OBJECTIVE TEST

If 4 - x = 3(4x + 5), find the value of x.

$\frac{11}{13}$

1 $\frac{6}{13}$

-1 $\frac{6}{13}$

$\frac{-11}{13}$

Set A is called ...... of set B, when all the numbers of set A are also members of set B.

the universal set

the union set

the null set

a subset

an empty set

On a map, two towns P and Q are 15.5 cm apart. The scale of the map is 1 cm: 4 km. Calculate the actual distance between P and Q.

15.5 km

31 km

46 km

60 km

62 km

It takes 6 students 1 hour to sweep their school compound. How long will it take 15 students to sweep the same compound?

24 minutes

12 minutes

3 hours

2 hours

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}

The product of three numbers is 1197. Two of the numbers are 3 and 19. Find the third number.

210

544

1175

If n(E) = 15, n(F) = 20 and n(E∩F) = 6, find n(E∪F).

Divide $(1 \frac{1}{2} + \frac{1}{4})$ by $(1 \frac{1}{2} - \frac{1}{4})$

$\frac{5}{7}$

1 $\frac{2}{5}$

1 $\frac{3}{4}$

In the diagram, Q is the set of numbers inside the circle and T is the set of numbers inside the triangle. Find Q U T.

{5}

{6, 7}

{3, 4, 5}

{5, 6, 7}

{3, 4, 5, 6, 7}

10.

In triangle PQR, |PQ| = |QR|, and angle PQR = 90°.

Find x.

30°

45°

60°

90°

180°

11.

Use the graph below to answer the question below.

The travel graph describes the journey of a cyclist from Town X to Town Y.

What was the average speed for the return journey from town Y to town X

100 kmh^-1

50 kmh^-1

33.33 kmh^-1

25 kmh^-1

20 kmh^-1

12.

If u = $(\begin{matrix} 1 \\ 3 \end{matrix})$ and v = $(\begin{matrix} 4 \\ -2 \end{matrix})$ , find 2u + 3v.

$(\begin{matrix} 5 \\ 1 \end{matrix})$

$(\begin{matrix} 11 \\ 5 \end{matrix})$

$(\begin{matrix} 11 \\ 13 \end{matrix})$

$(\begin{matrix} 14 \\ 0 \end{matrix})$

$(\begin{matrix} 14 \\ 12 \end{matrix})$

13.

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

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

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

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

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

14.

Which of the following fractions is equivalent to $\frac{3}{5}$ ?

$\frac{21}{30}$

$\frac{12}{20}$

$\frac{15}{45}$

$\frac{6}{15}$

15.

The pie chart shows the distribution of programmes offered by 720 students at Kofikrom.

Use this information to answer the question below.

Find the value of the angle marked y.

90°

100°

110°

120°

16.

A boy spent $\frac{2}{7}$ of his pocket money on transport and $\frac{1}{5}$ on sweets. What fraction of his pocket money does he spend on transport and sweets?

$\frac{2}{35}$

$\frac{3}{35}$

$\frac{1}{7}$

$\frac{17}{35}$

$\frac{18}{35}$

17.

Factorize completely the expression 4xy - 16x + 10y – 40.

(y + 4) (4x – 10)

(y – 4) (4x + 10)

(4 – y) (10 – 4x)

(y + 4) (4x + 10)

18.

Express 962 in standard form.

96.2 x 10

9.62 x 10²

0.962 x 10³

0.0962 x 10⁴

19.

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?

20.

Find the sum of 124.3, 0.275 and 74.06. (Correct your answer to one decimal place)

198.6

198.7

892.0

892.4

21.

If r = $(\begin{matrix} 2 \\ -1 \end{matrix})$ and s = $(\begin{matrix} -3 \\ 2 \end{matrix})$ , calculate 2r - 3s.

$(\begin{matrix} -5 \\ 12 \end{matrix})$

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

$(\begin{matrix} 13 \\ -3 \end{matrix})$

$(\begin{matrix} 13 \\ -8 \end{matrix})$

$(\begin{matrix} 13 \\ 8 \end{matrix})$

22.

A teacher is to be chosen at random from a group of 6 male and 2 female teachers for a patron of a Mathematics Club. What is the probability that a female teacher is chosen?

$\frac{3}{4}$

$\frac{2}{3}$

$\frac{1}{3}$

$\frac{1}{4}$

23.

In triangle ABC, |AB| = |BC| = 5 cm, and |AC| = 8 cm.

Find |BD|.

3 cm

4 cm

9 cm

33 cm

41 cm

24.

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.

What is the HCF of 18, 42 and 90?

25.

The bar chart shows the distances of 5 villages, P, Q, R, S and T from a market town.

Use it to answer the question below.

Which village is farthest from the market town?

26.

Arrange the following integers from the least to the highest -4,9,-10,-7,and 2.

-10,-7,-4,2,9

-10,9,-7,-4,2

-4,-7,-10,2,9

2,-4,-7,9,-10

27.

Which of the following is illustrated on the number line above?

–1 < x < $\frac{3}{2}$

–1 ≤ x < $\frac{3}{2}$

–1 ≤ x ≤ $\frac{3}{2}$

–1 < x ≤ $\frac{3}{2}$

$\frac{3}{2}$ ≤ x ≤ –1

28.

How many lines of symmetry has a rhombus?

29.

Mansah obtained 150 marks out of 240 marks in an English test. What was her percentage score?

33.33%

37.5%

41.67%

62.5%

79.1%

30.

What is the mode of the following numbers: 4, 5, 3, 3, 4, 2, 7, 6, 5, 4, 4, 1?

31.

How many lines of symmetry has a square?

32.

Factorize 22ab – 11ac + 6rb – 3rc.

(2b – c) (11a + 3r)

(2b + c) (11a – 3r)

(2b – c) (11a – 3r)

(2b + c) (11a + 3r)

33.

In the diagram below, the angle of elevation of K from M is

17°

73°

90°

107°

163°

34.

Simplify $\frac{36 a^{3} b^{2} x}{27 a b^{3} y}$ .

$\frac{4 a^{2} x}{3by}$

$\frac{4abx}{3y}$

$\frac{4 a^{2} bx}{3y}$

$\frac{4 a^{4} b^{5} x}{3y}$

35.

On a map, 1⁄3 cm represents 5km. If two towns A and B are 18 cm apart on the map, what is the actual distance between them?

27 km

30 km

240 km

270 km

36.

How many faces has a cube?

37.

L = $(\begin{matrix} 3 \\ -1 \end{matrix})$ and K = $(\begin{matrix} -4 \\ 2 \end{matrix})$ .

Find L + K.

$(\begin{matrix} -1 \\ -1 \end{matrix})$

$(\begin{matrix} -1 \\ 1 \end{matrix})$

$(\begin{matrix} 1 \\ -1 \end{matrix})$

$(\begin{matrix} 7 \\ -1 \end{matrix})$

$(\begin{matrix} 7 \\ 1 \end{matrix})$

38.

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

1 cm

4 cm

2 cm

3 cm

39.

Express

as a decimal fraction.

0.3200

0.3125

0.3676

0.3222

40.

If a = $(\begin{matrix} 2 \\ 1 \end{matrix})$ and b = $(\begin{matrix} 3 \\ -4 \end{matrix})$ , find 2a + b.

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

$(\begin{matrix} 5 \\ -3 \end{matrix})$

$(\begin{matrix} 8 \\ -7 \end{matrix})$

$(\begin{matrix} 3 \\ -4 \end{matrix})$

THEORY QUESTIONS

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?

(a)

Kofi is n years old now

(i)

How old was he 5 years ago?

(ii)

How old will he be 10 years from now?

(iii)

If his age in 10 years time will be four times his age 5 years ago, how old is he now?

(b)

Convert 2342_five to a base ten numeral

(c)

Given that f = $\frac{vu}{v + u}$ , find v, if f = 20 and u = 5

In the Venn diagram, M and N are intersecting sets in the universal set µ.

(a)

Express n(M) and n(N) in terms of x.

(b)

Given that n(M) = n(N), find the:

(i)

Value of x.

(ii)

n(µ)

(c)

Simplify: 2⁶ ÷ (2² x 2¹) ÷ 2⁵.

(a)

Anita bought 51 tubers of yam at 3 for GH₵10.00. If she sold them and made a loss of 40%, how much did she sell each tuber of yam?

(b)

The volume of a cylinder closed at one end is 1056 cm³. If its height is 21 cm, find its:

(i)

diameter;

(ii)

total surface area.

[Take π = $\frac{22}{7}$ ]

(a)

Given the vectors p = $(\begin{matrix} m + 3 \\ 2 - n \end{matrix})$ , q = $(\begin{matrix} 3m - 1 \\ n - 8 \end{matrix})$ and p = q, find the values of m and n.

(b)

A man shared an amount of money between his children Baaba and William in the ratio 6 : 5. Baaba received GH₵ 1,200.00

(i)

find the total amount shared.

(ii)

William invested his share in an account at the rate of 20% simple interest per annum for 2 years. Find the total amount in his account at the end of the 2 years.

(a)

Given that a = $(\begin{matrix} -3 \\ 3 \end{matrix})$ and b = $(\begin{matrix} 4 \\ -6 \end{matrix})$ , calculate

(i)

a + 2b;

(ii)

$\frac{1}{2}$ (2a - b)

(b)

The number of pupils in a primary school is given in the table below:

Class	One	Two	Three	Four	Five	Six
Number of pupils	24	35	35	20	21	45

(i)

Find the number of pupils in the school.

(ii)

What is the mean number of pupils in a class?

(iii)

What percentage of pupils are in class six?

(c)

Convert 312_five to base ten numeral.