 -2 (2 – y) = 7 (iv) – 16 = - 5(2 – p)Q.49. Solve the following equation.(i) − ( − ) = ( + ) −(ii) . + = . +(iii) − = −(iv) ( − ) − − = +Q.50. Solve the following :(i) − = (ii) + = (iii) = (iv) =Q.51. Solve each of the following equations by trial and error method :(a) (i) + = (ii) = (iii) − =(b) (i) y – 4 = 4 (ii) 10p = 100 (iii) + = +Q.52. Solve each of the following equations by systematic method and verifythe result :(a) (i) + = (ii) 13 = −



(iii) 16( − ) − ( − ) = (iv) − = −Q.53. Solve the following equations :(a) 5t + 28 = 10 (ii) 7m + = (iii) 34 – 5( − ) = −Q.54. Solve the following equations :(a) (i) ( − ) − { − ( − )} = +(ii) ( − ) + ( − ) = ( + )Q.55. The sum of two consecutive odd numbers is 76. Find the numbers.Q.56. Laxmi’s father is 49 years old. He is 4 years older than three timesLaxmi’s age. What is Laxmi’s age?Q.57. The length of a rectangle is four times its width. If the perimeter of therectangle is 100 metres, find the length and width of the rectangle.Q.58. A piggy bank contains only ₹ 2 and ₹ 1 coins. There are four times asmany ₹ 2 coins as there are ₹ 1 coins. If all the money in the piggy bank addsup to ₹ 225, find the number of ₹ 2 coins.Q.59. A car travelling at the rate of 30 km/h left Delhi. A second car leavesDelhi one hour later. At what speed must the second car travel to catch upwith the first car in three hours?Q.60. Aman travelled of his journey by bus, by train, by taxi and theremaining 8 km on foot. What is the length of his total journey ?Q.61. How much pure alcohol must be added to 400 ml of a 15% solution tomake its strength 32% ?Q.62. (a) Raju’s father’s age is 5 years more than three times Raju’s age. FindRaju’s age, if his father is 44 years old.



(b) The sum of ages of mother and her daughter is 70 years. If the age of thedaughter is 30 years, find the age of the mother.Q.63. (a) Rahul’s father is thrice as old as Rahul. After 12 years he will be justtwice his son. Find their present ages.(b) Raj is 19 years younger than Renu. After 5 years, their ages will be in theratio 2 : 3. Find their present ages.Q.64. (a) The length of a rectangle is three times its width. If the perimeter ofa rectangle is 96 m, find the width and breadth of the rectangle.(b) The length of a rectangle is five times its breadth. If the perimeter of therectangle is 144m, find the length and breadth of the rectangle.Q.65. (a) In an isosceles triangle, the base angles are equal. The vertex angleis times of either base angles. What are the angles of the triangle?(b) In an isosceles triangle the base angles are equal. The vertex angle is 40°.What are the base angles of the triangle?Q.66. (a) A piggy bank contains only ₹ 2 and ₹ 1 coins. There are five times asmany ₹ 1 coins as there are ₹ coins. If all the money in the piggy bank addsup to ₹ 105, find the number of ₹ 1 coins.(b) The teacher tells the class that the highest marks obtained by a studentin her class is twice the lowest marks plus 7. The highest score is 87. What isthe lowest score?Q.67. (a) A car travelling at the rate of 40 km/h left Bakaro. A second carleaves Bokaro one hour later. At what speed must the second car travel tocatch up with the first car in 4 hours?(b) Pujara scored twice as many runs as Mishra. Together, their runs fell twoshort of a double century. How many runs did each one score?



Q.68. (a) A man travelled of his journey by train, by bus, by taxi and theremaining 5 km on foot. What is the length of his total journey?(b) Irfan says that he has 7 marbles more than five times that marblesParmit has. Irfan has 37 marbles. How many marbles does Parmit have?Q.69. How much alcohol must be added to 500 ml of a 60% solution to makeits strength 75%?Q.70. The sum of three consecutive odd numbers is 87. Find the numbers.Q.71. A sum of ₹ 8400 is made up of 50, 20 ,10 and 5 rupees notes. Thenumber of 10 – rupees notes is five times the number of 50-rupees notes.What is the number of notes in each denomination?Q.72. People of Sundargram village planted a total of 102 trees in a villagegarden. Some of the tree were fruits trees. The number of non-fruits treeswere two more than three times the number of fruits trees. What was thenumber of fruits trees planted?Q.73. If z = 10, find the value of z3 – 3(z – 10).Q.74. If p = - 10, find the value of − − .Q.75. Simplify the expression and find its value when a = 5 and b = - 32(a2 + ab) + 3 - ab

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