OBJECTIVE TEST

The longest chord of a circle is the

segment.

sector.

circumference.

diameter.

Find the Greatest Common Factor (GCF) of 90, 126 and 72.

Which of the following can be made from the net below?

Triangular prism

Square pyramid

Triangular pyramid

Cuboid

In the diagram below, MNO is a triangle. Angle MON = 72° and angle OMN = 68°.

Find angle ONP.

40°

68°

72°

112°

140°

A man shared an amount of money between his two children, Esi and Ato in the ratio 2:3 respectively. If Ato received GH₵ 45.00, what was the total amount shared?

GH₵ 18.00

GH₵ 27.50

GH₵ 75.00

GH₵ 112.50

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

- 15

-30

Which of these best describes the given construction?

Bisecting a line

Constructing the bisector of a line segment

Constructing the perpendicular to a line

Constructing a perpendicular to a given line from a point outside the line

Constructing a perpendicular to a given line through a point on the line

What is the value of the digit 8 in the number 78000?

8 ten thousands

8 thousands

8 hundreds

8 tens

A rectangle has a length of 8 cm and a breadth of 6 cm. How long is its diagonal?

10.

Given that –1 = 2 – m, find m

- 3

- 1

11.

Express 0.125 as a fraction in its lowest form.

$\frac{1}{8}$

$\frac{1}{9}$

$\frac{1}{12}$

$\frac{1}{16}$

12.

A square of side 4 cm is enlarged by a scale factor of 3. Calculate the area of the enlarged square.

36 cm²

72 cm²

96 cm²

144 cm²

13.

Factorize: xy + 5x + 2y + 10.

(x + 5)(2y + 10)

(x + 2)(y + 10)

(x + 5)(y + 2)

(x + 2)(y + 5)

14.

In the diagram, QRS is a triangle. Angle QRS = 50° and angle RST = 120°. Find angle RQS.

60°

65°

70°

80°

15.

Arrange the following in descending order:

16.

The perimeter of the figure below is 71 cm. Find the diameter of the semi-circumference portion.

[Take π = $\frac{22}{7}$ ]

1.0 cm

3.5 cm

7.0 cm

14.0 cm

17.

In an enlargement with scale factor k, which of the following statements is not true?

Each length is multiplied by k

Each angle remains the same

The shape of the figure does not change

The size of the figure does not change

Corresponding lines are parallel

18.

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

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

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

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

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

19.

A student spends $\frac{17}{35}$ of his pocket money on transport and fruits. He spends $\frac{5}{6}$ of the remainder on sweets. What fraction of his pocket money does he spend on sweets?

$\frac{4}{7}$

$\frac{3}{7}$

$\frac{17}{35}$

$\frac{18}{35}$

$\frac{17}{42}$

20.

By how much is $\frac{5}{6}$ greater than $\frac{3}{4}$ ?

$\frac{1}{12}$

$\frac{1}{6}$

$\frac{5}{12}$

$\frac{2}{3}$

$\frac{4}{5}$

21.

Simplify: (8x²y³)( $\frac{3}{8}$ xy⁴)

3x³y⁷

3x²y⁷

3x³y⁴

3xy

22.

Find the rule for the following mapping:

x	1	2	3	4	5
↓	↓	↓	↓	↓	↓
y	1	4	9	16	25

y → x + 2

y → 2x

y → x²

y → 2x + 2

23.

Find the highest common factor of 15 and 21.

24.

A number of oranges are shared among 50 students and each got 15 oranges. If the same number of oranges are shared equally among 30 students, how many will each student get?

25.

Simplify $\frac{1}{3}$ - $\frac{1}{2}$ + $\frac{2}{5}$

$\frac{17}{30}$

$\frac{13}{30}$

$\frac{7}{30}$

- $\frac{7}{30}$

- $\frac{17}{30}$

26.

Expand the expression 2(3a + 2b)

6a + 2b

5a + 4b

6a + 4b

10ab

12ab

27.

Express 30 minutes as a percentage of 3 hours 20 minutes

12.5 %

15 %

16⅔ %

20 %

28.

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.

29.

The cost of 12 note books is GH₵ 54.84. Find the cost of one note book.

GH₵ 5.57

GH₵ 4.67

GH₵ 4.57

GH₵ 3.57

30.

Use the identity a² – b² = (a + b)(a – b) to evaluate 83² - 17²

660

6,600

7,178

7,600

8,317

31.

What is the H.C.F of 48, 30 and 18?

32.

If Q = {1,3,5,7,9,10,11,13,15} and T = {1,2,3,5,6,7,10,11,12}, find Q ∪ T.

{1,2,3,5,7,10,11}

{1,3,5,7,9,11,13,15}

{1,2,3,4,5,6,7,8,9,10,11,12,13}

{1,2,3,5,6,7,9,10,11,12,13,15}

33.

What is the value of 7 in the number 832713?

Seven thousand

Seven hundred

Seventy

Seven

34.

Use the following information to answer the question below.

The relation between the Celsius (C) and Fahrenheit (F) scale of temperature is given by:
C = $\frac{5}{9}$ (F - 32).

If C is 40, F will be

104.0

78.4

72.0

65.6

40.0

35.

The Venn diagram shows the number of pupils who offer Mathematics (M) and/or English (E) in a class.

Use this information to answer the question below.

How many pupils offer only one subject?

36.

If A = {2,6,8} and B = {4,6,8,10}, which of the following statements is true?

A ⊂ B

A ∩ B = {2,6,8}

A ∪ B = {2,4,6,8,10}

A ⊃ B

37.

What is the name of the figure above?

Cuboid

Kite

Triangle

Pyramid

38.

The area of a rectangular card is 15 cm². If each side of the card is enlarged by a scale factor 3, find the area of the enlarged card.

45 cm²

75 cm²

90 cm²

135 cm²

39.

Not drawn to scale

In the diagram, PQR is a right-angled triangle with |PR| = 15 cm and |QR| = 12 cm. Find the length PQ.

3.0 cm

8.0 cm

9.0 cm

19.2 cm

40.

Find the image of 5, under the mapping x → 4x - 7.

THEORY QUESTIONS

Using a ruler and a pair of compasses only,

(a)

construct the triangle XYZ, in which |YZ| = 6 cm, angle XYZ = 60° and |XZ| = 9 cm. Measure |XY|

(b)

(i)

construct the mediator of YZ.

(ii)

draw a circle, centre X and radius 5 cm. Measure |YA|, where A is the point of intersection of the mediator and the circle in the triangular region XYZ

(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?

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|.

(a)

Using a ruler and a pair of compass only:

(i)

construct triangle PQR such that |PR| = 8 cm, |PQ| = 6 cm and |QR| = 5 cm;

(ii)

construct the perpendicular bisector of |PR| and label it l₁;

(iii)

construct the perpendicular bisector of |QR| and label it l₂;

(iv)

Label the point of intersection of l₁ and l₂ as N.

(v)

With N as centre and radius equal to draw a circle.

(b)

(i)

Measure the radius of the circle.

(ii)

Calculate the circumference of the circle, correct to 3 significant figures.

[Take π = 3.14]

The following is the result of a survey conducted in a class of a junior secondary school to find the favourite soft drink of each pupil in the class.

Soft Drink	Number of pupils preferring soft drink
Coca-cola	6
Pepsi-cola	5
Pee-cola	8
Fanta	3
Muscatella	5
Mirinda	4
Club-cola	6
Sprite	3

(a)

Draw a bar chart showing this information, using a scale of 2 cm to 1 unit on the vertical axis.

(b)

How many pupils are in the class?

(c)

What is the percentage of pupils who prefer Club-cola?

Using a scale of 2 cm to 1 unit on both axis, draw two perpendicular lines OX and OY on a graph sheet. Mark the x-axis from –5 to 5 and the y-axis from –6 to 6. Mark the origin O.

(i)

Draw on the same graph sheet, indicating in each case, the co-ordinates of all the vertices the square ABCD where A(1, 2), B(4, 2), C(4, 5) and D(1, 5) are the respective points.

(ii)

Using the y-axis as a mirror line draw the image A₁B₁C₁D₁ of square ABCD where A→A₁,B→B₁, C→C₁ and D→D₁.

(iii)

Draw an enlargement A₂B₂C₂D₂ of the square ABCD with scale factor –1 from O, such that A→A₂, B→B₂, C→C₂ and D→D₂.

(iv)

What single transformation maps A₂B₂C₂D₂ onto the square A₁B₁C₁D₁?