CBSE Class 8 Mathematics Algebraic Expressions And Identities Worksheet Set 01

Question. Given that pq = 6 and p + q = 5, find the value of p² + q².
(A) 300
(B) 37
(C) 13
(D) 12
Answer : C

Question. The volume V, of a solid is given by the formula V = π (R² - r2)h. Find the value of V, given that R = 8,r = 5, h = 3(1/2) and n = 22/7 .
(A) 393
(B) 429
(C) 492
(D) 294
Answer : B

Question. If the product of two numbers is 10 and their sum is 7, what is the larger of the two numbers ?
(A) -2
(B) 2
(C) 5
(D) 4
Answer : C

Question. What is the value of (67.542) - (32.458)2/75.458-40.374 ?
(A) 1
(B) 10
(C) 100
(D) 1000
Answer : C

Question. Mother bought some vegetables for ₹ x and some fruits for ₹ 3. If she gave ₹ 1 0, to the shopkeeper, how much changed id she receive ?
(A) ₹ (13- x)
(B) ₹ (7 + x)
(C) ₹ (13 + x)
(D) ₹ (7 -x)
Answer : D

Question. What is the product of (4x - 3y) and (16x² + 12xy + 9y²) ?
(A) (4x - 3y)³
(B) (16x² + 12xy + 9y²)²
(C) 64x³ - 27y³
(D) 64x³ + 27y³
Answer : C

Question. lf x + y = 6 and 3x - y = 4 find the value of x- y.
(A) - 1
(B) 0
(C) 2
(D) 4
Answer : A

Question. The length of a rod is 4x + 5y- 3z em and the length of another is 6x- 3y + z em. By how much is the second rod longer than the first?
(A) 2x + 8y + 4z
(B) 2x - 8y - 4z
(C) 2x + 8y- 4z
(D) 2x - 8y + 4z
Answer : D

Question. Using the identity (a- b)² = a² - 2ab + b², find the value of 962.
(A) 9642
(B) 9461
(C) 9426
(D) 9216
Answer : D

Question. What must be subtracted from x³ - 3x² + 5x - 1 to get 2x³ + x² - 4x + 2?
(A) -x³ + 4x² - 9x + 3
(B) x³ + 4x² - 9x + 3
(C) x³ - 4x² + 9x - 3
(D) -x³ - 4x² + 9x - 3
Answer : D

Question. If x - 1/x = √6, find the value of x² + 1/x²
(A) 2
(B) 4
(C) 6
(D) 8
Answer : D

Question. The side of a square is 17 em and the side of another is 983 em. What is the difference of their areas in sq. cm ?
(A) 900660
(B) 966000
(C) 960600
(D) 906600
Answer : B

Question. Ajit is 21 years younger than his father. What is their total age in 7 years time ?
(A) (x + 28) years
(B) (x + 35) years
(C) (2x + 28) years
(D) (2x + 35) years
Answer : D

Question. A room is of dimensions 6x feet in length and 4y feet in breadth. A table measuring 2x feet in length and y feet in breadth is in a corner of the room. Find the area of the room not occupied by the table.
(A) 22 xy sq feet
(B) 24 xy sq feet
(C) 26 xy sq feet
(D) 20 xy sq feet
Answer : A

Question. Simplify 3(3x+4/2) + 5(x-3)/3 - 3(2x-5/4).
(A) 57x-56/12
(B) 56x+57/12
(C) 57x+56/12
(D) 56x-57/23
Answer : B

Question. Find the value of the product (3+ 5/x)(9 - 15/x + 25x²) at x = 1.
(A) 150
(B) 148
(C) 152
(D) 146
Answer : C

Question. Using the identity a² - b 2 = (a + b) (a -b), evaluate 24.7 x 25.3.
(A) 624.91
(B) 642.91
(C) 624.19
(D) 642.19
Answer : A

Very Short Answer type Questions

Question. Find the product of 9xy² and 4x³y.
Answer : 36x⁴y³

Question. Find the value of (5x + 7y) if x = 3 and y = 2.
Answer : 29

Question. Find (A + B) (A – B) (A² + B²) (A⁴ + B⁴)
Answer : A⁸ – B⁸.

Question. If x = 3 and y = 5. Find x² + y².
Answer : 34

Question. Multiply and give the answer in simplified form (z – 6) (z – 5).
Answer : z² – 11z + 30

Question. How much is (√19 + √17) (√19 – √17) ?
Answer : 2

Question. Add ab – bc, bc – ca, ca – ab.
Answer : 0

Question. Find the volume of a rectangular box with length, breadth and height respectively 2ax, 3cy and 5gz.
Answer : 30 acgxyz

Question. Find the product of (3n – 5p) (3n + 5p)
Answer : 9n² – 25p²

Question. Identify the coefficients in the algebric expression 3xyz² – 2zy.
Answer : (3, –2)

Question. Add : 7xy + 5yz – 3zx, – 5yz + 3zx, –6xy + yz + zx.
Answer : xy + yz + zx

Question. Subtract : 9a – 6ab + 3b + 5 from 12a – 9ab + 5b – 3.
Answer : 3a – 3ab + 2b – 8

Question. If a = 7 and b = 3. Find a² – b².
Answer : 40

Question. Simplify : (5x²p)³
Answer : 125x⁶p³

Question. Find the value of 472 – 432.
Answer : 360

Please refer to attached file for Algebraic Expressions