IGCSE Edexcel Paper 4H June 2017 Quiz

1) P = {p, o, r, t, u, g, a, l}
I = {i, t, a, l, y}
(a) List the members of the set
(i) P ∩ I

(ii) P ∪ I

F = {f, r, a, n, c, e}
(b) Is it true that I ∩ F = Ø?
Tick the appropriate box.



Explain your answer.

2) M = 2t² – 7t
(a) Work out the value of M when t = -3

(b) Solve 4(x + 3) = 9x – 10
Show clear algebraic working.

y is an integer.
-2 < y ≤ 3
(c) Write down all the possible values of y.

3) Lyn went on holiday to India.
She changed £250 into rupees.
The exchange rate was £1 = 97 rupees.
(a) How many rupees did Lyn get?

When she returns from holiday, Lyn has four 500 rupee notes.
She changes this money into pounds.
The exchange rate is now £1 = 93.5 rupees.
(b) Work out how many pounds Lyn gets.
Give your answer to the nearest pound.

4) Point A has coordinates (-4, 9)
Point B has coordinates (1, 5)
Find the coordinates of the midpoint of AB.

5) Each time Astrid plays a game of chess against her computer, she will win or draw or lose.
For each game of chess
the probability that she will win is 0.3
the probability that she will lose is three times the probability that she will draw.
On Monday, Astrid is going to play 20 games of chess against her computer.
(a) Work out an estimate for the number of games of chess Astrid wins on Monday.

On Tuesday, Astrid plays a game of chess against her computer.
(b) Work out the probability that she will lose.

6 There are 6 batteries in a small packet of batteries.
There are 9 batteries in a large packet of batteries.
Chow buys m small packets of batteries and g large packets of batteries.
The total number of batteries Chow buys is T.
Write down a formula, in terms of m and g, for T.

7) (a) Show that \[\frac{7}{12}\] + \[\frac{3}{8}\] = \[\frac{23}{24}\]

(b) Show that 1\[\frac{2}{3}\] x 2\[\frac{1}{15}\] = 3\[\frac{4}{9}\]

8) Each interior angle of a regular polygon is 156°
Work out the number of sides of the polygon.

9) Manu, Liam and Ned share £420 in the ratios 4 : 5 : 3
Liam then gives Ned £75
Express the amount of money that Ned now has as a percentage of the £420
Give your answer correct to the nearest whole number

10) (a) Simplify \[e^{8}\] x \[e^{7}\]

(b) Simplify fully 12\[\frac{12\[g^{10}\]}{3g²}\]

(c) Write down the value of mº

(d) Simplify fully

11)

A, B, C and D are points on a circle.
ABCD is a square of side 7 cm.
Work out the total area of the shaded regions.
Give your answer correct to the nearest whole number.

12) Here are the heights, in millimetres, of 11 seedlings.
16   12   19   17   24   27   19   15   23   27   10
Work out the interquartile range of these heights.

13) Here are the equations of four straight lines.
Line A     y = 2x + 3
Line B     2y = 6 - 3x
Line C     4x - 2y = 3
Line D     y = 3 - 2x
Two of these lines are parallel.
(a) Which two lines?

Line L has a gradient of -\[\frac{5}{2}\] and passes through the point with coordinates (1, 3)
(b) Find an equation of L.
Give your answer in the form ax + by = c where a, b and c are integers.

14)

A, B, C and D are points on a circle, centre O.
Angle ABD = 52°
(a) (i) Write down the size of angle ACD.

(ii) Give a reason for your answer.

(b) (i) Write down the size of angle AOD.

(ii) Give a reason for your answer.

15) Here is a trapezium.



All measurements are in centimetres.
The area of the trapezium is 60 cm².
(a) Show that 3x²  + 10x - 117 = 0

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

16) The probability that it will rain on Saturday is 0.8
If it rains on Saturday, the probability that it will rain on Sunday is 0.65
If it does not rain on Saturday, the probability that it will rain on Sunday is 0.4
(a) Use this information to complete the probability tree diagram.

(b) Work out the probability that it will rain on just one of these two days.

17 Curve C has equation y = 8x³ - 3x² - 25x
(a) Find \[\frac{dy}{dx}\]

(b) Find the x coordinates of the points on C where the gradient is 5
Show clear algebraic working.

18) The table gives information about the times, in minutes, some people waited in the
accident and emergency department at a hospital.



On the grid, draw a histogram for this information.

19) ABCD is a kite.



Work out the area of the kite.
Give your answer correct to 3 significant figures

20) A car travels a distance of 63.5 km, correct to the nearest 0.5 km.
The car takes 45.8 minutes correct to 1 decimal place.
Work out the lower bound for the average speed of the car.
Show your working clearly.
Give your answer in km/h correct to 1 decimal place.

21) LMNP is a quadrilateral.



Work out the size of angle MLP.
Give your answer correct to 3 significant figures

22) m = 8 × \[10^{9n}\]
where n is an integer.
Express \[m^{-1/3}\] in standard form.
Give your answer, in terms of n, as simply as possible.

23) The diagram shows a solid hemisphere.



The hemisphere has a total surface area of \[\frac{16}{3}\]πcm²
The hemisphere has a volume of kπcm³
Find the value of k.