IGCSE Edexcel 4H January 2015

1 Becky counted the number of matches in each of 50 boxes.
The table shows information about her results.


Work out the mean number of matches.

2

The diagram shows a circle inside a rectangle.
Work out the area of the shaded region.
Give your answer correct to 3 significant figures.

3 A bag contains only red counters, blue counters and yellow counters.
The number of red counters in the bag is the same as the number of blue counters.
Mikhail takes at random a counter from the bag.
The probability that the counter is yellow is 0.3
Work out the probability that the counter Mikhail takes is red.

4 On the grid, draw the graph of y = 3x – 4 for values of x from –2 to 3

5 


(a) Describe fully the single transformation that maps triangle A onto triangle B.

(b) On the grid, translate triangle A by the vector

6 E = {positive whole numbers less than 19}
A = {odd numbers}
B = {multiples of 5}
C = {multiples of 4}
(a) List the members of the set
(i) A ∩ B

(ii) B ∪ C

D = {prime numbers}
(b) Is it true that B ∩ D = Ø ?
Tick (✔) the appropriate box.

Explain your answer

7 Lisa, Max and Punita share £240 in the ratio 3 : 4 : 8
How much more money than Lisa does Punita get?

8 The diagram shows a triangle.


The lengths of the sides of the triangle are 3x cm, (3x – 5) cm and (4x + 2) cm.
The perimeter of the triangle is 62 cm.
Work out the value of x.
Show clear algebraic working

9 Three positive whole numbers are all different.
The numbers have a median of 8 and a mean of 6
Find the three numbers.

10 (a) Solve the inequality 3x + 8 < 35

(b) Write down the inequality shown on the number line.

11


R and T are points on a circle, centre O.
ROP is a straight line.
PT is a tangent to the circle.
Angle TPO = 46°
(a) Explain why angle OTP = 90°

(b) Work out the size of angle y.

12 (a) Factorise c² – 5c

(b) Simplify d⁵ × d⁷

(c) Factorise x² + x – 30

(d) Make b the subject of P = \[\frac{1}{2}\]a²

(e) Solve \[\frac{2x+1}{3}\] + \[\frac{x-5}{2}\] = 4
Show clear algebraic working.

13 (a) Write 0.000076 in standard form.

The area covered by the Pacific Ocean is 1.6 × 10⁸ km²
The area covered by the Arctic Ocean is 1.4 × 10⁷km²
(b) Write 1.6 × 10⁸ as an ordinary number.

The area covered by the Pacific Ocean is k times the area covered by the Arctic Ocean.
(c) Find, correct to the nearest integer, the value of k

14 Kwo invests HK$ 40000 for 3 years at 2.5% per year compound interest.
Work out the value of the investment at the end of 3 years.

15 Here is the graph of y = x² – 2x – 1

(a) Use the graph to solve the equation x² – 2x – 1 = 2

The equation x² + 5x – 7 = 0 can be solved by finding the points of intersection of the
line y = ax + b with the graph of y = x² – 2x – 1
(b) Find the value of a and the value of b.

16 Chris and Sunil each take a driving test.
The probability that Chris passes the driving test is 0.9
The probability that Sunil passes the driving test is 0.65
(a) Complete the probability tree diagram.

(b) Work out the probability that exactly one of Chris or Sunil passes the driving test.

17

The diagram shows a trapezium.
The trapezium has an area of 17 cm²
(a) Show that 2x² + 7x – 17 = 0

(b) Work out the value of x.
Give your answer correct to 3 significant figures.
Show your working clearly

18 An athlete runs 400 metres, correct to the nearest metre.
The athlete takes 50.2 seconds, correct to the nearest 0.1 of a second.
Work out the upper bound of the athlete’s average speed.
Give your answer correct to 3 significant figures.

(b) Write, as a column vector, 3b – c

(c) Work out the magnitude of a
Give your answer as a surd.

20 The histogram shows information about the heights of some tomato plants.


26 plants have a height of less than 20 cm.
Work out the total number of tomato plants.

21 The diagram shows a cylinder and a sphere.



The cylinder has radius r cm and height h cm.
The sphere has radius 2r cm.
The volume of the cylinder is equal to the volume of the sphere.
Find an expression for h in terms of r.
Give your answer in its simplest form.

22 (a) Write\[\frac{1}{32}\] as a power of 2

(b) Show that (4 +√12)(5 - √3) = 14 + 6√3
Show each stage of your working clearly.

23 Write 5 – (x + 2) ÷\[\frac{x² - 4}{x - 3}\] as a single fraction.
Simplify your answer fully.

24 The diagram shows a sector OAPB of a circle, centre O.
AB is a chord of the circle.
OA = OB = 6 cm.
The area of sector OAPB is 5πcm²
Calculate the perimeter of the shaded segment.
Give your answer correct to 3 significant figures.