MCQ Questions

Question No. 1

Solve these quadratic equations by completing the square. Give your answers in simplified surd form, where necessary.

Answer :

a) x² − 5x + 3 = 0

b) x² − 3x + 1 = 0

c) −x² + 6x + 9 = 0

d) ax² − x + 1 = 0

Question No. 2

Factorise these expressions.

Question No. 3

Factorise these binomials.

Question No. 4

Factorise these trinomials.

Question No. 5

Factorise these expressions fully.

Question No. 6

Solve for x.

Question No. 7

Solve these quadratic equations.

Question No. 8

Solve for x by factorising.

Question No. 9

Complete the square of each of these quadratic expressions.

Answer :

a) x² + 6x + 9

b) x² − 8x + 16

c) x² + x − 4

d) −x² − 2x + 3

e) 2x² + x − 4

f) −3x² + 6x + 1

Question No. 10

Decide whether these expressions have a maximum or minimum value.

Answer :

a) x² + 4x + 4

b) −x² + 10x − 25

c) 2x² + 2x − 8

d) −3x² − 6x + 9

Question No. 11

Calculate the coordinates of the minimum or maximum values of the expressions in question 3.

Answer :

Question No. 12

Solve these quadratic equations by completing the square.

Answer :

a) x² + 4x + 4 = 0

b) −x² + 10x − 25 = 0

c) x² − 8x − 9 = 0

d) 5x² − 30x + 25 = 0

Question No. 13

Solve these quadratic equations by completing the square. Give your answers correct to two decimal places.

Answer :

a) x² − 3x + 1 = 0

b) x² + 4x + 2 = 0

c) −x² + 7x − 5 = 0

d) −2x² − 12x + 3 = 0

e) 8x² + 6x − 3 = 0

f) 3x² − 4x − 6 = 0

Question No. 14

Solve these quadratic equations (give your answers in simplified surd form).

Answer :

a) x² + 4x − 6 = 0

b) −x² + 6x + 11 = 0

c) −x² − 8x − 9 = 0

d) 5x² − 20x − 20 = 0

e) x² + bx − c = 0

f) −ax² − bx + c = 0

Question No. 15

Solve for x, correct to two decimal places where necessary.

Answer :

a) x² − 5x + 3 = 0

b) x² − 3x − 5 = 0

c) −x² + 4x − 2 = 0

d) 3x² − x − 1 = 0

e) x² − 3x + 1 = 0

f) −x² + 4x + 2 = 0

Question No. 16

Determine the roots of the equations.

Answer :

a) 2x² + x − 6 = 0

b) x² + 4x + 2 = 0

c) −x² + 2x + 5 = 0

d) −2x² + 10x − 6 = 0

e) −2x² − 12x + 3 = 0

f) 8x² + 6x − 3 = 0

Question No. 17

Solve for x (give your answers in simplified surd form or to two decimal places where necessary).

Answer :

a) x(x + 1) = 6

b) x² = 4 − x

c) x(x + 3) = 7

d) (x − 3)² = 6

e) (2x)² − x(x − 14) = 5

f) ½ x² + 3x = 5

Question No. 18

Find the equation of each of these graphs.

Answer :

a) cuts the x axis at −6 and 4 and the y axis at −12

b) cuts the x axis at −1 and 5 and the y axis at −5

c) cuts the x axis at −3 and 1 and passes through point (−2; −6)

d) cuts the x axis at −3 and 0 and passes through point (1; −4)

Question No. 19

Use tables to draw these quadratic graphs for x ∈ [−3; 3].

Answer :

a) y = 3x²

b) y = −x²

c) y = x² − 4x + 4

d) y = 4x² − 1

e) y = x² − 3x − 4

Question No. 20

Given: the function y = x² + x − 2.

Answer :

a) What is the value of y when x = 0?

b) What are the values of x when y = 0?

c) Determine the equation of the axis of symmetry.

d) Will the arms of the graph go up or down?

e) Sketch the graph of the function.

Question No. 21

Find the line of symmetry of each of these functions.

Answer :

a) y = x² − 3x − 4

b) y = −x² + 6x − 5

c) y = 2x² − 8

d) y = 3x² − 7x + 2

Question No. 22

Find the coordinates of the turning point of each graph in question 3.

Answer :

Question No. 23

Decide whether the arms of these graphs go up or down.

Answer :

a) y = 4x² − 2x − 1

b) y = −2x² + x − 4

c) y = 2(x² − 3)

d) y = −x² + 12x + 6

Question No. 24

Draw these quadratic graphs.

Answer :

a) y = −x² + 9

b) y = x² − 9x + 14

c) y = x² − 2x − 15

d) y = −x² + x + 12

Question No. 25

In rectangle DEFG, DE = x cm and EF is 1.5 cm less than DE. If the area of the rectangle is 52 cm², find the dimensions of the rectangle.

Answer :

Question No. 26

The sides of a right-angled triangle are (x + 11) mm and (x − 3) mm and the hypotenuse is 2x mm. Find the value of x.

Answer :

Question No. 27

Solve:

Answer :

a) What are the dimensions of the largest rectangular area that can be enclosed using 12 m of fencing if an existing wall is used as one of the sides?

b) Calculate the maximum area.

Question No. 28

The sum of the digits of a two-digit number is 13 and the product of the digits is 36. Find the two numbers.

Answer :

Question No. 29

Mr Okonta travels 400 km from Lagos to visit his daughter. He drives by car and travels 20 km/h faster than the train going the same distance. He arrives at his daughter’s town one hour and forty minutes earlier than the train. If the speed of the train is x km/h, how fast does the train travel?

Answer :

Question No. 30

A painter and her apprentice paint a building in 24 days. If each woman had worked separately, the apprentice would have taken 20 days longer than the painter to complete the job. Calculate the number of days each woman would take to complete the job on her own.

Answer :

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