OBJECTIVE TEST

A rectangular tank has dimensions 2.5 m by 4 m by 5 m. It is filled with water to the brim. If 35 m³ of the water is used, how much water is left in the tank?

50 m³

35 m³

25 m³

15 m³

Solve: 3 - (3x+4) ≤ -4

x ≤ 1

x ≥ 1

x ≥ 1⅔

x < 1½

Express 25 as a percentage of 75.

300%

100%

50%

33.3%

25%

How many lines of symmetry has a square?

If the gradient of a straight line is zero, then the line

is vertical.

is horizontal.

falls to the right.

rises to the right.

Evaluate 53 - (-7) + (-15).

Which of the following is an even prime number?

Find the highest common factor of 18, 36 and 120.

2² × 3³ × 5

2 × 3 × 5

2 × 3

2³ × 2²

3² × 2²

Arrange the following from the highest to the lowest: $\frac{2}{3}$ , -9, $\frac{3}{5}$ and 0.

-9, $\frac{3}{5}$ , $\frac{2}{3}$

-9, 0, $\frac{3}{5}$ , $\frac{2}{3}$

$\frac{3}{5}$ , $\frac{2}{3}$ , 0, -9

$\frac{3}{5}$ , $\frac{2}{3}$ , -9, 0

$\frac{2}{3}$ , $\frac{3}{5}$ , 0, -9

10.

If Y = {house, tree} and V = {cat, house, tree} which of the following is true of Y and V?

Y = V

Y ⊂ V

V ⊂ Y

V ∈ Y

Y ∈ V

11.

In the diagram, line MN is parallel to line TU, line TS cuts line MN at O and ∠MOS = 115^o. Find ∠OTU.

65^o

55^o

45^o

25^o

12.

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

144^o.

900^o.

1,440^o.

1,800^o.

13.

The pie chart shows the monthly expenditure of Mr. Awuah whose monthly income is ₵18,000.00.

Use the chart to answer the question below.

What is the size of the angle that represents savings?

40°

60°

130°

230°

320°

14.

Which of the following is represented by vector AB→ in the diagram above?

(5 cm, 045°)

(5 cm, 135°)

(5 cm, 180°)

(5 cm, 225°)

15.

The point P moves in a plane such that it is always at equal distance from two fixed points, A and B in the same plane. Which of these is the locus of the point P?

The bisector of angle PAB

A circle centre B and radius AB

A circle with AB as the diameter

The perpendicular bisector of line AB.

16.

Simplify: 3x - 2(3 + 2x) + x(2x + 4).

2x² + 11x - 6

2x² + 3x - 6

2x² - 4x - 6

2x² + 4x - 6

17.

In a class of 23 students, the girls were 7 more than the boys. How many boys were in the class?

18.

The diagram shows the conversion graph for miles and kilometres.

Use it to answer the question below

Express 4 kilometres in miles.

6.4

3.5

2.5

19.

In an enlargement length AB = 3 cm and the length of its image A₁B₁ = 15 cm. Calculate the scale factor.

$\frac{1}{5}$

$\frac{2}{3}$

20.

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

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

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

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

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

21.

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

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

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

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

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

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

22.

Find the value of 4 + x⁰.

23.

Use the diagram below to answer the question below

Find the value of x.

68^o

75^o

112^o

124^o

24.

A train is travelling at a speed of 60 km/h. What distance will it cover from 10.45 am to 12.15 pm?

75 km

87 km

90 km

150 km

25.

Write the vector $(\begin{matrix} 6 cm W \\ 4 cm S \end{matrix})$ using cartesian components.

$(\begin{matrix} -6 \\ -4 \end{matrix})$

$(\begin{matrix} -4 \\ -6 \end{matrix})$

$(\begin{matrix} -6 \\ 4 \end{matrix})$

$(\begin{matrix} 6 \\ -4 \end{matrix})$

26.

Use the mapping below to answer the question below.

x	1	2	3	4	5
↓	↓	↓	↓	↓	↓
y	-4	-2	0	2	m

What is the rule for this mapping?

x→ 2(x - 3)

x→ x - 5

x→ 2(x - 2)

x→ 2x-3

27.

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

60°

65°

70°

80°

28.

Eric and Ebo are to share an amount of ₵800,000.00 in the ratio 5:3 respectively. What will be Ebo's share?

₵30,000.00

₵50,000.00

₵300,000.00

₵500,000.00

29.

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?

$\frac{1}{14}$

$\frac{7}{17}$

$\frac{5}{12}$

$\frac{7}{12}$

$\frac{7}{10}$

30.

Convert 222_five to a number in base ten.

31.

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

$(\begin{matrix} 2 \\ 8 \end{matrix})$

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

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

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

$(\begin{matrix} 8 \\ -2 \end{matrix})$

32.

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

(x + 5)(2y + 10)

(x + 2)(y + 10)

(x + 5)(y + 2)

(x + 2)(y + 5)

33.

Simplify $\frac{1}{2}$ - $\frac{2}{3}$ + $\frac{3}{4}$

$\frac{11}{12}$

$\frac{7}{12}$

$\frac{1}{6}$

$\frac{5}{12}$

34.

Simplify $\frac{6^{2}}{2^{2} x 3}$

35.

Express 2700 as a product of prime numbers.

2² × 3² × 5²

2 × 3³ × 5²

2² × 3³ × 5²

2 × 3² × 5³

36.

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

37.

Factorize: 5ay - by + 15a - 3b.

(y + 3)(5a - b)

(y + 5)(3a - b)

(y - 3)(5a + b)

(y - 5)(3a + b)

38.

Find the value of x in the diagram.

28^o

30^o

34^o

60^o

39.

Mark is 30 years old. Yaw is half as old as Mark. Paul is 10 years older than Yaw. How old is Paul?

30 years

25 years

20 years

15 years

10 years

40.

A certain number is subtracted from 12 and the result is multiplied by 3. If the answer is 21, find the number.

THEORY QUESTIONS

The table below shows the distribution of pupils in a JSS form one (1) class who speak some of the Ghanaian languages.

Ghanaian Language	No. of students who speak the language
Nzema	5
Ga	20
Twi	30
Ewe	25
Fante	10

(a)

Draw a pie chart for the distribution.

(b)

What is the modal Ghanaian language?

(c)

If a pupil is selected at random from the form, what is the probability that he speaks Ga?

(a)

Given that P = {factors of 36} and Q = {factors of 54},

(i)

list the members in the sets P and Q.

(ii)

Find:

P∩Q

n(P∩Q)

The Highest Common Factor (HCF) of 36 and 54.

(b)

Write down the next two terms of the sequence 1,4,9,...,...

(c)

The median of the ordered set of observations 2,3,(4m-3),(3m+1),11 and 13 in ascending order is 6. Find the value of m.

(a)

E and F are subsets of the universal set U such that

U = {natural numbers less than 15}

E = {even numbers between 1 and 15} and

F = {multiples of 4 between 9 and 15}

(i)

List the elements of U, E and F.

(ii)

Draw a Venn diagram to show the sets U, E and F.

(b)

In a school, $\frac{7}{10}$ of the pupils like Mathematics. Half of those pupils who like Mathematics are girls. If there are 240 pupils altogether in the school, how many girls like Mathematics?

(c)

A typist charges 28 Gp for the first five sheets and 8 Gp for each additional sheet she types. How much will she earn, if she types 36 sheets?

(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?

Given that X = {whole numbers from 4 to 13} and Y = {multiples of 3 between 2 and 20}, find X ∩ Y.

Find the Least Common Multiple (L.C.M) of the following numbers: 3,5 and 9.

, find the value of

(a)

A fair die and a fair coin are thrown together once.

(i)

Write down the set of all possible outcomes.

(ii)

Find the probability of obtaining a prime number and a tail.

(b)

The map of a field is drawn to a scale of 1 : 100. If the width and area of the field on the map are 8 cm and 88 cm² respectively, find in m², the area of the actual field.

(c)

Copy and complete the 3 x 3 magic square such that the sum of the numbers in each row, column and diagonal is equal to 21.

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