OBJECTIVE TEST

Given that a = $(\begin{matrix} -2 \\ 3 \end{matrix})$ and b = $(\begin{matrix} 2 \\ -5 \end{matrix})$ , find a + 2b.

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

$(\begin{matrix} 2 \\ 13 \end{matrix})$

$(\begin{matrix} 0 \\ -2 \end{matrix})$

$(\begin{matrix} 6 \\ 13 \end{matrix})$

$(\begin{matrix} 2 \\ -7 \end{matrix})$

Write 78910 correct to the nearest thousand.

70,000

78,000

79,000

80,000

The value of an obtuse angle lies between

0° and 90°

90° and 180°

90° and 270°

180° and 360°

Use the mapping below to answer the question below

-2	-1	0	2	3	4	......	x
↓	↓	↓	↓	↓	↓		↓
y	-1	1	5	7	9	......	21

Find the value of y

–1

–3

-5

What is the place value of 7 in 24.376?

Unit

Ten

Tenth

Hundredth

The circumference of a circle is 440 m. Find the area of the circle.

[Take π = $\frac{22}{7}$ ]

14,400 m²

15,400 m²

16,400 m²

18,000 m²

Which of the following inequalities is represented by the number line?

x ≤ -3

x ≥ -3

x < -3

x > -3

x = -3

Given that

, find the value of p.

If y = $\frac{1}{3}$ (x - 2) express x in terms of y.

x = 3y - 2

3y + 2

x = $\frac{3}{2}$ y

x = - $\frac{3}{2}$ y

10.

A match box contains 40 sticks. If 15 of them are spolit, find the probability that a stick chosen at random is not spoilt?

11.

Simplify: $\frac{2a}{3}$ - $\frac{a - b}{2}$ .

a - 3

$\frac{a - 3b}{6}$

$\frac{a + 3b}{6}$

a + 3b

a - b

12.

Factorize 4ab² – 20ba²

4a(b² – 5b)

4b(b – 5a)

4ab(b - 5a)

4ab(a - 5b)

13.

The point K(1,5) is rotated through 90^o anti-clockwise about the origin.

Find the coordinates of the image of K.

(5,-1)

(-5,1)

(-1,5)

(1,-5)

14.

Express 6 days is to 3 weeks as a ratio in its simplest form.

1 : 2

2 : 1

2 : 7

7 : 2

15.

Simplify $\frac{3x}{4}$ - $\frac{x - y}{3}$ .

$\frac{5x - 4y}{12}$

$\frac{13x - 4y}{12}$

$\frac{5x + 4y}{12}$

$\frac{13x + 4y}{12}$

16.

18 = 2 x 3²; 42 = 2 x 3 x 7; 90 = 2 x 3² x 5

Use the information above to answer the question below.

Find the LCM of 18, 42 and 90.

2 × 3²

2 × 3 × 7

2 × 3² × 5

2 × 3 × 5 × 7

2 × 3² × 5 × 7

17.

Solve for x, if $\frac{1}{2}$ x - 4x > 20

x < -13 $\frac{1}{3}$

x< -5 $\frac{5}{7}$

x > 5 $\frac{5}{7}$

x > 13 $\frac{1}{3}$

18.

Ama is three times as old as Kofi. The sum of their ages is 40. How old is Ama?

10 years

30 years

37 years

43 years

19.

The table below gives the distribution of ages of students in a class.

Use it to answer the question below.

Ages (years)	13	14	15	16	17
Number of students	3	10	6	7	4

How many students are in the class?

20.

Given the vectors m = $(\begin{matrix} 5 \\ -1 \end{matrix})$ and n = $(\begin{matrix} -4 \\ 2 \end{matrix})$ , find 2m + n.

$(\begin{matrix} 6 \\ 0 \end{matrix})$

$(\begin{matrix} -6 \\ 0 \end{matrix})$

$(\begin{matrix} 0 \\ 6 \end{matrix})$

$(\begin{matrix} 0 \\ -6 \end{matrix})$

21.

The marks obtained by 9 students in a test are 3, 3, 4, 5, 6, 7, 7, 7, 8.

Use this information to answer the question below.

Find the median

22.

Find the smallest number which is divisible by 16 and 20?

120

160

23.

Which of the following sets is well defined?

{Man, Kofi, Red, 14}

{Ink, Mango, Green, Nail}

{Car, Road, Glass, Book}

{Seth, Mary, Jacob, Evelyn}

24.

Given that 1 kilometre = $\frac{5}{8}$ mile, what is 240 miles in kilometres?

150 km

190 km

384 km

390 km

25.

Find the mean of the following set of numbers 10, 12, 14 and 16.

26.

Evelyn saved GH₵ 35.48 every month for 8 months. How much did she save?

GH₵ 183.60

GH₵ 280.63

GH₵ 283.20

GH₵ 283.84

27.

Find the rule for the mapping:

1	2	3	4	5	...	n
↓	↓	↓	↓	↓	↓	↓
10	21	32	43	54	...	-

n → 10n

n → (10n + 1)

n → (11n - 1)

n → (7n + 3)

28.

The difference between two numbers is 168. If the smaller number is 113, find the other number.

223

271

281

291

29.

In the diagram above, KGM is a right-angled triangle and angle GKM = 62°. Find the angle of elevation of K from M.

28°

62°

90°

118°

30.

A bag contains 24 marbles, 10 of which are blue and the rest green. A boy picks a marble at random from the bag. What is the probability that he picks a green marble?

$\frac{1}{14}$

$\frac{7}{17}$

$\frac{5}{12}$

$\frac{7}{12}$

$\frac{7}{10}$

31.

If y = $\frac{x + 8}{x - 4}$ , find the value of y when x = 2.

-5

-4

32.

Osei bought a hat for GH₵ 5.00. He sold it to Yaovi at a profit of 20%. How much did Yaovi pay for the hat?

GH₵ 4.80

GH₵ 5.50

GH₵ 6.00

GH₵ 7.00

33.

Use the mapping below to answer the question below

x	1	2	3	4
↓	↓	↓	↓	↓
y	3	5	7	9

What is the rule for the mapping?

x→ 4 - x

x→ x - 2

x→2x

x→2x + 1

x→3x

34.

In the diagram above, PQ is parallel to RS and |PR| = |QR|.

Use the diagram to answer the question below.

What is a?

134

35.

Find the median of the numbers 17,12,15,16,8,18,13 and 14.

14.5

15.5

36.

Find the circumference of a circle with radius 3.5 cm.

[Take π = $\frac{22}{7}$ ]

11 cm

22 cm

35 cm

38.5 cm

37.

Expand (a + 4)(a + 6)

2a + 24

a² + 6a + 10

a² + 10a + 10

a² + 10a + 24

38.

If 2^x = 8, what is the value of x?

39.

Solve the inequality 3x + 6 ≤ 5x - 2.

x ≤ 2

x ≥ 2

x ≤ 4

x ≥ 4

40.

The sum of the interior angles of a regular polygon with 10 sides is

144^o.

900^o.

1,440^o.

1,800^o.

THEORY QUESTIONS

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 following table shows the frequency distribution of the number of letters in the surnames of some students in a school.

No. of letters	4	5	6	7	8	9	10
No. of students	7	3	2	8	5	3	1

(a)

From the distribution, determine

(i)

the mode;

(ii)

the mean.

(b)

If a student is selected at random, find the probability that his/her name will contain more than 7 letters.

(c)

Draw a bar chart for the distribution.

(a)

Mansah earns a salary of ₵10,000.00 per month as a sales girl. In addition to the salary, she is given a commission of 1.5% of whatever sales she makes in a month. In January this year, she made sales of ₵7,500,000.00. What was the total amount Mansah earned at the end of January?

(b)

The diagram below shows a circle with centre O and radius 14 cm. The shaded region AOB is a sector with angle AOB = 72°.

Find:

(i)

The length of the minor arc AB

(ii)

The area of the shaded sector AOB

[Take π = $\frac{22}{7}$ ]

The diagram above is a plane figure made up of a rectangle of sides 50 cm by 28 cm and an equilateral triangle of height 24.25 cm. A circle is cut out of the rectangle as shown. If the circle touches three sides of the triangle,

Calculate

(a)

the perimeter of the figure;

(b)

the area of the remaining portion of the figure.

[Take π = $\frac{22}{7}$ ]

(a)

Fifty students in a class took an examination in French and Mathematics. If 14 of them passed French only, 23 passed in both French and Mathematics and 5 of them failed in both subjects, find

(i)

the number of students who passed in French

(ii)

the probability of selecting a student who passed in Mathematics

(b)

Solve the inequality 2x −1 $\frac{1}{2}$ ≥ 5x −6

Using a ruler and a pair of compasses only,

(a)

draw |PQ| = 9 cm

(b)

construct a perpendicular to PQ at Q

(c)

construct angle QPS = 60° at the point P on PQ such that |PS| = 6.5cm

(d)

construct a line parallel to PQ through S. let the perpendicular through Q and the parallel through S, meet at R. Measure |PR|.