IGCSE Mathematics Model Paper - 3

7/29/2019 IGCSE Mathematics Model Paper - 3

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IGCSE/Extended/Mathematics/Model Paper-3

1. The high tide at a point off the coast is 3.5 m above mean sea level whilst thelow tide was 1.6m below mean sea level.Calculate in metres, the difference between the high and low tide. [1]

2. When it is 12 00 in London the time in Singapore is 20 00.

a) What is the time in London when it is 12 30 in Singapore? [1]b) A plane leaves Singapore at 12 30 to fly to London.

The flight takes 13 hours 42 minutes.Calculate the time in London when it arrives. [2]

3. Given that y is directly proportional to the cube root ofx and thaty = 18 whenx = 27,a) Expressy in terms ofx, [2]

b) Calculate the value ofy whenx = 125. [1]

4. a) A sum of money is divided in the ratio 4:3. The larger part is $7.20.Find the smaller part. [1]

b) Express the ratio 700 g to 1.75 kg in its lowest terms.Give your answer in the form m : n, where m and n are integers. [2]

5. a) It is given that 5-2 5 k= 1.Write down the value ofk. [1]

b) It is given that 3 7 = 7m,

Write down the value ofm. [1]

6. a) A shopkeeper sold a pair of shoes for $176.

He made a profit of 10%.Calculate the cost price of the shoes. [2]

b) Calculate the Simple Interest when $280 is invested for 9 months at 8 %per annum.

[2]

7. Solve the simultaneous equationsy = 2x

2x 3y = 8. [3]

8. The formula used in an experiment is T= k(x a)a

a) Find, in terms ofk, the value ofTwhenx = 3a. [1]b) Express x in terms ofT, kand a. [2]

9. A model aeroplane is made to a scale of20

1

a) Calculate the length of the wings on the model, in centimetres, if the actuallength of the wings is 7.8 m. [1]

b) On the model, the area of the tail section is 70 cm2.Calculate the actual area of the tail section, giving your answer in squaremetres. [2]

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10. a) The side of an equilateral triangle is given as 8 cm, correct to the nearestcentimetre.What is the least possible length of its perimeter? [1]

b)ABCandACD are two identical equilateral triangles.

What is the special name given to quadrilateralABCD? [1]

11. The Matrix A =

4

3

2

1

Calculatea) The Value of the determinant ofA, [1]

b) The inverse ofA, [1]

c) AA

-1

2

4

[1]12.

The pointsA, B, C, D andElie on the circle with diameterAC.

EB andACmeet atF.

GA is a tangent to the circle atA.

CDE = 1280

and BFC = 650

. Calculate

a) GAE , [2]

b) AEB . [1]


650

1280

B

C

F

D

A

G

E


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13.

In the diagram, OAB is a quadrant of a circle, radius 14 cm.A semicircle is drawn on OB as diameter.

Take to be 7

22

, calculate

a) The arc lengthAB, [1]b) The perimeter of the shaded part of the diagram. [2]

14. a) A photograph is 5cm wide and 8 cm high.An enlargement of the photograph has a height of 10 cm.Calculate the width of the enlargement. [1]

b) A bucket with a height of 15 cm holds 3 litres.How many litres would a similar bucket hold if it had a height of 30 cm?[2]

15. The linesx + y = 2 andx 3y = 6are shown on the diagram.a) Find the gradient of the linex 3y = 6. [1]b) On the diagram, shade the region defined by the inequalitiesx + y 2,

x 3y 6andx + 1 0. [2]


A

14

O B

4

2

0

-2

-4

-2-4 2 4 6 x

y


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16. The bearing ofB fromA is 0310, the bearing ofCfrom A is 1290 andAB = AC.

Calculatea) The bearing ofA fromB, [1]

b) AngleACB, [1]c) The bearing ofCfromB. [1]


B

C

A

North


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17. In the diagram TC, TD andAB are straight lines.a) Construct the locus of the points which are equidistant from TCand TD.

b) Construct the locus of the points which are equidistant fromA andB.

c) The two loci meet atP. AB is a chord of a circle, centreP.

Draw the circle [4]

18. The quadrilateralABCD is such thatAB = 2p,BC= q and CD = -3p.a) What is the special name given to the quadrilateralABCD? [1]

b) Express DA in terms ofp and q, giving your answer in its simplest form [2]


T

C

A

B

D

- 3p

2p

q

A

D

B

C


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19. The weekly wages of the people who work in a small factory are given in thetable below.

Weekly wage ($) 200220

360 500

Number of people 9 8 2 1

a) Calculate the total weekly wages bill for the factory. [1]b) Find, for the distribution of weekly wages,

i) The mode, [1]

ii) The median, [1]

iii) The mean. [1]

c) One person is chosen at random from those who work in the factory.Another person is chosen at random from those remaining.

Expressing your answer as a fraction in its lowest terms, find theprobability that the sum of the wages of these two people is more than$ 410. [2]



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20.

a) i) Work out the area of triangleABD [1]


7

6

5

4

3

2

1

01 2 3 4 5 6 7 8 9 10

A

B C

D

E F

G

H

y

x


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ii) What is the ratio area of triangleABD: area of triangleHBF?Give your answer in its lowest terms. [2]

b) Describe fully the single transformation which maps triangle ABD onto

i) Triangle CDB [2]

ii) TriangleHBF [2]

21.

The diagram represents the speed-time graph of a cyclist.a) Calculate

i) The speed of the cyclist when t = 16, [1]

ii) The distance travelled in the first 35 seconds. [1]


12

0 20 35 t

v

Speed (v)

in m/s

Time (t) in seconds


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b) After 35 seconds the cyclist stops pedalling. She comes to rest after

travelling a further 48 metres. Calculate the time taken for the wholejourney. [3]


IGCSE Mathematics Model Paper - 3

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