ACS (Barker) 4NA Math Prelim Paper 1 (2009)

Anglo-Chinese School (Barker Road)

Mathematical Formulae

Compound Interest

Total amount

MensurationCurved Surface area of cone

Surface area of a sphere

Volume of a cone

Volume of a sphere

Area of a triangle

Arc length , where is in radians

Sector area , where is in radians

Trigonometry

Statistics

Mean

Standard deviation

Preliminary Examination 2009 2 Secondary 4 Normal (Academic) Mathematics Syllabus 4042 Paper 1


For Examiner’s

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Paper 1 [80 marks]Answer all questions in the space provided.

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1. Evaluate

(a) ,

(b) , giving your answer as a decimal.

Answer (a) [1]

(b) [1]

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2. (a) Given that x is a positive integer, 3 < x ≤ 6 and x ≠ 5, write down the possible

values of x.

(b) Make x the subject of the formula y =

Answer (a) x = [1]

(b) x = [1]

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For Examiner’s

Use3. (a) Express 7759 correct to 2 significant figures.

(b) In 2008 the number of adults in Singapore was .

The number of children was .

What was the total population of Singapore in 2008?

Give your answer in standard form.

Answer (a) [1]

(b) [1]

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4. (a) Ben left home at 0745 and arrived at school at 0839.

How many minutes did the journey take?

(b) On the return journey he traveled 7 km in 40 minutes.

Calculate his average speed in kilometers per hour.

Answer (a) mins [1]

(b) km/h [1]

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For Examiner’s

Use5. A bag contains 3 red balls, 2 white balls and 1 blue ball.

Two balls are taken from the bag at random, without replacement.

Find the probability that

(a) both balls are red,

(b) the two balls are the same colour.

Answer (a) [1]

(b) [1]

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6. PQRST are part of a regular 15-sided polygon. QRWX is a square. Find

(a) QRS

(b) RSW

Answer (a) QRS = o [1]

(b) RSW = o [1]

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Diagram is not drawn to scale

X W T

S

R Q

P


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Use7. Simplify

(a) .

(b) .

Answer (a) [1]

(b) [1]

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8. Joey paid $29.25 for high tea. This amount included 10% service charge and 7% Goods

and Services Tax (GST). How much did the high tea cost excluding service charge and

GST?

Answer $ [2]

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For Examiner’s

Use 9. The lengths of the sides of a triangle ABC are such that AB : BC : CA = 3 : 4 : 5.

The perimeter of the triangle is 30 cm.

Calculate the length of CA.

Answer cm [2]

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10. A farmer has a plot of land in the shape as shown. PQ = 44 m, QR = 66 m, and

angle PQR = 55o.

For each square metre of the field, he needs to use 50 ml of insecticide.

Find the amount of insecticide, in litres, he needs for the entire field.

Answer l [2]

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A

B C

P

Q

R

55o66

44


For Examiner’s

Use11. Find

(a) the missing number in the sequence 1, 3, 6, …., 15, 21, 28,

(b) the 7th term in the sequence whose nth term is 3n-1,

(c) an expression, in terms of n, for the nth term of the sequence 5, 9, 13, 17, 21, ….

Answer (a) [1]

(b) [1]

(c) [1]

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12. A soccer player scored the following number of goals in twelve matches:

3, 0, 0, 2, 2, 0, 1, 2, 3, 1, 2, 1

(a) Write down the modal score,

(b) Find the median,

(c) State the least number of goals the soccer player can score in the next match such that

the median is 1 goal.

Answer (a) [1]

(b) [1]

(c) [1]

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Examiner’s Use

13. (a) Express 84 as the product of its prime factors. For Examiner’s

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(b) Written as the product of its prime factors, 360 = . Find the lowest

common multiple of 84 and 360.

Give your answers as the product of its prime factors.

(c) Find the smallest positive integer k such that 84k is a square number.

Answer (a) [1]

(b) [1]

(c) k = [1]

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14. A pencil costs x cents and a notepad costs y cents.

(a) Roy bought 4 pencils and 2 notepads.

The total cost was $2.80.

Write down an equation in x and y and show that it reduces to .

(b) Given that the cost of 1 pencil is $0.30, find y.

Answer (a) Refer to working [1]

(b) y = [2]

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Examiner’s Use

15. The scale of the map is 4 cm to 100 km.

(a) Express this ratio in the form 1: n

(b) What is the distance in km between two towns which are drawn 8.7cm apart on the map? Give your answer in km.

Answer (a) [1]

(b) km [2]

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16. In the diagram, ABD and ACE are straight lines. Given that ACB = 62o,

find the values of

(a) reflex angle AED,

(b) x.

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62B C

A


Answer (a)reflex angle AED= º [1]

(b) x = º [2]

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17. (a) Factorise

(b) Expand and simplify .

Answer (a) [1]

(b) [2]

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ED

x


18. (a) W is directly proportional to . If W = 16 and x = 2,

find the value of x when W = 324.

(b) If each worker works 8 hours a day, 15 workers will take 3 days to paint a house.

How many workers are needed to paint the house in 5 days if each worker works

8 hours a day?

Answer (a) x = [2]

(b) workers [2]

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For Examiner’s

Use1. 19. In the diagram, PQ = 41 cm, QR = 9 cm, QRST is a straight line and SRP = 90.

Given that tan SPR = ,

Calculate

(a) PR,

(b) PS,

(c) sin TSP.

Answer (a) cm [1]

(b) cm [1]

(c) [2]

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For Examiner’s

Use

For Examiner’s

Use20. By completing the square, can be expressed in the form .

(a) Find

(i) a,

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S

T

R9

41

Q

P


(ii) b.

(b) Hence, or otherwise, solve = 0.

Answer (a)(i) a =

(a)(ii) b = [3]

(b) x = or [2]

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21. Solve the simultaneous equations.

Answer x = , y = [4]

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22. In triangle ABC, AB = 7.9 cm, BC = 5 cm and AC = 11 cm.

The side AB is drawn in the answer space below.

(a) Complete the two possible triangles.

(b) (b) For one of these triangles, construct

(i) the bisector of angle BAC,

(ii) the perpendicular bisector of the line AC.

(c) These two lines intersect at the point P.

Complete the sentence in the answer space.

Answer (a) and (b)

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A

B


[2]

[2]

Answer (c) The point P is equidistant from the points and and

equidistant from the lines and . [1]

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___________________________________________________________________ Preliminary Examination 2009 16 Secondary 4 Normal (Academic) Mathematics Syllabus 4042 Paper 1


For Examiner’s

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23. The diagram shows a container made up of a cylindrical top and a cone base.

The radius of the cylinder is 3 cm and its height is 4 cm.

[Volume of cone = x base area x height]

(a) Given that the height of the cone is 8 cm, find the volume of the container in

terms of .

(b) Two taps filled the container at the same time, at the rate of 3 cm³/s and x cm³/s

respectively.

Given that the container was filled to the brim with water in 8 seconds,

find the value of x.

(c) The container is filled to the brim with water. A small hole is cut at the vertex of the

cone and the water drips at a constant rate of 12 cm³/s. Calculate the amount of water

in terms of , left in the container after 4 seconds.

Answer (a) cm³ [2]

(b) [2]

(c) cm³ [1]

For

Examiner’s Use


4 cm

8 cmA

3 cm

Vertex


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24. The points A (3, 1) and B are shown on the grid below.

(a) Write down the coordinates of B.

(b) Find the gradient of the line AB.

(c) Find the equation of the line AB.

(d) Find the length of AB.

1 2

3

4 0 -1 -2

-1

1

2

3

4

x

y B

A

Answer (a) ( , ) [1]

(b) [1]

(c) [2]

(d) unit . [2]

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For Examiner’s

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25. PQRS is a parallelogram. M is the mid-point of PQ and N is a point on RS.

MR meets NQ at X.

(a) Prove that and are similar.

Answer:

____________________________________________________________ [2] ____________________________________________________________ ____________________________________________________________

(b) Given that RN = 3NS, find

(i)

(ii)

Answer (bi) [2]

(bii) [2]

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END OF PAPER 1


M

N RS

QP

X

ACS (Barker) 4NA Math Prelim Paper 1 (2009)

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Transcript of ACS (Barker) 4NA Math Prelim Paper 1 (2009)