MCQ Questions

Question No. 1

Factorise these expressions.

Answer :

a) 16ax − 32xy + 8axy

b) 4a² − 2a

c) 25a²b + 50ab²

d) 16x² − 25y²

e) 3y² − 11y + 6

f) 81 − a²

g) 4x² + 8x − 60

h) a² + 8a + 16

Question No. 2

Find the constant k that makes these expressions perfect squares.

Answer :

a) x² − 8x + k

b) x² + 20x + k

c) x² − 6x + k

d) x² + 16x + k

e) x² − 12x + k

f) x² + 14x + k

g) 9x² + 6x + k

h) 16x² + 24x + k

Question No. 3

Solve for x.

Answer :

b) x² − 5x + 6 = 0

a) 4x² − 1 = 0

c) x² − 20x = 0

d) 2x² − 6x = 0

e) x² − 7x + 12 = 0

f) x² + 14x + 49 = 0

g) 64x² = 1

h) x² − 6x + 9 = 0

Question No. 4

Solve for x by factorising.

Answer :

a) x² − 10x + 25 = 0

b) x² − 18x + 81 = 0

c) x² − 16x + 64 = 0

d) 2x² − 8x + 8 = 0

e) 4x² + 20x + 25 = 0

f) 3x² − 30x + 75 = 0

g) 9x² + 6x + 1 = 0

h) 25x² − 60x + 36 = 0

Question No. 5

Find the constant k which makes the quadratic equations a perfect square.

Answer :

a) x² − 12x + k = 0

b) x² + 18x + k = 0

c) x² − 22x + k = 0

d) x² − 28x + k = 0

e) x² + 14x + k = 0

f) 2x² − 8x + k = 0

g) 9x² − 6x + k = 0

h) 4x² + 12x + k = 0

Question No. 6

Solve the following equations by completing the square. Leave the answer in simplified surd form where necessary.

Answer :

a) x² − 4x − 7 = 0

b) x² + 8x − 5 = 0

c) x² − 6x − 12 = 0

d) −2x² − 3x + 8 = 0

e) x² + 7x − 11 = 0

f) 3x² − 12x + 10 = 0

g) 2x² + 4x − 3 = 0

h) 9x² − 24x + 2 = 0

Question No. 7

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

Answer :

a) x² − 3x − 1 = 0

b) −3x² − 10x + 4 = 0

c) x² + 2x − 1 = 0

d) 5x² − 20x − 20 = 0

e) 3x² + 2x − 4 = 0

f) −ax² − bx + c = 0

Question No. 8

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

Answer :

a) 3x² − 7x + 1 = 0

b) 5x² − x − 3 = 0

c) −x² + 4x − 2 = 0

d) 3x² − x − 1 = 0

e) 2x² − x − 2 = 0

f) 3x² − 7x + 3 = 0

Question No. 9

Write x² − 7x + 17 in the form (x − a)² + b, where a and b are constants. Hence state the minimum value of x² − 7x + 17.

Answer :

Question No. 10

If the solution to an equation is x = (−2 ± √(2p + 5))⁄7, for which values of p will the equation be a perfect square?

Answer :

Question No. 11

For which values of k will 2x² + kx + 18 = 0 have equal roots?

Answer :

Question No. 12

Find the equation that has these roots.

Answer :

a) −2; 3

b) 6; 7

c) ¼; 2

d) 3; −3

e) −2 ± √3

f) 3 ± √11

g) k; −k

h) k₁; k₂

Question No. 13

For which values will the following have equal roots?

Answer :

a) 2x² + (p − 3)x + 8 = 0 (find p)

b) 2x² − 2x − k = 0 (find k)

Question No. 14

The roots of a quadratic equation are 4 and −3. Write down the equation in the form ax² + bx + c = 0.

Answer :

Question No. 15

Given one root of each equation, find the parameter and the other root.

Answer :

a) One root of kx² − x − 2k = 0 is ¾. Find k and the other root.

b) One root of x² + kx − 3 = 0 is −1. Find k and the other root.

c) One root of 2x² + ax + 6 = 0 is ³⁄₂. Find a and the other root.

d) One root of px² − 5x + p = 0 is ½. Find p and the other root.

Question No. 16

If the roots of x² + kx + 4 = 0 are equal, find the roots of x² + kx − 6 = 0, correct to two d.p.

Answer :

Question No. 17

An experienced house painter will take two hours less to paint a wall than her apprentice. Working together, they can paint the wall in 4 4/9 hours. How long would it take the experienced painter to paint the wall if she was working on her own?

Answer :

Question No. 18

A group of students go to a café for some sodas after an exam. The bill totals ₦2 880 and must be paid by the group. Six students are unable to pay so all the others must pay an extra ₦40 each. Determine the number of students in the group.

Answer :

Question No. 19

A train covers a distance of 60 km at a constant speed. One day, due to bad weather, the train travels 10 km/h slower. The journey takes half an hour longer. Calculate the normal speed of the train.

Answer :

Question No. 20

Chinomso took part in a 90 km endurance running race. He ran the race at a speed of 5 km/h slower than when he ran it a few years earlier. The race took him three hours longer to run than his earlier time. At what average speed did he run when he ran the race a few years earlier?

Answer :

Question No. 21

The sum of the squares of two consecutive odd numbers is 290. What are the two numbers?

Answer :

Question No. 22

Kunmi and Mayowa work together to set up a new website in six hours. When working alone, Mayowa takes five hours longer than Kunmi to set up the website. How long would it take Kunmi to set up the website on his own?

Answer :

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