Unit Test (Solutions): We Distribute, Yet Things Multiply | Mathematics Class 8- New NCERT (Ganita Prakash) PDF Download

Time: 1 hour

M.M. 30

Attempt all questions.

• Question numbers 1 to 5 carry 1 mark each.
• Question numbers 6 to 8 carry 2 marks each.
• Question numbers 9 to 11 carry 3 marks each.
• Question number 12 carry 5 marks.

Q1: Which of the following is the distributive property of multiplication over addition?   (1 Mark)
a) (a + b)c = ab + c
b) a(b + c) = ab + ac
c) (a + b)c = a + bc
d) ab + c = (a + c)b

Answer: b) a(b + c) = ab + ac

Q2: When both numbers in a product ab are increased by 1, the increase in the product is:   (1 Mark)
a) a + b
b) a + b + 1
c) ab + 1
d) a² + b²

Answer: b) a + b + 1

Q3: Which identity represents the square of a sum?   (1 Mark)
a) (a – b)² = a² – 2ab + b²
b) (a + b)² = a² + 2ab + b²
c) (a + b)² = a² – 2ab + b²
d) (a – b)² = a² + 2ab + b²

Answer: b) (a + b)² = a² + 2ab + b²

Q4: If a = –5 and b = 8, then (a + 1)(b + 1) equals:   (1 Mark)
a) –36
b) –40
c) 36
d) –44

Answer: a) –36

Q5: Use distributivity to calculate: 98 × 102   (1 Mark)
a) 10,004
b) 9,996
c) 9,980
d) 10,020

Answer: b) 9,996

Q6: Evaluate algebraic expression ax² + by² – cz for x = 1, y = -1, z = 2, a = -2, b = 1, c = -2:   (2 Marks)

Solution: Given algebraic expression is:

ax² + by² – cz

Substituting x = 1, y = -1, z = 2, a = -2, b = 1 and c = -2 in the given expression, we get;

ax² + by² – cz = (-2)(1)² + (1)(-1)² – (-2)(2)

= -2 + 1 + 4

= 3

Q7: Solve (56 + a)(56 − a).  (2 Marks)

Solution: We use the identity

(x + y)(x - y) = x² - y²

Here, x = 56 and y = a.

So,
(56 + a)(56 - a) 
= 56² - a² 
= 3136 - a²

Q8: Solve 110 × 98   (2 Marks)

Solution: (x + y)(x - y) = x² - y²

Here, 110 × 98 can be written as:

110 × 98 = (104 + 6)(104 − 6)

= 104² − 6²
= 10816 − 36
= 10780

Q9: Simplify the algebraic expression: 2x²(x + 2) – 3x (x² – 3) – 5x(x + 5)  (3 Marks)

Solution:

2x²(x + 2) – 3x (x² – 3) – 5x(x + 5)

= 2x³ + 4x² – 3x³ + 9x – 5x² – 25x

= 2x³ – 3x³ – 5x² + 4x² + 9x – 25x

= -x³ – x² – 16x

Q10: Factorise the expression 10x² + 5x + 2xy + y.  (3 Marks)

Solution:

10x² + 5x + 2xy + y

Take the common factors out.

= 5x(2x + 1) + y(2x + 1)

Again, take the common terms out.

= (2x + 1)(5x + y)

Therefore, 10x² + 5x + 2xy + y = (2x + 1)(5x + y).