LEBOHANG MAKHANYA HEARTWOOD SCHOOL MATHEMATICS
NAME_________________________________ DATE: _________________________
MATHEMATICS
TIME: 1 HOUR 30 MINUTES TOTAL MARKS:80
INSTRUCTIONS TO CANDIDATES
a) Answer all the questions in this paper
b) Show all the workings on the same page as the rest of the answer
c) NEITHER ELECTRONIC CALCULATORS NOR MATHEMATICAL TABLES MAY BE
USED IN THIS PAPER
1. (a) Express 0.527 as a percentage
(b) Evaluate 5.6÷ 0.08
Answer (a) .................................. [1]
(b) ................................. [1]
2. Work out
6 1
(a) −
7 3
2 4
(b) ×
5 9
Answer (a) ............................. [1]
(b) ............................. [1]
1
3. 0.2 2 √2 3
0.83 8 81
From the numbers listed above, write down
(a) prime number
(b) cube number
(c) an irrational number
Answer (a) ............................ [1]
(b) ............................ [1]
(c) ........................... [1]
4. The rate of exchange between pounds (₤) and dollars ( $) was ₤1¿ $ 2.80. Calculate
(a) the number of dollars received in exchange for ₤120
(b) the number of pounds received in exchange for $224
Answer (a) ............................ [1]
(b) ............................. [1]
5. By writing each number correct to 1 significant figure, estimate the value of:
8.62× 2.042
0.285
Answer ............................... [2]
6. It is given that 68.2 ×0.235=16.027
Hence calculate
(a) 0.0682 ×2350
(b) 160.27 ÷ 0.0235
Answer (a) .................................. [1]
(b) .................................. [1]
7. (a) evaluate i. 52 ×50
1
ii. 49 2
Answer (a) i. ......................... [1]
ii. ........................... [1]
−2
(b) simplify i. ( 1x )
1
ii. ( x 6 ) 2
Answer (b) i. ........................... [1]
ii. ............................. [1]
1 n
(c) find the value of n , given that ()
2
=4
Answer (c) ........................ [1]
8. Arrange the following numbers in order of size starting with the smallest
7 7
0.7, 0.7 2, ,
11 9
Answer ..........., ..........., ..........., ........... [2]
9. The diagram shows a regular 9-sided polygon (nonagon) with centre O.
(a) Work out the size of x and size of y
Answer (a) x=¿ ........................ [1]
y=¿ .......................... [1]
(b) Use your answer to part (a) to work out the size of each interior angle of the polygon.
Answer (b) .............................. [1]
10. Green line buses run every 10 minutes
Red line buses run every 20 minutes
Purple line buses run every 35 minutes
One bus from each line leaves the city centre at 0900. After how many minutes will buses all
three lines next leave the city centre at the same time?
Answer ............................. [2]
11. It is given that N=87 ×132
(a) Complete the statements in the answer space
Answer (a) 88 ×132=N +¿ ........... [1]
87 ×131=N−¿ ........... [1]
(b) Hence evaluate 88 ×132−87 ×131
Answer (b) ........................... [1]
12. A swarm of locust contains 40 billion locusts.
A billion is thousand millions.
a) Write down in standard form, the number of locusts in this swarm
Answer a) ............................................. [2]
b) Each locust eats 2 grams of food every day.
Find the amount of food eaten by this swarm in one week.
(Give your answer in kilograms using standard form)
Answer b) .............................................. [2]
13. In the diagram, the straight line AB is parallel to CD.
Angle A ^BC¿ 52°
a) Give the name of triangle ABC.
Answer a) ........................................ [1]
b) Work out the value of p and q
Answer b) p¿ ................... [1]
q¿ .................... [1]
c) State, with the reason, the value of r .
Answer c) r =¿............ reason: ............................................................
..................................................................................................[2]
14. a) The population of a city is given as 280 000, correct to the nearest ten thousand. State the
greatest possible error in the given value
Answer a) .............................. [1]
b) The dimensions of a rectangular card are 7cm by 4cm, correct to the nearest centimetre.
Calculate the smallest possible perimeter of the card.
Answer b) ................................ [2]
15. a) Factorise
i. a 2 b+ 6 a b2
ii. b 2−36
Answer a) i. ...................................... [2]
ii. ........................................ [2]
1 1
b) Simplify x− + x+
3 2
Answer b) .................................. [2]
16. a) Solve 4 ( x−0.3 )=3 ( x−0.2 )
Answer a) x=¿ ................................. [2]
b) Solve the simultaneous equations
3 x+ 2 y =9
2 x−4 y=2
Answer b) x=¿ ....................
y=¿ ..................... [3]
17. a) Express as a single fraction in its simplest form.
3 2
−
2t−1 t−1
Answer a) ........................ [3]
5
b) Given that C= ( F−32 )
9
i. Calculate C when F=−4
ii. Express F in terms of C .
Answer b) i. .......................................... [1]
ii. ....................................... [2]
18. A,B and S are points on a circle, centre O
TA and TB are tangents.
A T^ B=52 °
^ B,OB
Calculate A O ^ A and A S^ B
^ B=¿
AO
Answer .......................[1]
^ A¿........................ [1]
OB
A S^ B¿........................... [1]
19. a) On the venn diagram, shade the set A ∩ B∩ C
ı
[1]
b) ξ= {2 , 3 , 4 , 5 , 6 , 7 , 8 ,9 , 10 }
P= { x : x is a prime number }
Q= { x : x ≥ 5 }
i. Find the value of n ( P ∩Q )
ii. List the elements of P ∪ Q ı
iii. List the elements of Pı ∩Q
Answer b) i................................................ [1]
ii. ................................................... [1]
iii. ................................................. [1]
c) Express, in set notation, the subset shaded in the diagram.
Answer c) .................................... [1]
20. The table shows the height, in metres, above sea level of the highest and lowest points in
some continents.
A negative value indicates a point below sea level
Asia Africa Europe South America
Highest points
(m) 8850 5963 5633 6959
Lowest points
(m) -409 -156 -28 -40
a) What is the height above sea level of the highest point in Africa? Give your
answer in kilometres
Answer a) ................................ [1]
b) In South America, how much higher is the highest point than the lowest
point? Give your answer in metres.
Answer b) ................................. [1]
c) How much higher is the lowest point in Europe than the lowest point? Give
your answer in metres.
Answer c) ................................ [1]
21. a) i. Express 7056 as the product of its prime factors.
ii. Hence evaluate √ 7056
Answer a) i. ...................................... [2]
ii. ...................................... [1]
22. a) A car decelerates uniformly from 20 m/s to 5 m/s in 5 seconds.
Calculate the retardation
b) Express 20 metres per second in kilometres per hour.
Answer a) .............................. [1]
b) .............................. [2]
23. The diagram shows a rectangle with length ( x−3 ) m and width ( x−6 )m
a) The area of the rectangle is 54cm 2.
Form an equation in x and show that it reduces to x 2−9 x−36=0
[2]
b) Solve x 2−9 x−36=0
Answer b) x=¿ ................ or .............. [2]
c) Find the perimeter of the rectangle
Answer c) ............................ [2]
