MCQ Questions

Question No. 1

Multiply and simplify.

Answer :

a) 3(4x – 2x) – (3x – 2x)

b) (a – 1)(a – 2)(a – 3)

c) 8(b – 2)(b – 3)

d) 6 – (c – 2)(c – 3)

e) x(x + 1) – (x + 1)(x + 2)

f) 3(a + 2)² – (a + 2)(a – 2)

Question No. 2

Find the HCF of the following expressions.

Answer :

a) x², –x⁶

b) t⁴, t⁷

c) 2x², 12x

d) 36x⁴, 18x³

e) u²v, u³v²

f) x⁶y⁴, –xy

g) 9y⁸z⁴, –12y⁵z⁴

Question No. 3

Factorise the following expressions:

Answer :

a) x² – 5x

b) am – bm

c) 9x – 12y

d) ay – y

e) 3x² – 6

f) x² – bx²

g) 6xy + 9x

h) 15g + 10hg²

Question No. 4

Factorise.

Question No. 5

Factorise the following expressions completely.

Answer :

a) 3(k + 1) – k(k + 1)

b) (m – 2) + p(m – 2)

c) 2x(2b + a) – (a + 2b)

d) a(x + y) – b(y + x)

e) x(a – b) + y(b – a)

f) x²(2a + b) – x(2a + b)

Question No. 6

Factorise the following expressions.

Answer :

a) ap – 2aq + bp – 2bq

b) ay + az + by + bz

c) 2ax + 2ay + bx + by

d) cx – dx + dy – cy

e) 2ax – bx – 2a + b

f) a² – ab + ax – bx

Question No. 7

Without using a calculator, calculate:

Answer :

a) 121² – 120²

b) 57² – 56²

c) 31² – 29²

d) 145² – 135²

Question No. 8

Expand and simplify.

Answer :

a) (x + 1)(x + 2)

b) (x + 1)(x − 3)

c) (x + 8)(x − 1)

d) (x − 2)(x + 2)

e) (x + 2)(x + 7)

f) (x − 2)(x − 3)

g) (x − 5)(x + 3)

Question No. 9

Fill in the missing values for the following factor boxes.

Answer :

a) x² + 3x + 2 = __

b) x² + 10x + 24 = __

Question No. 10

Factorise the following trinomials using the box method.

Answer :

a) x² + 8x + 15

b) x² + 10x + 24

c) x² + 9x + 8

d) x² + 9x + 14

e) x² + 15x + 36

f) x² + 5x + 4

Question No. 11

Expand the following:

Answer :

a) (x + 1)²

b) (x − 3)²

c) (x + 4)²

d) (x − 5)²

e) (x − y)²

f) (3x − 2)²

Question No. 12

Explain how you would factorise each of the following expressions.

Answer :

a) x² + 14x + 49

b) 4x² − 36

c) 2x² + 8x + 6

d) xy − 5y − 2x + 10

e) −7x² − 21x + 28

f) 125a⁴ − 16b⁸

Question No. 13

Match the expressions (a) to (f) with the method you would use to factorise each expression.

Answer :

Question No. 14

Factorise completely.

Question No. 15

The square of a number equals nine times that number. Find the number.

Answer :

Question No. 16

The area of a square is numerically equal to five times its perimeter. Find the length of a side of the square.

Answer :

Question No. 17

Forty-nine less than the square of a number equals zero. Find the number.

Answer :

Question No. 18

The difference of the areas of two squares is 75 square metres. Each side of the larger square is twice the length of a side of the smaller square. Find the length of a side of each square.

Answer :

Question No. 19

The money made from selling x chocolates at the school tuck shop over one month is given by 2x³ − 2x. Factorise the expression, and then determine the number of sweets, if x = 5.

Answer :

Question No. 20

The diagram below shows two circles. The radius of the small circle is 1 cm and that of the large circle is 3 cm. Use factorising to find the area of the shaded part. Use the value of π = 3.14.

Answer :

Question No. 21

The Olabiyi family had a square patch of lawn in their backyard. The lawn’s original area was x² square metres. They increased the length and the breadth of the lawn. The area then became x² + 8x + 15 square metres. How much did they add to the length and breadth of the lawn?

Answer :

Question No. 22

The length of the two sides of a right-angled triangle are given as 12 cm and 15 cm respectively. Use Pythagoras’ theorem and the difference of squares to find the length of the missing side.

Answer :

Question No. 23

The area of a rectangular chicken enclosure that a farmer wants to fence off is x² − 8x + 15. Find the dimensions of the enclosed area.

Answer :

Question No. 24

The volume of a cylinder is given by 9x⁴ − 36. Factorise the expression completely and calculate the volume of the cylinder, if x = 3.

Answer :

Question No. 25

The volume of a swimming pool is given by V = 180x − 58x² + 4x³. Factorise this expression.

Answer :

Question No. 26

Determine the length of the sides of the square of which the area is x² − 8x + 16.

Answer :

Question No. 27

A rectangular plot is 6 m longer than it is wide. The area of the plot is 16 m². Find the length and width of the plot.

Answer :

Question No. 28

Find two consecutive even whole numbers whose product is 168.

Answer :

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