answer all questions · web view2018/01/01 · igcse 3h jan 2017 time: 2 hours paper total: 100...

MATHS

Year 11

IGCSE 3H

JAN 2017

TIME: 2 HOURSPAPER TOTAL: 100

Name …………………….

Tutor Group………………

Class Teacher…………………..

Instructions to candidates

CALCULATORS MAY BE USED______________________________________________

JUMEIRAH ENGLISH SPEAKING SCHOOL

ARABIAN RANCHES

International GCSE MATHEMATICS

FORMULAE SHEET – HIGHER TIER

2

Answer ALL TWENTY TWO questions.

Write your answers in the spaces provided.

You must write down all stages in your working.

1 Work out the value of

........................................................(2)

(Total for Question is 2 marks)

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

Lentil Soup (for 6 people)

120 g lentils300 g carrots800 ml vegetable stock3 onions

Jenny wants to make lentil soup for 24 people.

(a) Work out the amount of vegetable stock she needs..

....................................... ml(2)

3

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)


3 Lizzy drove by car to visit her aunt.She left home at 9 30 am.

Lizzy arrived at her aunt’s house at 11 15 am.She drove a distance of 140 km.

Work out, in km/h, Lizzy’s average speed for the journey.

........................................km/h


4

4 Show that


5 (a) Factorise 15r + 10

.......................................................(1)

(b) Simplify y7 × y2

.........................................(1)

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

....................................................................(2)

(d) Expand and simplify

....................................................................(2)


5

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

Number of text messages sent Frequency0 to 4 6

5 to 9 3

10 to 14 515 to 19 12

20 to 24 14

(a) Write down the modal class.

..........................................(1)

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

...........................................(4)

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

.........................................% (2)

(Total for Question 5 is marks)

6

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


8 (a) Solve the inequality e – 2 < 0

........................................................(1)

7

(b) Solve the inequality 5 – 3e < 4

........................................................(2)

(c) Write down the integer value of e that satisfies both of the inequalities

e – 2 < 0 and 5 – 3e < 4

........................................................(1)


9 In 1981, the population of India was 683 million.Between 1981 and 1991, the population of India increased by 163 million.

(a) Express 163 million as a percentage of 683 million.Give your answer correct to 3 significant figures.

........................................................%(2)

8

In 2001, the population of India was 1028 million.Between 2001 and 2011, the population of India increased by 17.6%

(b) Increase 1028 million by 17.6%Give your answer to the nearest million.

........................................................ million(3)

In 2001, the population of India was 1028 million.Between 1971 and 2001, the population of India increased by 87.6%

(c) Work out the population of India in 1971.Give your answer correct to the nearest million.

........................................................ million(3)


9

10 The point A has coordinates (0, 2)The point B has coordinates (–4, –1)

(a) Find the coordinates of the midpoint of AB.

........................................................(2)

(b) Work out the gradient of the line AB.

........................................................(2)

(c) Find an equation of the line AB.

........................................................(2)


10

11 The diagram shows a circle with centre O.The points A, B and C lie on the circle.

Angle AOB = 96°

(a) Work out the size of angle ACB.

........................................................°(1)

AB = 16cm

(b) Work out the radius of the circle.Give your answer correct to 3 significant figures.

........................................................ cm(4)


11

12 Solve the simultaneous equations

c + 5d = –134c – 5d = 48

Show clear algebraic working.

c = ........................................................

d = ........................................................


13 A stone is thrown vertically upwards from a point O.

The height above O of the stone t seconds after it was thrown from O is h metres,where h = 17t – 5t2

Work out the values of t when the height of the stone above O is 12 metres.Show your working clearly.

........................................................


12

14 Here is the quadrilateral ABCD.

Angle BAD = 90° and angle BCD = 90°AB = 9.8 cmAD = 3.6 cmBC = 8.4 cm

Calculate the length of DC.

....................................................... cm

(Total for Question is 4 marks)___________________________________________________________________________

13

15 Linford and Alan race against each other in a competition.

If one of them wins a race, he wins the competition.If the race is a draw, they run another race.

They run a maximum of three races.

Each time they race, the probability that Linford wins is 0.35.Each time they race, the probability that there is a draw is 0.05.

(a) Complete the probability tree diagram.

(2)

(b) Calculate the probability that Linford wins the competition.

......................................................(3)

(Total for Question is 5 marks)_______________________________________________________________________________

14

16 The diagram shows two mathematically similar vases, A and B.

Vase A has a surface area of 120 cm2

Vase B has a surface area of 750 cm2 and a volume of 1600 cm3

Work out the volume of vase A.

....................................................... cm3


15

17 ABCDEFGH is a cuboid.

The cuboid haslength 17 cmwidth 5 cmheight 8 cm

Work out the size of the angle that AH makes with the plane EFGH.Give your answer correct to 1 decimal place.

....................................................... °


16

18 The diagram shows a trapezium.

All measurements on the diagram are in centimetres.

The area of the trapezium is 119 cm2

(i) Show that 2x2 – x – 120 = 0

(ii) Find the value of x.Show your working clearly.

x = .......................................................


17

19 Make t the subject of the formula m =

.......................................................


18

20

A, B and C are points on a circle, centre O.PA and PC are tangents to the circle.Angle ABC = 100°

Calculate the size of angle APC.

.......................................................°


19

21 (a) Simplify fully

Show clear algebraic working.

.......................................................(3)

(b) Given that a is a positive integer, show that

is always a multiple of 3.

(3)


20

22 Solve 3 × 42k+8 = 24Show your working clearly.

k = .......................................................


21

23

The diagram shows a circle, centre C.PR is a chord of the circle.The area of the shaded region is 100 cm2.Angle PCR = 30°

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

....................................................... cm


TOTAL FOR PAPER IS 100 MARKS

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answer all questions · web view2018/01/01 · igcse 3h jan 2017 time: 2 hours paper total: 100...

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