OBJECTIVE TEST

Find the tangent of the angle marked y in the diagram below.

$\frac{3}{5}$

$\frac{3}{4}$

$\frac{4}{5}$

$\frac{4}{3}$

$\frac{5}{3}$

If R = $\frac{1}{2}$ (a + b)k, find k in terms of R, a and b.

$\frac{a + b}{2R}$

$\frac{2R}{a + b}$

$\frac{2R - a}{b}$

$\frac{2R - b}{a}$

$\frac{R}{2(a + b)}$

A man travelled a distance of 1.2 km in 30 minutes. What distance can he cover in 55 minutes travelling at the same speed?

1.375 km

2.02 km

2.2 km

12.02 km

13.25 km

The marks obtained by 10 children in a mental drill are: 0, 1, 3, 3, 5, 7, 8, 9, 9, 9.

Use this information to answer the question below.

Find the median mark.

The following data show the marks of students in a test:

10,4,1,4,3,3,2,1,1,7,8.

Use the information to answer the question below.

Find the mean mark

Which of the following is not a factor of 18?

Arrange the following fractions in ascending order: $\frac{5}{8}$ , $\frac{11}{20}$ , $\frac{7}{10}$ .

$\frac{5}{8}$ , $\frac{11}{20}$ , $\frac{7}{10}$

$\frac{7}{10}$ , $\frac{5}{8}$ , $\frac{11}{20}$

$\frac{11}{20}$ , $\frac{5}{8}$ , $\frac{7}{10}$

$\frac{5}{8}$ , $\frac{7}{10}$ , $\frac{11}{20}$

M = {multiples of 3 between 10 and 20}
N = {even numbers between 10 and 20}.

Find M ∩ N.

{12, 18}

{12, 15, 18}

{12, 14, 16, 18}

{12, 14, 15, 16, 18}

{10, 12, 14, 15, 18, 20}

The length of a rectangular fence is 25 m. The ratio of the length to the width is 5:3. Find the width of the rectangular fence.

9 m

13 m

15 m

16 m

10.

Express 4037 in standard form.

4.037 x 10^-4

4.037 x 10^-3

4.037 x 10³

4.037 x 10⁴

11.

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

12.

Three children share an amount of ₵910,800.00 in the ratio 2 : 3 : 4. What will be the highest share?

₵202,400.00

₵303,600.00

₵404,800.00

₵455,400.00

13.

The point K(3, 4) is rotated through 180° about the origin. Find its image.

(-3, 4)

(-4, 3)

(-3, -4)

(3, -4)

14.

The product of 2x and 3 is 138. Find x

138

15.

Use the diagram below to answer the question below.

What is the value of b°?

68°

75°

105°

112°

124°

16.

The diagonal of a rectangle is 10 cm long. If the length of the rectangle is 8cm, find its breadth.

2 cm

3 cm

5 cm

6 cm

17.

Factorize completely 5xy + 10ny

5y(x + n)

5y(x + 2n)

5xy(1 + 2n)

5(xy + 2ny)

x(5x + 10n)

18.

In the diagram above, the bearing of point B from A is

340^o

220^o

140^o

50^o

19.

If r = $(\begin{matrix} -10 \\ -3 \end{matrix})$ and n = $(\begin{matrix} 8 \\ -6 \end{matrix})$ , find n + r.

$(\begin{matrix} -2 \\ -9 \end{matrix})$

$(\begin{matrix} 2 \\ -9 \end{matrix})$

$(\begin{matrix} 18 \\ 9 \end{matrix})$

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

20.

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

350

275

237.5

42.5

21.

P = {2, 4, 6, 8} and Q = {even counting numbers less than 12}.

What is the relationship between P and Q?

P = Q

P ⊂ Q

P < Q

Q ⊂ P

P ∈ Q

22.

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

23.

A fair coin and a fair die are rolled together once. Find the probability of obtaining a tail and an odd number.

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{2}{3}$

$\frac{1}{2}$

24.

What is the name of the line segment drawn to join any two points on the circumference of a circle?

arc

chord

radius

sector

segment

25.

J = $\frac{1}{2}$ mv², If v = 4 and J = 12, find m

1.5

3.0

3.6

6.3

26.

If 2x = 5(x - 2) + 7, find the value of x.

-5 $\frac{2}{3}$

-1

5 $\frac{2}{3}$

27.

Find the set of integers within the interval -2 < x < 2

{-2,-1,2}

{-2,-1,0}

{-1,0,1}

{-1,1,2}

28.

Which of the following is an even prime number?

29.

Evaluate $\frac{2^{3} x 3^{4} x 3^{3}}{2^{2} x 2 x 3^{5}}$

30.

Round 8921465 to the nearest hundred.

8921000

8921400

8921460

8921500

31.

X is a point on the line segment AB such that |AB| = 10 cm and |AX| = 4 cm.

Find the ratio |AX| : |XB|

5 : 3

3 : 2

5 : 4

1 : 1

2 : 3

32.

A frog leaps in such a way that its distance, in metres, from its starting position after each leap is given by 4, 7, 10, ...

Find its distance from the starting position after the 10th leap.

33.

Express 5 as a percentage of 4.

125%

120%

25%

20%

34.

The simple interest on GH₵ 450.00 for 4 years is GH₵ 45.00, find the rate of interest

2.5 %

10 %

25 %

6.5 %

35.

If P = {x:x is an even number greater than two and less or equal to twelve}, list the members of P

{2, 4, 2, 8, 10, 12}

{3,4,6,8,10,12}

{2, 4, 6, 8, 10}

{4, 6, 8, 10, 12}

36.

Use the information below to answer the question below

The scores obtained by 8 pupils in a test are 2, 3, 4, 5, 7, 8, 8 and 9

Find the mean score.

4.50

5.75

6.00

8.75

10.00

37.

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

What is the modal age?

38.

The value of an obtuse angle lies between

0° and 90°

90° and 180°

90° and 270°

180° and 360°

39.

If 22% of the length of a rope is 55 cm, find the full length of the rope.

12.1 cm

25 cm

121 cm

250 cm

2500 cm

40.

If P = {7, 9, 13}, Q = {1, 7, 13}. Find P ∩ Q.

{1, 7, 13}

{1, 9, 13}

{7, 13}

{7, 9, 13}

{13}

THEORY QUESTIONS

(a)

Using a pair of compasses and ruler only,

(i)

Construct the triangle ABC with |AB| = 8 cm, |BC| = 8cm and |AC| = 7cm.

(ii)

Bisect angle ABC and let the bisector meet AC at D. Produce |BD| to P such that |BD| = |DP|. Join AP and CP.

(b)

Measure

(i)

angle ADB;

(ii)

|AP|.

(c)

What kind of quadrilateral is ABCP?

(a)

A doctor treated 2,000 patients over a period of time. If he worked for 5 hours a day and spend 15 minutes on each patient, how many days did the doctor spend to treat all the patients?

(b)

The pie chart shows the distribution of textbooks to six classes A,B,C,D,E and F in a school.

(i)

If class D was given 720 textbooks, how many textbooks were distributed to each of the remaining classes?

(ii)

What is the average number of textbooks distributed to the classes?

(iii)

How many classes had less than the average number of textbooks distributed?

The diagram shows a running track ABCDEFA. AB and ED are the straight sides. The ends AFE and BCD are semi circular shapes.

|AB| = |ED| = 90 m and |AE| = |BD| = 70 m.

Find

(a)

the total length of the two semi circular ends, AFE and BCD;

(b)

the perimeter of the running track ABCDEFA;

(c)

the total area of the running track ABCDEF.

[Take π = $\frac{22}{7}$ ]

Simplify: 5(6 - ab) + 2(-7 + 3ab)

The equation of a straight line is given by 3x - 2y - 6 = 0. Find the:
(i) gradient of the line;
(ii) y-intercept

Adwoa received a commission of 20% on bread she sold. In one week, Adwoa's commission was GH₵ 540.00.
(i) How much bread did she sell during that week?
(ii) Find her average daily commission.

ξ = {1, 2, 3, 4, ...,18}
A = {Prime numbers}
B= {Odd numbers greater than 3}

(a)

If A and B are subsets of the Universal set, ξ, list the members of A and B.

(b)

Find the set

(i)

A ∩ B;

(ii)

A ∪ B.

(c)

(i)

Illustrate ξ, A and B on a Venn diagram.

(ii)

Shade the region for prime factors of 18 on the Venn diagram.

(a)

A man deposited ₵350,000.00 in his account in a bank. A simple interest of 4% per annum was paid on his deposit. Calculate the total amount at the end of 4 years.

(b)

The cost of sending a telegram is ₵500 for the first 12 words and ₵25.00 for every extra word.

Find the cost of sending a telegram containing 20 words.