IGCSE Edexcel 4H June 2012

1 Work out the value of\[\frac{6.6 × 1.2}{4.4 - 2.75}\]

2 A group of students take a test.
The group consists of 12 boys and 8 girls.
The mean mark for the boys is 18
The mean mark for the girls is 16.5
Calculate the mean mark for the whole group.

3 Bhavik left his home at 12 00 to cycle to Sam’s house.
On the way Bhavik stopped for a rest, and then continued his journey.
The distance-time graph shows his journey.

(a) (i) For how many minutes did Bhavik stop for a rest?

(ii) After his rest, how many more kilometres did Bhavik cycle to Sam’s house?

(b) Bhavik stayed at Sam’s house for 2 hours.
He then cycled back to his home.
He arrived home at 17 15.
Show all this information on the graph.

(c) Write down the times at which Bhavik was 24 kilometres from his home.

(d) Work out the average speed, in kilometres per hour, of Bhavik’s journey from Sam’s
house back to his home.
Give your answer correct to 1 decimal place.

4

(a) Describe fully the single transformation that maps shape P onto shape Q.

(b) On the grid, rotate shape P 90° clockwise about the point (2, 0).
Label the new shape R.

5 (a) Show that \[\frac{5}{4}\] ÷ \[\frac{7}{15}\] = 1\[\frac{5}{7}\]

(b) Show that 5\[\frac{1}{4}\] - 1\[\frac{2}{3}\] =  3\[\frac{7}{12}\]

6

Calculate the length of MN.
Give your answer correct to 3 significant figures.

7 Showing clear algebraic working, solve the simultaneous equations
 3a + 2b = 1
a + 2b = 5

8 Express 300 as a product of its prime factors.

9 The table shows information about the snowfall in Ottawa in January one year.


Work out an estimate for the total snowfall in January.

10 (a) Expand and simplify
(i)  5(2x + 1) – 3(3x – 1)

(ii) (y + 5)(y – 7)

(b) Make r the subject of the formula V = πr²h where r is positive.

11 The mass of the Space Shuttle is 7.8 × 10⁴ kilograms.
(a) Write 7.8 × 10⁴ as an ordinary number.

The Space Shuttle docks with the International Space Station.
The mass of the International Space Station is 4.62 × 10⁵ kilograms.
(b) Calculate the total mass of the Space Shuttle and the International Space Station.
Give your answer in standard form.

12 A, B and C are three sets.
A ∩ B = Ø and C ⊂ A

(a) Complete the Venn diagram to show the sets B and C

(b) On the Venn diagram, shade the region that represents A ∩ C′

13 (a) Complete the table of values for y = x³ – 3x – 1

(b) On the grid, draw the graph of y = x³ – 3x – 1 for –2 ≤ x ≤ 3

(c) By drawing a suitable straight line on the grid, find an estimate for the solution of
the equation x² – 3x – 6 = 0
Give your answer correct to 1 decimal place.

(d) For the curve with equation y = x³ - 3x - 1
(i) find \[\frac{dy}{dx}\]

(ii) find the gradient of the curve at the point where x = 4

14 There are 31 students in a class.
The only languages available for the class to study are French and Spanish.
17 students study French.
15 students study Spanish.
6 students study neither French nor Spanish.
Using a Venn diagram, or otherwise, work out how many students study only one
language.

15

A, B, C and D are four points on a circle, centre O.
AD is a diameter of the circle.
Angle BAD = 58°
(a) Calculate the size of angle ADB.

(b) (i) Calculate the size of angle BCD.

(ii) Give a reason for your answer.

16

A, B, C and D are four points on a circle.
ABX and DCX are straight lines.
AB = 7 cm, BX = 5 cm and CX = 6 cm.
Angle BXC = 28°
(a) Calculate the length of AC.
Give your answer correct to 3 significant figures.

(b) Calculate the length of DC.

17 The histogram shows information about the times, t minutes, patients spent at a doctors’
surgery on one day.
No patient spent more than 40 minutes at the surgery

(a) Calculate the percentage of the patients who spent between 25 and 40 minutes at the
surgery.

(b) 16 patients spent between 10 and 15 minutes at the surgery.
Calculate the total number of patients at the surgery that day.

18 Bill and Jo play some games of table tennis.
The probability that Bill wins the first game is 0.7
When Bill wins a game, the probability that he wins the next game is 0.8
When Jo wins a game, the probability that she wins the next game is 0.5
The first person to win two games wins the match.
(a) Complete the probability tree diagram.

(b) Calculate the probability that Bill wins the match.

19 f(x) = 3x - 2
    g(x) = \[\frac{10}{y+2}\]
(a) Express the inverse function f ⁻¹ in the form f⁻¹(x) = ...

(b) Find gf(x)
Simplify your answer.

20 Show that (6-√8)² = 44-24√2
Show each stage of your working clearly.

21 Solve\[\frac{5}{x+2}\] + \[\frac{9}{y-2}\] = 2
Show clear algebraic working.

22

Two solid spheres, each of radius r cm, fit exactly inside a hollow cylinder.
The radius of the cylinder is r cm.
The height of the cylinder is equal to 4r cm.
The volume of the space inside the cylinder, not occupied by the spheres, is \[\frac{125}{6}\]πcm³
Calculate the value of r.
Show your working clearly.