JUNE PAPERS
PAPER 1
GRADE 9
DATE: 07.06.2024
ANSWER ALL QUESTIONS
1. 𝜀 = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
𝐴 = {𝑜𝑑𝑑 𝑛𝑢𝑚𝑏𝑒𝑟𝑠}
𝐵 = {𝑃𝑟𝑖𝑚𝑒 𝑛𝑢𝑚𝑏𝑒𝑟𝑠}
List the members of the set.
i.
𝐴∩𝐵
ii.
𝐴∪𝐵
2. 𝑝 =
4.8×1.98276
16.83
a) In this space provided, write each number in this calculation correct to 1 significant figure.
________ × ___________
___________
b) Use your answer to part (a) to estimate the value of p.
3
−8
3. 𝑎 = ( )
𝑏=( )
5
7
Write each of the following as a single vector
i.
3𝑎
1
ii.
𝑎−𝑏
4. Simplify
6𝑢𝑤 −3 × 4𝑢𝑤 6
5. Calculate AB.
6. i.
ii.
The equation of a line L is 2𝑥 − 3𝑦 = 6
Find the gradient of L.
Find the equation of the line which is parallel to L and passes through the point (6 , 9 )
2
7. Solve the simultaneous equation
𝑦 − 2𝑥 = 6
𝑦 + 2𝑥 = 0
Show clear algebraic working.
8. 𝑦 is directly proportional to the positive square root of 𝑥.
When 𝑥 = 9, 𝑦 = 12.
Find 𝑦 when 𝑥 =
1
4
9. Find the value of 𝑟
1
2𝑟 =
16
3
JUNE PAPERS
PAPER 2
GRADE 9
DATE: 14.06.2024
4
ANSWER ALL QUESTIONS
1. Find the value of 𝑡
5
3𝑡 = √3
2. i.
Correct to the nearest millimetre, the length of a side of a regular hexagon is 3.6cm.
Calculate the upper bound for the perimeter of the regular hexagon.
ii.
Correct 1 significant figure, the area of a rectangle is 80𝑐𝑚2 .
Correct to 2 significant figures, the length of the rectangle is 12cm.
Calculate the lower bound for the width of the rectangle. Show your workings clearly.
3. The diagram shows a circle with centre O. The points A, B and C lies
on the circle.
Angle AOB=960
i.
Work out the size of angle ACB.
5
ii.
AB=16cm.
Workout the radius of the circle. Give your answer correct to 3 significant figures.
4. Town B is 35km east and 80km north of town A. Workout the
bearing of A from B. Give your answer correct to the nearest
degree.
5. The straight line L passes through the points (-2 , 3) and (6 , 9 )
Find the equation of the line that is parallel to L and passes through the point (5 , -1).
Give your answer in the form 𝑎𝑥 + 𝑏𝑦 = 𝑐 where a, b and c are integers.
6
6. Simplify leaving your answers in index form
i.
65 × 62 × 6
ii.
(97 )2
7. Find the value of n.
5𝑛 × 53
= 54
56
8. Solve the simultaneous equations You must show all your workings.
𝑦 = 5𝑥 2 + 4𝑥 − 9
𝑦 = 4𝑥 + 1
7
JUNE PAPERS
PAPER 3
GRADE 9
DATE: 28.06.2024
8
ANSWER ALL QUESTIONS
1. Six numbers have a mean of 5. Five of the numbers are
3
2
7
6
2
Work out the value of x.
2. The mass of the space shuttle is 7.8 × 104 kilograms.
i.
Write 7.8 × 104 as an ordinary number.
The space shuttle docks with the international space station. The mass of the international space
station is 4.62 × 105 kilograms.
ii.
Calculate the mass of the space shuttle and the international space station. Give your
answer in standard form.
3. Solve 5𝑥 2 + 2𝑥 − 4 = 0
Give your solutions correct to 3 siginificant figures. Show your working clearly.
9
4. Green paint can be made by mixing yellow paint and blue paint in the ratio 2:3. Wendy makes 15
litres of green paint. Work out how many litres of blue paint Wendy uses.
5. A piece of rope is wound around a cylindric pipe 18 times. If the diameter of the pipe is 600mm,
how long is the rope?
6. Find the perimeter and area of this shape.
10
7. A cylindrical rain water tank is 1.5m tall with a diameter of 1.4m. What is the maximum volume of
rainwater it can hold?
8. A 400m running track has two straight sections,
each of length 120 meters, and 2 semicircular
ends.
i.
Calculate the total length of the curved
section of the track.
ii.
Calculate 𝑑, the distance between the parallel sections of the track.
9. A large conference table is made from four rectangular
sections and four corner sections. Each rectangular section
4m long and 1.2m wide. Each corner section is a quarter
circle of radius 1.2m. Each person sitting at the conference
table requires one meter of its outside perimeter. Calculate
the greatest number of people who can sit around the
outside of the table. Show all your working.
is
11