NAME: _____________________________________ CLASS:_____________

Madiba Senior Secondary School

Mathematics Department
FORM FIVE COMMON TEST
MATHEMATICS 0563/02
Paper 2
May 2018
1 hour 30 minutes
Additional Materials:
Electronic calculator
Geometrical instruments

Read the following carefully before you start

Write your names at the top of this page.

Answer all questions
Write your answers in the spaces provided on this question paper.
All working must clearly be shown. Marks will be given for working, which shows that
you know how to solve the problem even if you get the answer wrong.
The number of marks is given in brackets [ ] at the end of each question or part question.
The total number of marks for this paper is 50.
Electronic calculators may be used.
If the degree of accuracy is not specified in the question and if the answer is not exact,
the answer should be given to three significant figures. Answers in degrees should be
given to one decimal place.
In any question where the value of is required, use the value from your calculator or
take as .

This document consists of 11 printed pages

[Turn over
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Mathematical formulae for papers 1 and 2

Surface area and volume of solids

Name of solid Total surface area Volume

Cone

base area height

Pyramid

Sphere

Trigonometry

Sine Rule

Area of a triangle

1. The table below shows the mass of nutrients in 40 g of cereal.

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Nutrients Mass (g)

Fibre 1.2
Protein 3.0
Carbohydrates 34.0
Other nutrients ………

Calculate

(a) the mass of other nutrients,

Answer (a) ………………………….. g [1]

(b) the percentage of fibre, by mass, in the cereal,

Answer (b) …………………………… [2]

(c) the mass of carbohydrates in 100 g of the cereal.

Answer (c) ………………………….. g [2]

2. Evaluate

Answer ……………………………… [2]

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3. In a ‘Win a House’ competition, customers send the message ‘HOUSE’ to a

telephone company as many times as they can.
The value of the house that could be won depends on the number of messages sent by
the customer.
The table below shows the number of messages sent and the value of the house that
could be won.

Number of messages Value of house (Pula)

1 to 5 260 000
6 to 9 280 000
10 to 14 320 000
15 to 18 365 000
≥ 19 400 000

(a) Write down the smallest possible number of messages that qualify a customer to
win a house valued at P280 000.

Answer (a) ………………………… [1]

(b) Each message sent costs P5.

(i) Find the least amount of money that the customer has to spend to qualify to
win a house valued at P365 000.

Answer (b)(i) P…………………….. [1]

(ii) A customer spends P65 on the messages.

What is the value of the house they qualify to win?

Answer (b)(ii) P……………………. [2]

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4. The number of people, to the nearest hundred, in a village is 25 400.

Write down the number of people in the village in standard form, correct to two
significant figures.

Answer …………………… [2]

5. A straight line, k, passes through the points A ( 6,5 ) and B ( 0,8 ).

(a) Calculate the distance between A and B.

Answer (a) ………………………[2]

(b) C is another point on k such that AB = BC.

Find the coordinates of C.

Answer (b) …………………….. [2]

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6. The diagram below shows a triangle RST such that RS = 7cm,

ST = 10 cm and RT = 13 cm. The size of = 98.20.

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98.20
S 10 T

Calculate

(a) the area of the triangle,

Answer (a) ……………………… cm2 [2]

(b) the size of .

Answer (b) …………………………… [3]

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7. The diagram below shows a wooden block of length 25 cm. The wooden block has
a pentagonal cross section ABCDE such that DC = 18 cm, AB = AE = 11 cm and
ED = BC = 13 cm. .

A
11
B
E
13
25
D 18 C

(a) Calculate the shortest distance from A to BE.

Answer (a) ………………………… cm [2]

(b) Show that the area of the cross section ABCDE is 291 cm2, correct to
3 significant figures.

Answer (b) ……………………….. cm2 [3]

(c) The whole wooden block is to be painted.

Calculate the total surface area to be painted.

Answer (c) ……………………….. cm2 [3]

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8. An aeroplane arrived at its destination at 16 30 after flying for 5 hours 35 minutes.

(a) At what time did the aeroplane depart?

Answer (a) …………………………. [2]

(b) The distance traveled by the aeroplane is 4420 km.

Calculate the average speed of the aeroplane in km/h.

Answer (b) …………………….. km/h [2]

9. Solve the pair of simultaneous equations and .

Answer x = ………… y = ………….. [3]

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10. A cup costs Px and a plate costs P3 more than a cup.

(a) Write down an expression, in terms of x, for the cost of a plate.

Answer (a) ………………………….. [1]

(b) Martha buys 4 cups and 2 plates.

Write down an expression, in terms of x, for the total amount of money Martha
used.

Answer (b) ………………………….. [1]

(c) The total amount of money Martha used is P27.

Write down an equation, in terms of x, for this information.

Answer (c) ………………………….. [1]

(d) Solve the equation in part (c).

Answer (d) ………………………….. [2]

(e) How much money does a plate cost?

Answer (e) P…………………………. [1]

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11. In the diagram below, DC is a tangent to the circle with centre O.

The length of CD = 8.4 cm and the size of = 270.

O . 270
D

8.4

(a) What is the size of ?

Answer (a) ………………………… [1]

(b) Calculate the radius of the circle.

Answer (b) ……………………….. cm [2]

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12. The table below shows the shoe sizes of 40 students in a class.

Shoe size Number of students

4 4
5 7
6 10
7 11
8 6
9 2

(a) What is the range of the shoe sizes?

Answer (a) ………………………………… [1]

(b) Calculate the mean shoe size.

Answer (b) ………………………………… [3]

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