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SURNAME: __________________________________CANDIDATE NUMBER _________

FIRSTNAME(S) _________________________________________ CLASS __________

Madiba Senior Secondary School

Mathematics Department
FORM 5 MID-YEAR EXAMINATIONS
MATHEMATICS 0563/02
Paper 2 2 Hours
July/August 2021

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 75.
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 π is required, use the value from your calculator or take π as
3 .142 .

This document consists of 14 printed pages

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[Turn over
Mathematical formulae for papers 1 and 2

Surface area and volume of solids

Name of solid Total surface area Volume

Cone πr 2 + π rl 1 2
πr h
3
1
Pyramid 3 base area ¿ height

Sphere 4 πr 2 4 3
πr
3

Trigonometry

sin A sin B sin C

= =
a b c
a b c
= =
Sine Rule sin A sin B sin C

1
= ab sinC
Area of a triangle 2

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

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]

71 .9×83 . 4
2. Evaluate 7 .08+ √21 . 7 , giving your answer to 2 decimal places.

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Answer ……………………………… [2]

3. A car starts at the first set of traffic lights and reaches a speed of 30 m/s in 20
seconds. It maintains the speed of 30 m/s for 25 seconds. Thereafter it decelerates
until it stops at the second set of traffic lights after 15 seconds.

(a) Draw a speed-time graph to represent this information on the pair of axes
provided below. [3]

40

30
Speed

(m/s)
20

10

0
0 10 20 30 40 50 60

Time, t (seconds)

(b) What is the speed of the car when t = 55 seconds?

Answer (b) ……………………… m/s [1]

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4. The diagram below shows a circle, centre O. The points S (-1, 3 ) and T ( 5, 9 ) are
End points of a diameter, ST.

.O
S

Calculate

(a) the coordinates of the centre of the circle,

Answer (a) ………………………… [2]

(b) the length of the diameter ST.

Answer (b) …………………… units [2]

5. (a) Solve the inequality 2 y +15≥4 y−2 .

Answer (a) ……………………………. [2]

(b) Write down the rectangle numbers which satisfy the inequality 2 y +15≥4 y−2 .

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Answer (b) …………………………….. [2]

6. The diagram below shows the cross-section of a cylindrical tunnel with internal
diameter 4.4 m and external diameter 5.4 m.

4.4

5.4

Calculate

(a) the area of the circular opening of the tunnel,

Answer (a) ………………………………… m2 [2]

(b) the shaded area,

Answer (b) ………………………………… m2 [3]

(c) the volume of the material in a 2.5 m stretch of the tunnel.

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Answer (c) ………………………………… m3 [2]

7. The cash price of a new car is P125 000. There are two options, A and B, of paying for
the car as shown in the table below.

Option Payment
A P125 000 cash
B 23 % of cash price deposit plus
48 months instalments of P2470

Bakang chooses option B to pay for the car.

(a) Calculate

(i) the amount that she will pay as deposit,

Answer (a)(i) P………………………............... [2]

(ii) the total amount she will have to pay.

Answer (a)(ii) P………………………………… [2]

(b) Bakang pays more money by choosing option B than option A.

How much more does she have to pay?

Answer (b) P…………………………............... [1]

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^
8. The diagram shows a triangle RST. RS = 9.4 m, ST = 7.2 m and S T R=68 .
0

9.4

680
S T
7.2

^
Calculate the size of S R T .

Answer ……………………………… [3]

9. Kabo is given 30 tablets. He has to take 3 tablets each day until he has taken them all.

(a) How many tablets were left at the end of the fourth day?

Answer (a) …………………………….. [2]

(b) After how many days will Kabo finish the tablets?

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Answer (b) ……………………………… [2]

10. 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]

11. In a science laboratory a student measured the thickness of four types of cardboard paper
using a micrometer. The results of the measurements in metres were

2×10−3 , 6×10−4 , 1 .2×10−3 , 7×10−4 .

Arrange the measurements in order of size starting with the smallest.

Answer ……………………………………………………………………………………. [2]

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12. A quadrilateral KLMN is such that KL = 8.5 cm, KN = 6 cm and MN = 7cm.

Angle LKN = 750 and KL is parallel to NM.

(a) Construct the quadrilateral KLMN. [3]

(b) What is the geometrical name of the quadrilateral?

Answer (b) …………………………………… [1]

(c) Measure and write down the

(i) length of LM,

^
(ii) size of L M N .

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Answer (c)(i) …………………………………. [1]

(c)(ii) ………………………………… [1]

13. The diagram below shows a line l and triangles M and N.

-6

-5

-4

-3

-2
M
-1

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
y

4
N
5

6
x l

(a) Describe fully a single transformation that maps triangle N onto triangle M.
Answer (a)

…………………………………………………………………………………….

…………………………………………………………………………………….

…………………………………………………………………………………… [3]

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(b) Reflect triangle N in the line l and label the image R. [2]

14. A cuboid has a length of 25 cm, a width of 5 cm and a height of (x-2) cm.

(a) Write an expression, in terms of x, for the volume of the cuboid.

Answer (a) ………………………………….. [1]

(b) The volume of the cuboid is 750 cm3.

(i) Form an equation, in terms of x, to represent this information.

Answer (b)(i) ………………………………… [1]

(ii) Solve the equation in (b)(i).

Answer (b)(ii) ………………………………… [2]

(c) Hence, or otherwise, calculate the height of the cuboid.

Answer (c) ………………………………… cm [2]

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15. The table below shows some values of x and the corresponding values of y for the
2
equation y=− x −3 x +5 .
x -5 -4 -3 -2 -1 0 1 2
y -5 1 5 7 7 5 1 p

(a) Calculate the value of p.

Answer (a) ……………………………. [1]

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(b) On the axes provided below, draw the graph of y=− x −3 x +5 for -5 ≤ x ≤ 2. [3]
y
8

x
-5 -4 -3 -2 -1 0 1 2

-1

-2

-3

-4

-5

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(c) Use the graph to find values of x such that −x −3 x +5=0 .

Answer (c) x = …………. or x = ………………. [2]

16. In a survey, 50 families were asked to state the number of cars they own.
The results are displayed in a bar chart below.

Number of cars owned by 50 families

25

20

Number of 15
families

10

0
0 1 2 3 4

Number of cars

(a) Find

(i) the modal number of cars per family,

(ii) the total number of cars in the 50 families,
(iii) the mean number of cars per family.
Answer (a) (i) ……………………….. [1]

(ii) ………………………. [2]

(iii) ……………………… [2]

(b) What is the probability that a family picked at random has no car?

Answer (b) ………………………… [1]

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(c) One of the cars is picked at random.

What is the probability that it belongs to a family with 2 cars?

Answer (c) …………………………. [2]

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