IGCSE Edexcel 3H January 2016

1 Here is a list of the ingredients needed to make lentil soup for 6 people.



Jenny wants to make lentil soup for 24 people.
(a) Work out the amount of vegetable stock she needs.

Ravi is going to make lentil soup.
He uses 450 g of carrots.
(b) How many people is Ravi making the lentil soup for?

2 Lizzy drove by car to visit her aunt.
She left home at 930 am.
Lizzy arrived at her aunt’s house at 1115 am.
She drove a distance of 140 km.
Work out, in km/h, Lizzy’s average speed for the journey

3 Show that \[\frac{3}{8}\] ÷ \[\frac{7}{12}\] = \[\frac{9}{14}\]

4 (a) Factorise 15r + 10

(b) Simplify y⁷ × y²

(c) Expand and simplify (x + 5)(x – 1)

(d) Simplify fully \[\frac{36k³m⁴}{30k⁵m}\]

5 Kim asked 40 people how many text messages they each sent on Monday.
The table shows her results.



(a) Write down the modal class.

(b) Calculate an estimate for the mean number of text messages sent.

(c) What percentage of these 40 people sent 20 or more text messages?

6 Use ruler and compasses only to construct the perpendicular bisector of line AB.
You must show all your construction lines.

7 E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 3, 4, 5, 6}
B = {odd numbers}
(a) List the members of A ∪ B

C is a set such that A ∩ C = {4, 5}
The set C has 4 members.
(b) List the members of one possible set C

8 Solve 3(2x + 5) = 4 – x
Show clear algebraic working

9


A cylinder has radius 5.4 cm and height 16 cm.
(a) Work out the volume of the cylinder.
Give your answer correct to the nearest whole number.

The radius 5.4 cm is correct to 2 significant figures.
(b) (i) Write down the upper bound of the radius.

(ii) Write down the lower bound of the radius.

10 (a) On the grid, draw the graph of y = 2x + 3 for values of x from –2 to 4

(b) Show, by shading on the grid, the region that satisfies all three of the inequalities
x ≤ 3 and y ≥ 2 and y ≤ 2x + 3
Label your region R.

11


Work out the size of angle ACB.
Give your answer correct to 1 decimal place.

12 Make t the subject of 5(t – g) = 2t + 7

13 Here are the marks that James scored in eleven maths tests.
16 12 19 18 17 13 13 20 11 19 17
(a) Find the interquartile range of these marks.

Sunil did the same eleven maths tests.
The median mark Sunil scored in his tests is 17
The interquartile range is 8
(b) Which one of Sunil or James has the more consistent marks?
Give a reason for your answer.

Sunil did four more maths tests.
His scores in these four tests were 16, 20, 18 and 10
(c) How does his new median mark for the fifteen tests compare with his median mark of
17 for the eleven tests?

Explain your answer.

14 Liam invests £8000 in a savings account for 4 years.
The savings account pays compound interest at a rate of
4.5 % for the first year
2.75 % for all subsequent years.
(a) Work out the value of Liam’s investment at the end of 4 years.

Max invests some money in a savings bond.
The savings bond pays interest at a rate of 2% per year.
At the end of the first year, his savings bond is worth £5763
(b) How much money did Max invest in the savings bond?

15 The diagram shows the graph of y = f(x) for –3.5 ≤ x ≤ 1.5



(a) Find f(0)

(b) For which values of k does the equation f(x) = k have only one solution?

(c) Find an estimate for the gradient of the curve at the point where x = –2.5

g(x) = \[\frac{1}{2 + x}\]  
(d) State which value of x must be excluded from any domain of g

(e) Find fg( –3)

16 Solve the inequality 5x² – 13 < 32
Show clear algebraic working.

17



L, M and P are points on a circle, centre O
Angle LMP = 48°
(a) (i) Write down the size of angle LOP

(ii) Give a reason for your answer

Q, R, S and T are points on a circle.
ATB is the tangent to the circle at T
Angle STR = 26°
Angle RQT = 73°
(b) Work out the size of angle STA
Give a reason for each stage in your working.

18 A is the point with coordinates (1, 3)
B is the point with coordinates (–2, –1)
The line L has equation 3y = 4 – 2x
Is line L parallel to AB?
Show your working clearly.

19 The diagram shows a sphere and a cone.



The cone has height h cm.
The radius of the base of the cone is 3 times the radius of the sphere.
Given that the volume of the sphere is equal to the volume of the cone,
find an expression for the radius of the sphere in terms of h.
Give your expression in its simplest form.

20


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

21 Peter travels to work either by bus or by bike.
The probability that Peter will travel to work by bus on any one day is 0.7
Whenever Peter travels to work by bus, the probability that he will be late is 0.1
Whenever Peter travels to work by bike, the probability that he will be late is 0.05
Peter is going to go to work on Monday and on Tuesday.
Work out the probability that he will be late for work on at least one of these days.

22 The diagram shows a rectangle.


The width of the rectangle is x cm.
The length of a diagonal of the rectangle is 12 cm.
The perimeter of the rectangle is 28 cm.
Find the possible values of x.
Give your values correct to 3 significant figures.
Show your working clearly.

23


OAB is a triangle.
P is the point on OA such that OP : PA = 2 : 1
C is the point such that B is the midpoint of OC.
M is the midpoint of AB.
OA = 6a OB = 4b
Show that PMC is a straight line.