End of Unit Assessment
Grade 10 – Chapter 21 (Ratio, rate and proportion)
Name ………………………………………………….……………………….
For Teacher’s Use
Question
1
Additional materials: Ruler
Calculator allowed
READ THESE INSTRUCTIONS FIRST
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•
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Answer all questions in the spaces provided on the question paper.
You should show all your working on the question paper.
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 29.
2
3
4
5
6
7
8
Total
/29
1
1
Annette cycles a distance of 70 km from Midville to Newtown.
Leaving Midville, she cycles for 1 hour 30 minutes at a constant speed of 20 km/h and then stops for
30 minutes.
She then continues the journey to Newtown at a constant speed of 16 km/h.
(a) On the grid, draw the distance–time graph for the journey.
[3]
(b) Calculate the average speed for the whole journey.
................................................... km/h
[3]
[Total: 6]
2
2
y is directly proportional to the cube root of (x + 3).
When x = 5, y =
.
Find y when x = 24.
y = ...................................................
[3]
[Total: 3]
3
The people who work for a company are in the following age groups.
Group A
Group B
Group C
Under 30 years
30 to 50 years
Over 50 years
The ratio of the number in group A to the number in group B is 7 : 10.
The ratio of the number in group B to the number in group C is 4 : 3.
(a) Find the ratio of the number in group A to the number in group C.
Give your answer in its simplest form.
.............................. : ..............................
[3]
3
(b) There are 45 people in group C.
Find the total number of people who work for the company.
...................................................
[3]
[Total: 6]
4
A car starts from rest and accelerates at a rate of 3 m/s2 for 4 seconds.
The car then travels at a constant speed for 10 seconds.
V
Speed
(m/s)
NOT TO
SCALE
0
0
4
Time (seconds)
14
The diagram shows the speed–time graph for this journey.
(a) Find the value of V.
V = ...................................................
[1]
(b) Calculate the total distance travelled by the car during the 14 seconds.
................................................... m
[2]
[Total: 3]
4
5
Tins of paint are filled at the rate of 2 m3 per minute.
How many 750 ml tins of paint can be filled in 1 hour?
Answer...................................................
[3]
[Total: 3]
6
F is inversely proportional to the square of d.
Explain what happens to F when d is halved.
....................................................................................................................................................................
[1]
[Total: 1]
7
The force of attraction, F Newtons, between two magnets is inversely proportional to the square of the
distance, d cm, between the magnets.
When d = 1.5, F = 48.
(a) Find an expression for F in terms of d.
F = ...................................................
[2]
5
(b) When the distance between the two magnets is doubled the new force is n times the original force.
Work out the value of n.
n = ...................................................
[1]
[Total: 3]
8 The following is a velocity-time graph over the course of 6 minutes.
(a) Estimate the distance covered in the first 4 minutes.
………………………… m
[3]
(b) Is your answer to part (a) an overestimate or underestimate? Explain your reasoning.
…………………………………………………………………………………………………………………………………………
…………………………………………………………………………………………………………………………………………
[1]
[Total: 4]