Cambridge IGCSE
Cambridge IGCSE
Cambridge IGCSE
* 8 4 8 7 8 2 9 3 5 7 *
1 hour 40 minutes
INSTRUCTIONS
● Answer both part A (Questions 1 to 6) and part B (Questions 7 to 10).
● 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 graphic display calculator where appropriate.
● You may use tracing paper.
● You must show all necessary working clearly, including sketches, to gain full marks for correct methods.
● In this paper you will be awarded marks for providing full reasons, examples and steps in your working
to communicate your mathematics clearly and precisely.
INFORMATION
● The total mark for this paper is 60.
● The number of marks for each question or part question is shown in brackets [ ].
DC (LK/SG) 187927/2
© UCLES 2020 [Turn over
2
A INVESTIGATION (QUESTIONS 1 to 6)
This investigation is about the number of dots in shapes that are regular polygons.
Complete this sum for the total number of dots in the triangle.
[3]
(a) Find an expression, in terms of n, for the total number of dots in the nth dotty square.
................................................. [1]
................................................. [2]
d = ( p - 2) n - p + 3 .
[1]
Complete the diagram to show the 4th and 5th dotty pentagons.
[2]
4 (a) This table shows the total number of dots in some dotty polygons.
Use Question 2, Question 3 and any patterns you notice to help you complete this table.
Triangle 3 1 3 6 10 n2 n
+
2 2
Square 4 1 4 9 16
Pentagon 5 1 5 12
Hexagon 6 1 6
[8]
(b) Complete this expression, in terms of n, for the total number of dots in any dotty pentagon.
3n 2
2 ................................................ [3]
5 (a) Use Question 4 and any patterns you notice to help you complete this table.
Triangle 3 n2 n
+
2 2
Square 4
Pentagon 5
Hexagon 6
................... - n
[2]
(b) Find, in terms of n and p, an expression for the total number of dots in any dotty polygon.
................................................. [3]
6 When p = 50,
................................................. [4]
[2]
................................................. [2]
Distance
(metres)
0
0 3 t
Time (seconds)
[3]
(d) On your sketch, shade the region showing the distances travelled at speeds from 80 km/h to
130 km/h for 0 G t G 3. [1]
8 When a driver looks at a mobile phone they do not look at the road.
On average, they look at their mobile phone for 2 seconds.
For speeds between 80 km/h and 130 km/h, find the range of distances that the car travels in these
2 seconds.
Write, and simplify, the model for b when the road is dry.
................................................. [2]
Write, and simplify, the model for b when the road is icy.
................................................. [2]
Braking
distance
(metres)
0 v
0 20
Speed (m/s)
[3]
(i) On the diagram in part (c), sketch a vertical line at 60 km/h. [2]
(ii) Find how much greater the braking distance is when the road is icy than when the road is dry.
................................................. [3]
The weather is wet and the measure of grip the tyre has on the road is 0.5 .
Glen is driving at x km/h.
[2]
(b) The total stopping distance is the distance the car travels from when the emergency happens to
when the car stops.
Use Question 8 and Question 9 to find, in terms of x, a model for Glen’s total stopping distance in
metres.
Give your answer as simply as possible.
................................................. [5]
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