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Final term Examination / 2nd Term (2023/2024)
Cambridge International Lower Secondary Stage 8
Student Section
Name
CAMBRIDGE INTERNATIONAL LOWER SECONDARY MATHEMATICS (0862)
Date ____ /___/ 2023/2024
Time allowed: 60 minutes
You must answer on the question paper
INSTRUCTIONS
Answer all questions.
Use a black or blue pen. You may use an HB pencil for any diagrams or graphs.
Write your name, date and section in the boxes at the top of the page.
Write your answer to each question in the space provided.
Do not use an erasable pen or correction fluid.
Do not write on any bar codes.
You should show all your working in the booklet.
You may use a calculator.
INFORMATION
The total mark for this paper is 30.
The number of marks for each question or part question is shown in brackets [ ].
You will get partial marks for the correct methods even though your final answer is incorrect
or incomplete.
Give non-exact numerical answers correct to 2 significant figures, or 1 decimal place.
This document has 12 pages
1. (a) The password for a laptop is one of the five shown.
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245tcb3 541tcb2 315tcc1 924tcc5 815tce2
1
Angelique says the probability the password contains the letter b is
5
Tick (√) to show if Angelique is correct or not correct.
correct not correct
Explain your answer.
[1]
(b) The code for Angelique’s phone is four different digits from 1 to 9
The first digit is 6 and the other three digits are even.
Write a list of all the possible four-digit codes for Angelique’s phone.
[2]
2. Hassan buys an apartment for $78 000
after one year the value decreases by
5%.
Work out the new value of Hassan’s apartment.
$............................................. [2]
3. Draw a ring around all the fractions that are equivalent to recurring decimals.
1 1 1 1
3 5 7 8
[1]
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4. x is a whole number.
x ≥ 0.5
Write down the smallest possible value of x.
x= …………… [1]
5. When a fair spinner is spun the arrow is equally likely to point in any
direction. Chen has these four fair spinners.
R S R S R S
S R T
T V T R T
V
He spins one of the spinners 600 times and the arrow points to the letter R 205
times. Draw a ring around the spinner he is most likely to have used.
[1]
6. Mike has these four number cards.
2 2 2 5
He uses each card once to make a four-digit number.
Work out how many different four-digit numbers he could make.
………………… [1]
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7. Work out.
112 – 5 ×2.6 + √ 92 +63
…………………… [2]
8. The probability of spinning a blue colour on a spinner is 0.4
Find the probability of not spinning a blue colour.
……………… [1]
9. Solve.
8x = 52 – 4(x – 2)
……………… [2]
10. Multiplying a number by 3 and then
Adding 5 gives the same answer as adding 23 to the number.
What is the number?
……………… [2]
11. A and B are the points with coordinates (-2,5) and (4, 2)
Find the coordinates of the midpoint of the line segment AB.
……………… [2]
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12. Draw a ring around the inequality that is equivalent to x ≤ 4
x–1≤5 2x < 8 x<5 x+1≤5 x–3≥1
[1]
13. Six students start to solve 50 – 2x = 28 in different ways.
For each student’s work, tick (√) to show if the statements are true or false.
50 – 2x = 28 50 – 2x = 28
so 2x = 28 – 50 so 50 = 28 2x
True False True False
50 – 2x = 28 50 – 2x = 28
so 2x = 28 50 so 25 – x = 14
True False True False
50 – 2x = 28 50 – 2x = 28
so 50 – 28 = 2x so –2x = 28 – 50
True False True False
[2]
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14. Rewrite each recurring decimals using dot notation.
a) 0.444…
b) 2.3535….
……………… [2]
15. Write each of the followings as a fraction and as a percentage.
Write the fraction in their simplest form.
a) 18 out of 20
b) 78kg out of 120kg
……………… [2]
16. D is the midpoint of CE.
Complete the coordinates for C and E.
C (–5, …..) D (3, 10) E (…... 8)
…………….[2]
17. Draw a ring around all the fractions that are equivalent to recurring decimals.
1 1 1 1
3 5 7 8
[1]
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18. Safia is investigating how the number of websites in the world has changed over time.
a) In the year 1999 there were 3 177 453 websites.
Write this number of websites correct to 2 significant figures.
……………… [1]
b) The graph shows the number of websites between the years 2004 and 2018
(i) Write down the first year that the number of websites reached over 200
million.
……………… [1]
(ii) Write down the two consecutive years with the biggest increase in the number
of websites.
……………… and ………………
……………… [1]
c) In 1991 there was 1 website.
In 1992 there were 10 websites.
Work out the percentage change in the number of websites from 1991 to 1992
………….. % [1]
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19. Mike is investigating to see if there is a relationship between the score in a quiz and
the score in a mathematics test for people in his class.
He collects data from 3 people out of his class
of 30 He then draws this scatter graph.
a) Mike says, ‘A higher score in the quiz means a higher score in the mathematics
test.’ Explain how Mike can improve his investigation to see if this is true.
[1]
b) Tick (√) to show if each statement about lines of best fit in a scatter graph are true
or false.
Lines of best fit must
always
True False
go through the origin
have a positive gradient
pass as close as possible to the points
[3]
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20. Rajiv does an experiment with four 6-sided dice, A, B, C and D.
He rolls each dice a total of 60 times and records the number of times he rolls the
number 6
Dice A B C D
Number of times
12 11 17 9
6 is rolled
Write down the letter of the dice that is most likely not to be fair.
……………… [1]
21. The time-series graph shows information about the number of students studying
media studies or computing.
Complete these sentences.
The first one has been done for you.
The trend in the number of students studying media studies is decreasing .
The computing course was first studied in the year .
The trend in the number of students studying computing is .
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In the year 2015 there were thousand more
students studying media studies than computing.
In the year there were 37 000 more
students studying computing than media studies.
[4]
22. Yuri has two boxes containing red, black and blue pens only.
Box A contains 3 red pens, 5 black pens and 2
blue pens. Box B contains 2 red pens, 2 black
pens and 1 blue pen.
Yuri picks a pen from one of the boxes at random.
a) Yuri thinks the probability that the pen will be green is 0
Explain why Yuri is correct.
………………………………………………………………………
………………………………………………………………………
[1]
b) Yuri says,
‘I am more likely to pick a red pen from box A than from box B because there
are more red pens in box A than box B.’
Explain why Yuri is not correct.
……………………………………………………………………………………
……………………………………………………………………………………
[1]
23. Samira has a bag containing
coloured balls. Some of the
balls are red.
The number of balls in the bag that are not red is four times the number of red
balls. Samira picks a ball at random from the bag.
Work out the probability the ball is red.
[2]
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24. Jamila has p pencils.
Hassan has 3 fewer pencils than
Jamila. Naomi has 4 times as
many pencils as Hassan.
Write an expression, in terms of p, for the total number of pencils the three
children have. Write your expression in its simplest form.
…………………. [3]
3
25. n lies in the interval 3.5 < n < 3
16
Find a possible value of n.
Give your answer as a mixed number.
n=……………………… [2]
26. Rajiv has two pieces of string measuring 240 cm and 168 cm in length.
He cuts both pieces of string into smaller pieces that are all equal in length.
Work out the greatest possible length for each smaller piece.
…………..cm [3]
27. Here is Eva’s calculation.
5 3 22 32
Explain why Eva is not correct.
………………………………………………………………………………………
………………………………………………………………………………………
[2]
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28. Work out.
94 32 × 5
…………………….. [2]
29. Solve these equations .
Give any non-integer solution as fraction.
a) 5h-2=3-5h
…………… [1]
b) 11p+4=3p-36
………..… [1]
30. If -1.89 ≤ x ≤ -0.61,
Write the greatest and least possible values of x.
greatest value……………. and least value …………….. [2]
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