M12/5/MATSD/SP1/ENG/TZ1/XX

Maximum marks will be given for correct answers. Where an answer is incorrect, some marks may be given for a correct method, provided this is shown by written working. Write your answers in the answer IGCSE Revision

3

boxes provided. Solutions found from a graphic display calculator should be supported by suitable working,

1.

1. The following six integers are arranged from smallest to largest 1 , x , 3 , y , 14 , z The mode is 1 , the median is 5 and the mean is 7. Find (a) (b) (c) x; y; z. –4–

[1 mark] [2 marks] [3 marks] M12/5/MATSD/SP1/ENG/TZ1/XX

2.

2.Working: The coordinates of point A are (−4 , p ) and the coordinates of point B are (2 , − 3) . The mid-point of the line segment AB, has coordinates (q , 1) . (a) Find the value of (i) (ii) (b) q; p. [4 marks] [2 marks]

Calculate the distance AB.

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–5–

M12/5/MATSD/SP1/ENG/TZ1/XX

Working: is a star that is 82 414 080 000 000 km away from Earth. A spacecraft, 3. Ross launched from Earth, travels at 48 000 kmh–1 towards Ross. Answers: (a) Calculate the exact time, in hours, for the spacecraft to reach the star Ross. [2 marks] (a) . . . . . . . . . . . . . . . . . . . . . . . . . . . (b) Give your answer to part (a) in years. (Assume 1 year(b) 365. days). . . . . . . . . . . . . . .[2.marks] = .. .... . ...

(c)

(c) . . . . . . . . . . . . . . . . . . . . . . . . . . . Give your answer to part (b) in the form a ×10k , where 1 ≤ a < 10 and k ∈ » . [2 marks]

4. Working:

Turn over

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Hansraj

Sir

Answers:

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– 12 – 9.

M12/5/MATSD/SP1/ENG/TZ1/XX

Line L is given by the equation 3 y + 2 x = 9 and point P has coordinates (6 , –5). (a) (b) (c) Explain why point P is not on the line L . Find the gradient of line L . (i) (ii) Write down the gradient of a line perpendicular to line L . Find the equation of the line perpendicular to L and passing through point P . [3 marks] [1 mark] [2 marks]

Working: 10. The diagram shows quadrilateral ABCD in which AB = 13 m , AD = 6 m and DC = 10 m. Angle ADC = 120 and angle ABC = 40 .

5.

– 13 –

M12/5/MATSD/SP1/ENG/TZ1/XX

C diagram not to scale 10 m

D

120 6m 40 A 13 m B

(a) (b) Working:

Calculate the length of AC.

Answers:

[3 marks]

Calculate the size of angle ACB. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .[3. marks] (a) . ..... ................................................. (b) ................................................. ............................................. ............................................. (ii) (c) (i)

6.

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Answers:

Hansraj

Sir

(a) . . . . . . . . . . . . . . . . . . . . . . . . . . . (b)

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– 15 – 12. M12/5/MATSD/SP1/ENG/TZ1/XX Merryn plans to travel to a concert tomorrow. Due to bad weather, there is a 60 % will travel by car. will be late for the concert is 10 %. will not be late for the concert is 25 %. (a) Complete the tree diagram below. 0.10 Travel by plane Not late Late 0.6 Travel by car 0.25 Not late [3 marks] Late [1 mark]

0.4

(b)

Find the probability that Merryn will not be late for the concert.

Merryn was not late for the concert the next day. [2 marks]

7. Working:

Answers: (b) . . . . . . . . . . . . . . . . . . . . . . . . . . . (c) . . . . . . . . . . . . . . . . . . . . . . . . . . .

Turn over

1520

Hansraj

Sir

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3

– 16 – 13. ABC = 30 .

M12/5/MATSD/SP1/ENG/TZ1/XX

110 , angle CAB = 40 , and angle

A 40

diagram not to scale

30 B (a) (b) Find the length of AC. Find the area of triangle ABC. 8m

110 C [3 marks] [3 marks]

8. Working: 14. A function f ( x) = p × 2 x + q

x

– 17 –

M12/5/MATSD/SP1/ENG/TZ1/XX

f (x)

0 1 2 s

r 11 17 197

(a)

Find the value of (i) (ii) p; q.

Answers: (a) . . . . . . . . . . . . . . . . . . . . ....