OBJECTIVE TEST

Expand (a + 4)(a + 6)

2a + 24

a² + 6a + 10

a² + 10a + 10

a² + 10a + 24

When a number is doubled and the result is decreased by 9, the answer is 19. Find the number.

Find the rule for the following mapping:

x	0	1	2	3	4
↓	↓	↓	↓	↓	↓
y	-1	1	3	5	7

y = 2x + 1

y = 2x – 1

y = x²-1

y=x²+1

The points M(1, 3) and N(4, 5) are in the number plane. Find the vector MN→.

$(\begin{matrix} 3 \\ 2 \end{matrix})$

$(\begin{matrix} -3 \\ -2 \end{matrix})$

$(\begin{matrix} 5 \\ 8 \end{matrix})$

$(\begin{matrix} -5 \\ -8 \end{matrix})$

Which of the following numbers is the next prime number greater than 23 ?

A trader buys a dozen pens at GH₵ 4.80 and sells them at 48 Gp each. Find her percentage profit.

10%

15%

20%

An article costs ₵60,000.00. The price was increased by 10%. Find the new price.

₵54,000.00

₵61,000.00

₵66,000.00

₵70,000.00

If n² + 4 = 40, find n.

In an office, $\frac{2}{3}$ of the telephone bill is paid by Tom, $\frac{1}{5}$ by Azuma and the remaining by Tina. What fraction is paid by Tina?

$\frac{2}{15}$

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{7}{15}$

10.

In the diagrams below, triangle A₁B₁C₁ is an enlargement of triangle ABC. Determine the scale factor.

0.50

0.75

2.00

4.00

11.

Write 1204_five as a number in base ten.

9996

179

12.

Name the geometrical figure shown in the diagram below.

Cuboid

Cone

Pyramid

Sphere

13.

If q = ut + $\frac{1}{2}$ ft, find q when u = 20, t = 10 and f = 15

350

275

237.5

42.5

14.

Calculate, correct to two decimal places, 0.61 ÷ 0.8

0.07

0.08

0.76

0.83

7.62

15.

Evaluate 0.25 x 0.006, correct to three decimal places

0.001

0.002

0.015

0.075

0.105

16.

Arrange the following fractions from the lowest to the highest: $\frac{3}{4}$ , $\frac{2}{3}$ and $\frac{3}{5}$ .

$\frac{3}{5}$ , $\frac{2}{3}$ , $\frac{3}{4}$

$\frac{3}{5}$ , $\frac{3}{4}$ , $\frac{2}{3}$

$\frac{3}{4}$ , $\frac{2}{3}$ , $\frac{3}{5}$

$\frac{3}{4}$ , $\frac{3}{5}$ , $\frac{2}{3}$

$\frac{2}{3}$ , $\frac{3}{5}$ , $\frac{3}{4}$

17.

The table below shows the ages of children at a birthday party.

Ages(years)	No. of Children
1	3
2	4
3	2
4	5
5	4
6	4
7	6
8	4
9	2
10	1

Use this table to answer the question below.

How many children are 7 or more years old?

18.

A farmer has 1853 pineapple suckers. He plants 17 pineapples in a row. How many rows can he plant?

109

190

19.

Correct 0.024561 to three significant figures.

0.03

0.025

0.0245

0.0246

20.

Solve 2^x = 8 x 2⁰.

x = 3

x = 2

x = -2

x = -3

21.

Simplify $\frac{1}{3}$ + $\frac{1}{9}$ + $\frac{1}{27}$

$\frac{5}{27}$

$\frac{7}{27}$

$\frac{11}{27}$

$\frac{13}{27}$

22.

The product of three numbers is 1197. Two of the numbers are 3 and 21. Find the third number.

399

1134

23.

If one-third of a number is added to one-fifth of the same number, the result is 8. Find the number.

24.

In the above diagram, |RS| = |RT|. Find a

146°

81°

73°

65°

34°

25.

Which of the following sets is equal to {1, 2, 3, 4}?

{2, 4, 1, 5}

{2, 1, 4, 3}

{1, 2, 3, 4, ...}

{2, 3, 4, 5, ...}

26.

Make m the subject of the relation $\frac{1}{m}$ = $\frac{1}{p}$ + $\frac{1}{r}$ .

m = $\frac{pr}{r + p}$

m = $\frac{pr}{r - p}$

m = $\frac{r - p}{pr}$

m = $\frac{r + p}{pr}$

27.

Express 30 minutes as a percentage of 3 hours 20 minutes

12.5 %

15 %

16⅔ %

20 %

28.

Arrange the following fractions in descending order of magnitude:

$\frac{2}{3}$ , $\frac{5}{7}$ , $\frac{2}{5}$ , $\frac{1}{2}$ .

$\frac{5}{7}$ , $\frac{2}{5}$ , $\frac{2}{3}$ , $\frac{1}{2}$

$\frac{5}{7}$ , $\frac{2}{3}$ , $\frac{1}{2}$ , $\frac{2}{5}$

$\frac{1}{2}$ , $\frac{2}{5}$ , $\frac{5}{7}$ , $\frac{2}{3}$

$\frac{1}{2}$ , $\frac{5}{7}$ , $\frac{2}{3}$ , $\frac{2}{5}$

29.

If a × b × c = 1197 and a = 21, b = 3, find c.

49.9

399

30.

In a class of 20 pupils, 8 pupils read Mathematics, 13 read English and 3 read both Mathematics and English.

Use this information to answer the question below.

How many pupils read English only?

31.

x	0	1	2	3	4
↓	↓	↓	↓	↓	↓
y	0	1	4	9	16

What is the rule for the mapping above?

x→x + 3

x→x + 1

x→x - 1

x→x + 2

x→x²

32.

Factorize x² – 5x + 6

(x + 3)(x – 2)

(x – 2)(x – 3)

(x + 1)(x –6)

(x + 2)(x + 3)

(x + 6)(x – 1)

33.

8 men can do a piece of work in 12 days. How long will 6 men take to do the same work if they work at the same rate?

14 days

16 days

18 days

20 days

34.

Simplify 3(6b – 9a) + 7(6a – 5b)

17b + 6a

-17b + 6a

17b + 48a

15a – 17b

17b – 15a

35.

In the following diagram, rectangle OABC is enlarged into rectangle OA₁B₁C₁ from center O. OC = 5 cm, OA = 2 cm and AA₁ = 1 cm.

Use the diagram to answer the question below.

Find the scale factor of the enlargement.

1.5

2.5

36.

What is the Highest Common Factor (HCF) of 24, 32 and 64?

37.

John's uncle sent him ₵120,000.00 through a bank which charges 5% commission. How much commission was paid?

₵5,000.00

₵6,000.00

₵7,000.00

₵7,200.00

38.

Round 8921465 to the nearest hundred.

8921000

8921400

8921460

8921500

39.

How many faces has a cube?

40.

P = {0, 2, 4, 6} and Q = {1, 2, 4, 5}. Find P ∩ Q.

{0, 6}

{2, 4}

{0, 4}

{0, 2, 6}

{0, 1, 2, 4, 5}

THEORY QUESTIONS

(a)

Factorize completely 6xy - 3y + 4x - 2.

(b)

The diagram shows a ladder AB which leans against a vertical wall PQ at B. If |PB| is 8 m and the other end of the ladder is 6 m away from the foot of the wall (at P), find the length of the ladder (AB).

(c)

Kojo had 1,800 bags of rice in stock for sale. In January, he sold $\frac{2}{3}$ of it. In February, he sold $\frac{3}{4}$ of what was left.

(i)

What fraction of the stock of rice did he sell

(α)

in February?

(β)

in January and February?

(ii)

How many bags of rice were left unsold by the end of February?

Using a rule and a pair of compasses only, construct:

a triangle ABC with |BC| = 9 cm, |AC| = 8 cm and |AB| = 6 cm;

the perpendicular bisector of line BC;

iii

the bisector of angle ACB.

Label the point of intersection of the two bisectors as Y.

Draw a line to join B and Y.

Measure:

|BY|;

|YC|;

iii

the base angles of triangle BYC.

What type of triangle is BYC?

The sum of the interior angles of a regular polygon is 900^o. Find the number of sides of the polygon.

Using a ruler and a pair of compasses only, construct:

triangle XYZ such that length XY = 10 cm, angle XYZ = 30^o and length YZ = 9 cm;

perpendicular from Z to meet line XY at P;

iii

measure the:

length PZ;

angle XYZ.

calculate, correct to the nearest whole number, the area of triangle XYZ.

(a)

M is a set consisting of all positive integers between 1 and 10. P and Q are subsets of M such that P = {factors of 6}, Q = {multiples of 2}

(i)

List the elements of M, P and Q

(ii)

Represent M, P and Q on a Venn diagram

(iii)

Find P ∩ Q

(b)

(i)

Solve the inequality $\frac{2x - 2}{4}$ - $\frac{2x - 1}{3}$ ≤ 1

(ii)

Illustrate your answer on the number line.

A woman borrowed ₵2,000,000.00 from a bank at a rate of 15% per annum simple interest for 2 years.

(a)

Find

(i)

the interest for the 2 years;

(ii)

how much she paid in all to the bank after the 2 years.

(b)

She used the ₵2,000,000.00 to purchase a fridge and sold it at a profit of 45%. Find the selling price of the fridge.

(c)

If she used the amount raised from the sale of the fridge to pay for the bank loan and interest, find how much money is left.

(a)

Simplify 6 $(3 \frac{5}{6} - 1 \frac{1}{4})$ .

(b)

Copy and complete the magic square so that the sum of numbers in each row or column or diagonal is 18.

	4

7	8

(c)

Find the sum of all the factors of 24.

(d)

Given that m = $(\begin{matrix} 3 \\ -1 \end{matrix})$ , n = $(\begin{matrix} -1 \\ 2 \end{matrix})$ and r = $(\begin{matrix} 18 \\ -6 \end{matrix})$

Find m + n + r.