Question 1

Express 108 as a product of prime factors.

A. \( 2^2 \times 3^3 \)
B. \( 2^3 \times 3^2 \)
C. \( 2 \times 3^4 \)
D. \( 2^3 \times 3 \)

Question 2

A football match starts at 2.20 p.m. and lasts for 1 hour 50 minutes. At what time will the game end?

A. 3.10 p.m.
B. 4.10 p.m.
C. 5.10 p.m.
D. 6.10 p.m.

Question 3

Which of the following is not a quadrilateral?

A. Rhombus
B. Parallelogram
C. Rectangle
D. Triangle

Question 4

Solve: 5x - (7x - 3) ≤ 9.

A. x ≥ -3
B. x ≤ -3
C. x ≥ -6
D. x ≤ 3

Question 5

Simplify \( 1 \frac{1}{15} \div 2 \frac{1}{10} \)

A. \( 2\frac{1}{15} \)
B. \( \frac{12}{63}\)
C. \( \frac{25}{63}\)
D. \( \frac{4}{7}\)

Question 6

Given that, \( \overrightarrow{PQ} = \begin{pmatrix} -3 \\ 8 \end{pmatrix}\) find, \( \overrightarrow{QP}\) .

A. \( \begin{pmatrix} -3 \\ -8 \end{pmatrix} \)
B. \( \begin{pmatrix} -8 \\ 3 \end{pmatrix} \)
C. \( \begin{pmatrix} 3 \\ -8 \end{pmatrix} \)
D. \( \begin{pmatrix} -3 \\ -8 \end{pmatrix} \)

Question 7

The point S(4, 3) is reflected in the y-axis, Find the coordinates of the image of S.

A. (-3,4)
B. (4,-3)
C. (3,-4)
D. (-4,3)

Question 8

Solve:\( (x - 1) = \frac{1}{2} (x + 2) \)

A. 4
B. \( 1 \frac{1}{2} \)
C. \( 1 \frac{1}{3} \)
D. 0

Question 9

The longest chord of a circle is the

A. segment.
B. sector.
C. circumference.
D. diameter.

Question 10

Factorize completely \( xy - xm - my + m^2 \)

A. (m-y)(x-m)
B. (x-m)(y-m)
C. (m-y)(m-x)
D. (y-m)(m-x)

Question 11

Given that P(3,-2) and Q(-2,4) are points in a plane, find the gradient of the line joining P to Q.

A. \( -\frac{(6)}{5} \)
B. \( \frac{(6)}{5} \)
C. \( \frac{(5)}{6} \)
D. \( -\frac{(5)}{6} \)

Question 12

If \( \frac{n}{100} = 10.5\) find the value of n.

A. 0.0105
B. 0.105
C. 105
D. 1050

Question 13

The rule of mapping is x → 2x² - 1. What number does x = 2 map to?

A. 9
B. 8
C. 7
D. 3

Question 14

If \( x=\frac{b^2-4ac}{2a} \), find x when a = 2, b = -4 and c = -2.

A. 0
B. 8
C. 4
D. 16

Question 15

Arrange the following fractions from the lowest to the highest:\( \frac{3}{5} \), \( \frac{1}{4} \), \( \frac{2}{3} \)

A. \( \frac{1}{4} \) , \( \frac{3}{5} \) , \( \frac{2}{3} \)
B. \( \frac{2}{3} \) , \( \frac{1}{4} \) , \( \frac{3}{5} \)
C. \( \frac{2}{3} \) , \( \frac{3}{5} \) , \( \frac{1}{4} \)
D. \( \frac{3}{5} \) , \( \frac{1}{4} \) , \( \frac{2}{3} \)

Question 16

A shop is rented at GH₵ 9.00 per month. How much money is paid in 1½ years?

A. GH₵ 162.00
B. GH₵ 135.00
C. GH₵ 6.00
D. GH₵ 13.00

Question 17

A certain number is subtracted from 12 and the result is multiplied by 3. If the answer is 21, find the number.

A. 6
B. 8
C. 5
D. 4

Question 18

In the diagram, AB is parallel to DE, angle ABC = 81° and angle DCE = 20°.

Use the information to answer the question below:

What is the value of x?

A. 20°
B. 61°
C. 81°
D. 101°

Question 19

Find the value of y.

A. 20°
B. 81°
C. 79°
D. 101°

Question 20

Adjoa travelled 12km due north and 5km due east. How much far was she from her starting point?

A. 60km
B. 17km
C. 13km
D. 7km

Question 21

Which of the following is the largest set?

A. {Whole numbers}
B. {Composite}
C. {Natural numbers}
D. {Integers}

Question 22

Write 1930.54 in standard form.

A. \(1.93054 \times 10^3\)
B. \(1.93054 \times 10^-3\)
C. \(1.93054 \times 10^-2\)
D. \(1.93054 \times 10^2\)

Question 23

Expand: (2a - b)(a - b)

A. \(2a^2 + 3ab - b\)
B. \(2a^2 - 3ab - b^2\)
C. \(2a^2 + 3ab + b\)
D. \(2a^2 - 3ab + b^2\)

Question 24

The stem and leaf plot shows the weights (kg) of cocoa bags weighed in a week.

Use the information to answer the question below:

\( \begin{array}{|c|c|} \hline \text{Stem} & \text{Leaf} \\ \hline 4 & 0, 5, 7, 9 \\ \hline 5 & 1, 3, 4, 5, 7, 8 \\ \hline 6 & 0, 2, 3, 4, 4, 4, 4, 5, 6, 8 \\ \hline 7 & 1, 2, 3, 4, 5, 8, 8, 9 \\ \hline 8 & 2, 3, 5, 6, 9 \\ \hline 9 & 4, 5 \\ \hline \end{array} \)

How many bags of cocoa were weighed in the week?

A. 35
B. 29
C. 6
D. 41

Question 25

What is the median weight of the bags of cocoa?

A. 62 kg
B. 65 kg
C. 61 kg
D. 68 kg

Question 26

What is the modal weight of the bags of cocoa?

A. 68 kg
B. 60 kg
C. 64 kg
D. 65 kg

Question 27

If \( a =\begin{pmatrix} -2 \\ -3 \end{pmatrix}\) and \( b =\begin{pmatrix} -2 \\ 3 \end{pmatrix}\), \(find a + b\)

A. \( \begin{pmatrix} 0 \\ 0 \end{pmatrix} \)
B. \( \begin{pmatrix} 2 \\ 3 \end{pmatrix} \)
C. \( \begin{pmatrix} 4 \\ 0 \end{pmatrix} \)
D. \( \begin{pmatrix} 0 \\ 6 \end{pmatrix} \)

Question 28

For what value of x is 3^x = 81?

A. 2
B. 27
C. 4
D. 9

Question 29

Simplify: -15 - (-20) + (-10).

A. -45
B. -5
C. -25
D. 5

Question 30

Express \( \frac{3}{8}\) as a decimal fraction.

A. 0.429
B. 0.375
C. 0.365
D. 0.625

Question 31

What is the length of the side of a square of area 225 cm²?

A. 15.00cm
B. 12.00cm
C. 11.25cm
D. 56.25cm

Question 32

What is the probability that a number greater than 5 shows up when a die is thrown?

A. 5/6
B. 1/6
C. 2/3
D. 1/3

Question 33

Given that 117(12+18) = 117(15+k), find the value of k

A. 15
B. -15
C. -30
D. 30

Question 34

A mother has GH₵ 5.00 and gives each of her 3 children GH₵ 1.50 as pocket money. How much is left for her?

A. GH₵ 3.50
B. GH₵ 4.50
C. GH₵ 0.15
D. GH₵ 0.50

Question 35

A car travels 36 kilometres in an hour. Find its speed in metres per second.

A. 10 m/s^-1
B. 100 m/s^-1
C. 20 m/s^-1
D. 200 m/s^-1

Question 36

Peter had GH₵ 200.00 and spent GH₵ 83.00. What percentage of the money is left?

A. 29.06%
B. 70.94%
C. 58.50%
D. 41.50%

Question 37

If a trader made a profit of 10% in selling a shirt for GH₵ 44.00, find the cost price

A. GH₵ 39.60
B. GH₵ 38.50
C. GH₵ 48.40
D. GH₵ 40.00

Question 38

Express 15 : 12 in the form 1 : n.

A. 1 : 0.8
B. 1 : 12
C. 1 : 15
D. 1 : 1.2

Question 39

The ratio of farmers to children in a village is 13 : 11. If there were 312 farmers in the village, how many children were there?

A. 264
B. 143
C. 48
D. 169

Question 40

The volume of a cylinder is 40π cm³. If the height of the cylinder is 10 cm, find the base radius

A. 1 cm
B. 4 cm
C. 2 cm
D. 3 cm