IGCSE Edexcel Paper 4H June 2011

1) In a sale, normal prices are reduced by 15%.
The normal price of a television was $640
Work out the sale price of the television.

2) John throws a biased coin 120 times.
It shows heads 90 times.
(a) John throws the coin once more.
Work out an estimate for the probability that the coin shows tails.

Carly throws the same coin 200 times.
(b) Work out an estimate for the number of times the coin shows tails.

3) Here is a list of ingredients for making Apple and Raspberry Crumble for 6 people.

Sam wants to make Apple and Raspberry Crumble for 15 people.
She has enough plain flour, soft brown sugar and butter.
Work out the amount of apples and the amount of raspberries Sam needs.

4) The length of Rachael’s journey from her home to work is 72 km.
The journey takes 1 hour 20 minutes.
Work out her average speed in km/h.

5 (a) Simplify
(i) aaaa

(ii) 5a × 6b ,

(iii) \[q^{8}\] ÷ \[q^{2}\]

(b) Solve 5 - 2y = 12

(c) v = w² - 2w.
Work out the value of v when w = 6

6) The diagram shows a trapezium PQRS.

(a) Calculate the area of the trapezium PQRS.

(b) Calculate the length PQ.
Give your answer correct to 3 significant figures.

7) Six numbers have a mean of 5
Five of the numbers are
3 2 7 6 2
The other number is x.
Work out the value of x.

8) Use compasses and a ruler only to construct the perpendicular bisector of the line PQ.
You must show all construction lines.

9 The length of a fence is 137 metres, correct to the nearest metre.
Write down
(i) the lower bound for the length of the fence,

(ii) the upper bound for the length of the fence.

10) Express 126 as a product of its prime factors.

11) Calculate the length of LM.
Give your answer correct to 3 significant figures.

12 (i) Solve the inequality 2x + 13 ≥ 6

(ii) n is a negative integer.
Write down all the values of n which satisfy 2n + 13 ≥ 6

13) The table gives the diameters, in metres, of four planets.

(a) Which planet has the largest diameter?

(b) Write 6.79 × \[10^{6}\] as an ordinary number.

(c) Calculate the difference, in metres, between the diameter of Venus and the diameter
of Mercury.
Give your answer in standard form.

14) Here are two supermarket price tickets.

The two supermarket price tickets are mathematically similar.
The area of the smaller ticket is 7 cm².
Calculate the area of the larger ticket.

15) (a) Simplify \[\frac{8(x - 3)²}{4(x - 3)}\]

(c) Make q the subject of the formula p = √q - 5r

(d) Solve \[\frac{4}{y - 4}\] = 5

16) The incomplete histogram and table give information about the ages of people living in
a village.

(i) Use the histogram to complete the table.

(ii) Use the table to complete the histogram.

17 Alan has to attend a meeting on Monday and on Tuesday.
The probability that he is late for a meeting is \[\frac{1}{8}\]
(a) Complete the probability tree diagram.

(b) Calculate the probability that Alan is late for at least one of these meetings.

18) Show that the recurring decimal

19) The diagram shows triangle ABC.



Angle BCA = 28°
Angle CAB = 134°
BC =10.2 cm.
Calculate the length of AB.
Give your answer correct to 3 significant figures.

20) f(x) = \[\frac{3}{x}\]
g(x) = \[\frac{x+1}{x}\]
(a) State which value of x cannot be included in the domain of f or g.

(b) Solve gf(a) = 3

(c) Express the inverse function \[g^{-1}\] in the form \[g^{-1}\](x)

21) Clare buys some shares for $50x.
Later, she sells the shares for $(600 + 5x).
She makes a profit of x%
(a) Show that x² + 90x − 1200 = 0

(b) Solve x² + 90x − 1200 = 0
Find the value of x correct to 3 significant figures.

22)

The diagram shows a cuboid ABCDEFGH.
AB = 5cm
BC = 7cm
AE = 3cm
(a) Calculate the length of AG.
Give your answer correct to 3 significant figures.

(b) Calculate the size of the angle between AG and the plane ABCD.
Give your answer correct to 1 decimal place.

23) Express √48 + √108 in the form k √6 where k is a surd.

24)

The diagram shows a trapezium PQRS.
PS is parallel to QR.
PS = 4QR.
PQ = a                QR = b
(a) Find, in terms of a and/or b,
(i) PS

(ii) PR

(iii) RS.

The point T lies on the line PR such that PT : TR = 4 : 1
(b) Given that TS = k QT, find the value of k.