Cambridge IGCSE™
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Answer all questions.
Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
Write your name, centre number and candidate number 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 use a calculator where appropriate.
You may use tracing paper.
You must show all necessary working clearly.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
For π, use either your calculator value or 3.142.
INFORMATION
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The total mark for this paper is 130.
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The number of marks for each question or part question is shown in brackets [ ].
This document has 19 pages. Blank pages are indicated.
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2
1
(a) Draw the image of shape A after a translation by the vector
( )
8
−8
[2]
(b) Draw the image of shape A after a reflection in the line 𝑥 =− 1. [2]
(c) Describe fully the single transformation that maps shape B onto shape A.
.....................................................................................................................................................
..................................................................................................................................................... [3]
(d) Describe fully the single transformation that maps shape A onto shape C.
.....................................................................................................................................................
..................................................................................................................................................... [3]
3
2
(i)
(a) Hanna invests $3000 at a rate of 2% per year compound interest.
Calculate the value of this investment at the end of 5 years.
$ ................................................ [2]
(ii)
Calculate the overall percentage increase in the value of Hanna’s investment at the end of 5
years.
............................................. % [2]
(iii)
Calculate the minimum number of complete years it takes for the value of Hanna’s
investment to increase from $3000 to more than $4000.
................................................. [3]
(b) The population of a village decreases exponentially at a rate of 5% each year.
The population is now 695 rounded to the nearest person.
Calculate the population 15 years ago
................................................. [3]
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4
3
The height, h cm, of each of 120 plants is measured.
The cumulative frequency diagram shows this information.
Height (cm)
(a) Use the cumulative frequency diagram to find an estimate of
(i)
the median,
............................................ cm [1]
(ii)
the interquartile range,
(iii)
the 70th percentile,
............................................ cm [2]
............................................ cm [1]
(iv)
the number of plants with a height greater than 30 cm.
................................................. [2]
5
(b) The cumulative frequency diagram above can be displayed in a table:
Height h cm
0≤ℎ ≤10
Frequency
(i) Complete the table above
(ii)
10≤ℎ ≤20
18
20≤ℎ ≤30
62
30≤ℎ ≤50
(2)
Calculate an estimate of the mean height.
............................................ cm [4]
(iii) A histogram is drawn to show the information in the frequency table.
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The height of the bar representing the interval 10≤ℎ ≤20 is 7.2 cm.
Calculate the height of the bar representing the interval 20≤ℎ ≤30
............................................ cm [2]
4
(a) A rectangle measures 8.5 cm by 10.7 cm, both correct to 1 decimal place.
Calculate the lower bound of the perimeter of the rectangle.
............................................ cm [3]
(b)
ABDF is a parallelogram and BCDE is a straight line.
AF = 14 cm, AB = 9 cm, angle CFD = 40° and angle FDE = 80°.
(i) Calculate the height, h, of the parallelogram.
h = ........................................... cm [2]
(ii)
Explain why triangle CDF is isosceles.
7
.............................................................................................................................................
............................................................................................................................................. [2]
(iii) Calculate the area of the trapezium ABCF.
.......................................... cm2 [3]
(c)
B
NOT TO SCALE
A, B, C and D are points on the circle, centre O.
Angle ABD = 21° and CD = 14 cm.
Calculate the area of the circle.
.......................................... cm2 [5]
5
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8
Red
Yellow
Blue
Blue
Yellow
Blue
The diagram shows six discs.
Each disc has a colour and a number.
(a)
One disc is picked at random.
Write down the probability that
(i) the disc has the number 4,
................................................. [1]
(ii) the disc is red and has the number 3,
................................................. [1]
(iii) the disc is blue and has the number 4.
................................................. [1]
(b) Two of the six discs are picked at random without replacement.
Find the probability that
a. both discs have the number 3,
................................................. [2]
b. both discs have the same colour.
................................................. [3]
(c) Two of the six discs are picked at random with replacement.
Find the probability that both discs have the same colour.
................................................. [3]
6
B
A
The diagram shows a field, ABCD, on horizontal ground.
BC = 192 m, CD = 287.9 m, BD = 168 m and AD = 205.8 m.
(a) (i) Calculate angle CBD and show that it rounds to 106.0°, correct to 1 decimal place.
[4]
10
(ii)
The bearing of D from B is 038°.
Find the bearing of C from B.
................................................. [1]
(iii) A is due east of B.
Calculate the bearing of D from A.
................................................. [5]
(b) (i) Calculate the area of triangle BCD.
............................................ m2 [2]
(ii) Clara buys the triangular part of the field.
The cost is $35 750 per hectare. Calculate the amount she pays. Give your answer correct to the nearest
$100. [1 hectare = 10 000 m2]
$ ................................................ [2]
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7
(a) Factorise completely.
2
2 2
3𝑎 𝑏 − 𝑎 𝑏
................................................. [2]
(b) Solve the inequality.
2𝑥 + 12 < 5𝑥 − 9
................................................. [2]
(c) Simplify.
3 5 3
`(3𝑥 𝑦 )
................................................. [2]
(d) Solve.
3
𝑥
=
5
2−𝑥
x = ................................................ [3]
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(e) Expand and simplify.
(𝑥 − 2)(𝑥 + 3)(2𝑥 − 3)
................................................. [3]
9 (a) The equation of line L is 4𝑥 − 8𝑦 + 20 = 0.
(i)
Find the gradient of line L.
................................................. [2]
(ii) Find the coordinates of the point where line L cuts the y-axis.
( ................... , ................... ) [1]
(b) The coordinates of P are (-3, 10) and the coordinates of Q are (9, -2).
(i)
Calculate the length PQ.
13
................................................. [3]
(ii)
Find the equation of the line parallel to PQ that passes through the point (6, -1).
................................................. [3]
(iii) Find the equation of the perpendicular bisector of PQ.
................................................. [4]
10 (a)
NOT TO
SCALE
2
The diagram shows a sketch of the curve 𝑦 = 𝑥 + 3𝑥 − 4.
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(i)
Find the coordinates of the points A, B and C.
A ( .............. , .............. )
B ( .............. , .............. )
(ii)
C ( .............. , .............. ) [4]
2
Differentiate 𝑥 + 3𝑥 − 4.
................................................. [2]
(iii) Find the equation of the tangent to the curve at the point (3, 14).
................................................. [3]
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(b)
(i) On the diagram, sketch the graph of 𝑦 = 𝑠𝑖𝑛⁡(𝑥) 𝑓𝑜𝑟 0°≤𝑥≤360°.
[2]
(ii) Solve the equation 5 𝑠𝑖𝑛⁡(𝑥) =− 4 𝑓𝑜𝑟 0°≤𝑥≤360°
x = .................... or x = .................... [3]
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(a)
Find g(5).
................................................. [1]
(b) Find fg(1).
................................................. [2]
(c)
Find hf(x), expanding and simplifying your answer.
................................................. [2]
(d) Find
𝑓(𝑥)
3
+ 𝑔(𝑥).
Give your answer as a single fraction, in terms of x, in its simplest form.
................................................. [3]
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(e) Find the value of x when 𝑓(𝑥 + 2) =− 11.
x = ................................................ [2]
(f) Find the values of p that satisfy ℎ(𝑝) = 𝑝 − 6.
................................................. [3]
3
(g) Let 𝑗(𝑥) = 𝑥 − 27𝑥
Find the co-ordinates of the stationary points of 𝑗(𝑥), stating clearly with clear reasoning whether the
stationary point is a maximum or minimum point.
18
................................................. [4]
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