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DPS INTERNATIONAL SCHOOL
36 Aroozoo Avenue (Opp Surin Park) Singapore 539842
Tel: (65) 62856300 Fax: (65) 62851670 Website: www.dps.edu.sg
TERM EXAMINATION
IX IGCSE : 2023
SUBJECT: MATHEMATICS
NAME: ……………………..
DATE: 22/05/23
MARKS: 100
TIME: 2 Hour
READ THESE INSTRUCTIONS FIRST :
Write your name on all the work you hand in.
Write in dark blue or black pen.
You may use a soft pencil for any diagrams, graphs or rough working.
Do not use staples, paper clips, highlighters, and glue or correction fluid.
Answer all questions.
At the end of the examination, fasten all your work securely together.
The number of marks is given in brackets [ ] at the end of each question or part
For Examiner's Use
Q. No.
1
2
3
4
5
6
7
8
9
10
11
TOTAL
Marks
2
1. (a) In 2016, a company sold 9600 cars, correct to the nearest hundred.
(i) Write down the lower bound for the number of cars sold.
.................................................. [1]
(ii)The average profit on each car sold was $2430, correct to the nearest $10.
Calculate the lower bound for the total profit. Write down the exact answer.
$................................................... [2]
(iii) Write your answer to part (a)(ii) correct to 4 significant figures.
$................................................... [1]
(iv) Write your answer to part (a)(iii) in standard form.
$...............................................[1]
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(b) In April, the number of cars sold was 546. This was an increase of 5% on the number
of cars sold in March. Calculate the number of cars sold in March.
................................................... [3]
(c) The price of a new car grows exponentially by 3% per year. A new car has a price of
$3000 in 2013. Find the price of a new car 4 years later.
$.............................................[2]
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2. (a)The diagram shows a logo that is made up of 5 identical parallelograms.
Find the area of one parallelogram.
..........................cm²[3]
(b) Kate wants to give a kite-shaped chocolate box to her friend.
She wants to paste a picture of herself with her friend to cover the top of the box.
Determine the area of the top of the box if the diagonals of the lid of the box are 9 inch
and 12 inch.
…………………….in2 [2]
(c) Solve the given inequality and show the result on a number line
− x + 4 ≤ −8
[3]
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(d) By drawing suitable lines and shading unwanted regions, find the region R,
where x ≥ 2 , y ≥ x and 2x + y ≤ 8
[5]
3. (a)(i) Given that G = ab . Find the percentage increase in G when both a and b increase
by 10 %.
[2]
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(ii) If a restaurant’s salad dressing is made entirely of oil and vinegar at a ratio of
oil to
1
4
3
4
cup
cup vinegar, how many cups of vinegar are there in 6 cups of salad dressing?
[2]
2
(b) Solve the equation 3𝑥 − 2𝑥 − 2 = 0
Show all your working and give your answers correct to 2 decimal places
[4]
2
2
(c) 𝑦 = 𝑚 − 4𝑛
(i) Factorise 𝑚2 − 4𝑛2
[2]
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(ii) Find the value of y when m= 4.4 and n = 2.8
[2]
(iii)If 𝑚 = 2𝑥 + 3 𝑎𝑛𝑑 𝑛 = 𝑥 − 1
Find y in terms of 𝑥, in its simplest form
[2]
(iv) Make n the subject of the formula 𝑦 = 𝑚2 − 4𝑛2
[3]
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(d) (i) 𝑚4 − 16𝑛4 can be written as ( 𝑚2 − 𝑘𝑛2 )(𝑚2 + 𝑘𝑛2 )
Write down the value of k
[2]
4
(ii) Factorise completely 𝑚 𝑛 − 16𝑛
5
[2]
4. Let 𝑛 represent the number of dogs and 𝑑 represent the number of days.
A bag of biscuits feeds 4 dogs for 12 days.
Given that 𝑑
∝
1
𝑛2
,In how many days would the same bag feed 5 dogs
(i) Write down the inverse proportion formula.
[1]
(ii) Determine the value of k
[2]
(iii) Using the formula and value of k, find in how many days would the same bag
feed 5 dog?
[3]
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5.
The diagram shows a field, ABCD , on horizontal ground.
(a) There is a vertical post at C.
º.
From B, the angle of elevation of the top of the post is 19 Find the height of the post.
………………………….m[2]
(b) Use the cosine rule to find angle BAC.
Angle BAC= ……………………………[4]
10
(c) Use the sine rule to find angle CAD.
Angle CAD =……………………………[3]
(d) Calculate the area of the field.
……………………….m[3]
(e) The bearing of D from A is 070
º
Find the bearing of A from C.
………………………….[2]
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6.Two rectangular picture frames are mathematically similar.
(a) The areas of the frames are 350 cm2 and 1134 cm2 .
The width of the smaller frame is 17.5cm.
Calculate the width of the larger frame.
[3]
(b) A picture in the smaller frame has length 15cm and width 10.5cm,
both correct to the nearest 5mm.
Calculate the upper bound for the area of this picture
.
.
........................................ cm2 [2]
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(c) In a sale, the price of a large frame is reduced by 18%.
Parthi pays $166.05 for 5 large frames in the sale.
Calculate the original price of one large frame.
$ ................................................ [2]
(d) Parthi advertises a large frame for a price of $57 or 48.20 euros.
The exchange rate is $1= 0.88 euros.
Calculate the difference between these prices, in dollars and cents, correct to the
nearest cent.
$ ................................................ [3]
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7. (a) Write as a single fraction in its simplest form.
𝑥+3
𝑥−2
𝑥−3
−
𝑥+2
[4]
𝑘
2
(b) 212 ÷ 2 = 32
Find the value of k.
k = ................................................ [2]
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(c) Expand and simplify. ( 𝑦 + 3)( 𝑦 − 4)( 2𝑦 − 1)
................................................ [3]
(e) Make x the subject of the formula.
𝑥=
3+𝑥
𝑦
x = .................................................[3]
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8.(a) In the diagram, BC represents a building 30m tall.
A flagpole, DC, stands on top of the building.
From a point, A, the angle of elevation of the top of the building is 31°.
The angle of elevation of the top of the flagpole is 37°.
Calculate the height, DC, of the flagpole.
Answer ............................................ m [5]
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(b) Find the area of shaded region of the given trapezium.
…………………………………….cm2[3]
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(c) Shown below is a parallelogram. Each side is measured in centimetres.
Work out the perimeter of the parallelogram
.........................cm (6)
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Answers
1.
2.i) https://corbettmaths.files.wordpress.com/2015/03/area-of-aparallelogram.pdf
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(ii) https://www.cuemath.com/measurement/area-of-a-kite/
iii)
https://www.expii.com/t/solve-inequalities-with-negative-multiplicationor-division-examples-4272
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(iv) https://www.savemyexams.co.uk/igcse/maths_extended/cie/23/topicquestions/2-algebra-and-graphs/2-16-solving-and-graphing-inequalities//paper-2-and-paper-4/hard/
Plot these two points and then join together with a straight line.
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drawn correctly [1]
drawn correctly [1]
drawn correctly [2]
Pick a point that does not lie on any of the lines, using (0, 1) is easy, and
substitute its x and y values (x = 0 and y = 1) into the inequalities.
If the inequality is satisfied then (0, 1) is in the region R so shade the side of
the line which does not have (0, 1) in it.
If the inequality is not satisfied then shade the side of the line which has (0, 1)
in it.
is not true so (0, 1) does not satisfy
, shade the region to the left of
the line
is true so (0, 1) satisfies
, shade the region below the line
is true so (0, 1) satisfies
, shade the region above the line
Label the unshaded region R.
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[1
3.(a) (i) 21%
(ii) https://www.testprepreview.com/modules/ratios.htm
Determine what the ratio of vinegar to the salad dressing as a whole is. Vinegar is 1/4 of a
cup and the salad dressing as a whole is 1/4 cup vinegar plus 3/4 cup oil, or 1 cup. Thus,
vinegar is 1/4 of the salad dressing. Therefore, 1/4 of 6 cups is 3/2 or 1 1/2 cups of vinegar.
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4,
https://thirdspacelearning.com/gcse-maths/ratio-and-proportion/inverse-proportion/
5.
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6.
7.
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8.(a)
Question 7 (b)
8 (b)
https://www.tes.com/teaching-resource/area-of-compound-shapes-and-functional-gcseexam-q-s-6449721
8 © https://corbettmaths.com/wp-content/uploads/2022/10/Simultaneous-EquationsAnswers.pdf
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