IGCSE Edexcel 4H June 2016

1 Here are the first five terms of an arithmetic sequence.
7 10 13 16 19
Find an expression for the nth term of the sequence.

2 Solve 8y – 18 = 3( y + 3)
Show clear algebraic working.

3 In a sale, all normal prices are reduced by 20%
(a) The normal price of a television set is 485 euros.
Work out the sale price of the television set.

(b) In the sale, the normal price of a tablet computer is reduced by 79 euros.
Work out the normal price of the tablet computer.

4


EFG is a triangle.
AB is parallel to CD.
(a) Write down the value of p

(b) Write down the value of q

Here is a hexagon.


(c) Work out the value of x

5 (a) Simplify m⁵ × m²

(b) Simplify c¹¹ ÷ c³

(c) Simplify (a⁵)³

(d) Expand and simplify 4(2x + 3) + 2(x + 5)

6 Students in class 9Y took part in a sponsored swim.
The table gives information about the amount of money, in £, raised by each student.



Work out an estimate for the total amount of money raised by the students in class 9Y.

7 (a) Complete the table of values for y = x² – 4x + 2

(b) On the grid, draw the graph of y = x² – 4x + 2 for all values of x from –1 to 5

8


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

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

Label the new shape C.

(c) On the grid, rotate triangle D 90º anticlockwise with centre (3, 1)

9

Work out the perimeter of the triangle.

10 The highest common factor (HCF) of 140 and x is 20
The lowest common multiple (LCM) of 140 and x is 420
Find the value of x.

11 The table gives the populations of each of five countries in 2014



(a) Write 9.7 × 10⁷ as an ordinary number.

The population of Russia in 2014 was 140000000
(b) Write 140000000 in standard form.

In 2014, there were more people living in China than were living in the USA.
(c) How many more?
Give your answer in standard form.

In 2014, the population of India was k times the population of Mexico.
(d) Work out the value of k.
Give your answer to the nearest whole number.

12


The diagram shows triangle ACD.
B is a point on AC and E is a point on AD so that BE is parallel to CD.
AE = 4 cm
AC = 11.7 cm
BE = 6 cm
CD = 13.5 cm
(a) Calculate the length of AB.

(b) Calculate the length of ED.

13 M is directly proportional to p³
M = 128 when p = 8
(a) Find a formula for M in terms of p.

(b) Find the value of M when p = 5

14 Simplify \[\frac{x² - 25}{2x²-9x-5}\]

15 (a) Write\[\frac{x+3}{5}\] + \[\frac{x-2}{3}\] as a single fraction in its simplest form.

(b) Simplify (8a⁹e⁶)¹/³

(c) Solve \[\frac{2}{3}\]y +\[\frac{3}{8}\]y = 5
Show clear algebraic working.

16 In a bag there is a total of 20 coins.
10 coins are 20 cent coins
6 coins are 10 cent coins
4 coins are 5 cent coins
Emma takes at random two of the coins from the bag.
(a) Complete the probability tree diagram.

(b) Work out the probability that Emma takes two 5 cent coins.

(c) Work out the probability that the total value of the two coins is 20 cents or less.

17 f is the function such that f(x) = 2x – 5
g is the function such that g(x) = x² – 10
(a) Find f(4)

(b) Find fg(–4)

(c) Express the inverse function f⁻¹ in the form f⁻¹(x) = ...

(d) Solve gf(x) = –1

18 Miss Cook asked each student in her class how long it took them, in minutes, to travel to
school that morning.
The incomplete histogram shows information about the times it took the students who
took no more than 30 minutes to travel to school.



9 students took between 15 minutes and 30 minutes to travel to school.
(a) How many students took no more than 30 minutes to travel to school?

12 students took between 30 and 55 minutes to travel to school.
(b) Use this information to complete the histogram.

19 Simplify (7 + 2√50 )(5 − 2√2)
Give your answer in the form a + b√18 where a and b are integers.
Show your working clearly

20



The diagram shows a solid shape made from a cone on top of a cylinder.
The cone has a radius of 10 cm and a height of 10 cm.
The cylinder has a radius of 10 cm and a height of 10 cm.
The centre of the base of the cone coincides with the centre of the top face of the cylinder.
The total surface area of the solid is A cm²
Show that A = (300 + 100√2 )π

21 Each student in a group of 32 students was asked the following question.
“Do you have a desktop computer (D), a laptop (L) or a tablet (T )?”
Their answers showed that
19 students have a desktop computer
17 students have a laptop
16 students have a tablet
9 students have both a desktop computer and a laptop
11 students have both a desktop computer and a tablet
7 students have both a laptop and a tablet
5 students have all three.
(a) Using this information, complete the Venn diagram to show the number of students in
each appropriate subset.

One of the students with both a desktop computer and a laptop is chosen at random.
(b) Find the probability that this student also has a tablet.

22

OMN is a triangle.
P is the point on OM such that OP =\[\frac{1}{4}\]OM
Q is the midpoint of ON
R is the midpoint of PN
OP = p
OQ = q
(a) Find, in terms of p and q,
(i) MN

(ii) PR

(b) Use a vector method to prove that QR is parallel to OP