ASEAN Scholarship sample Maths paper

section A ✎

Multiple choice

20 questions · 20 marks

1. 1

   Question 1

   The temperature inside a freezer is −18 °C. It rises by 5 °C, then falls by 9 °C.

   Find the final temperature.

   1. (1)−14 °C
   2. (2)−13 °C
   3. (3)−4 °C
   4. (4)−22 °C
2. 2

   Question 2

   Written correct to 3 significant figures, 0.040596 is ________.

   1. (1)0.040
   2. (2)0.0405
   3. (3)0.0406
   4. (4)0.041
3. 3

   Question 3

   A pen costs $p. A notebook costs $3 more than a pen.

   Nurul buys 4 pens and 2 notebooks. Which expression gives her total cost, in dollars?

   1. (1)6p + 6
   2. (2)6p + 3
   3. (3)6p + 12
   4. (4)4p + 6
4. 4

   Question 4

   A shirt costs $45. In a sale, its price is reduced by 20%.

   Find the sale price.

   1. (1)$9
   2. (2)$25
   3. (3)$36
   4. (4)$54
5. 5

   Question 5

   A bag contains 5 red, 8 blue and 7 green marbles. One marble is taken from the bag at random.

   Find the probability that it is not blue.

   1. (1)13
   2. (2)25
   3. (3)34
   4. (4)35
6. 6

   Question 6

   Three angles at a point are 5x, 3x and 4x.

   Find the value of x.

   1. (1)15
   2. (2)30
   3. (3)36
   4. (4)45
7. 7

   Question 7

   The ratio of Minh's savings to Bao's savings is 5 : 3. Minh has $96 more than Bao.

   How much does Bao have?

   1. (1)$144
   2. (2)$36
   3. (3)$240
   4. (4)$384
8. 8

   Question 8

   Solve the inequality 5 − 2x ≤ 11.

   1. (1)x ≤ −3
   2. (2)x ≥ −3
   3. (3)x ≤ 3
   4. (4)x ≥ 3
9. 9

   Question 9

   A school wants to show what fraction of its students chose each of four co-curricular activities.

   Which diagram is the most appropriate?

   1. (1)A line graph
   2. (2)A pie chart
   3. (3)A stem-and-leaf diagram
   4. (4)A histogram
10. 10

    Question 10

    A cylinder has radius 7 cm and height 10 cm.

    Find its volume, correct to 3 significant figures.

    1. (1)440 cm³
    2. (2)748 cm³
    3. (3)1540 cm³
    4. (4)3080 cm³
11. 11

    Question 11

    The mean mass of 8 boxes is 12 kg. One box, of mass 26 kg, is removed.

    Find the mean mass of the remaining 7 boxes.

    1. (1)10 kg
    2. (2)8.75 kg
    3. (3)12 kg
    4. (4)13.7 kg
12. 12

    Question 12

    Each interior angle of a regular polygon is 156°.

    How many sides does the polygon have?

    1. (1)12
    2. (2)15
    3. (3)18
    4. (4)24
13. 13

    Question 13

    Simplify (2a³b)⁴ ÷ (4a⁵b²).

    1. (1)4a¹²b²
    2. (2)4a⁷b³
    3. (3)8a⁷b²
    4. (4)4a⁷b²
14. 14

    Question 14

    Find the gradient of the line passing through A(−2, 7) and B(4, −5).

    1. (1)−2
    2. (2)−12
    3. (3)12
    4. (4)2
15. 15

    Question 15

    After its price is increased by 12%, a bicycle costs $560.

    Find its price before the increase.

    1. (1)$448.00
    2. (2)$492.80
    3. (3)$500.00
    4. (4)$627.20
16. 16

    Question 16

    y is inversely proportional to x². When x = 3, y = 8.

    Find the value of y when x = 6.

    1. (1)2
    2. (2)4
    3. (3)16
    4. (4)32
17. 17

    Question 17

    A solid metal sphere of radius 6 cm is melted down and recast into small cones, each of radius 3 cm and height 4 cm.

    How many complete cones can be made?

    1. (1)12
    2. (2)18
    3. (3)8
    4. (4)24
18. 18

    Question 18

    Given that 3x − 2 = 5x + 4, find the value of x.

    1. (1)7
    2. (2)1
    3. (3)11
    4. (4)−13
19. 19

    Question 19

    The curve y = x² − 8x + 7 has a minimum point at

    1. (1)(−4, 55)
    2. (2)(4, −9)
    3. (3)(4, 9)
    4. (4)(8, 7)
20. 20

    Question 20

    Two solid cylinders are geometrically similar. Their volumes are 27 cm³ and 125 cm³.

    The curved surface area of the smaller cylinder is 18 cm².

    Find the curved surface area of the larger cylinder.

    1. (1)30 cm²
    2. (2)38.7 cm²
    3. (3)83.3 cm²
    4. (4)50 cm²

section B ✎

Short answer

20 questions · 60 marks

1. 1

   Question 1

   Find the square root of 3136 using prime factorisation. Show your working.

   Ans:

2. 2

   Question 2

   Expand and simplify 5(2x − 3) − 2(4x − 7).

   Ans:

3. 3

   Question 3

   The numbers of books borrowed by 7 students in one week are

   6, 2, 9, 4, 6, 3, 5.

   Find (a) the mode, (b) the median, (c) the mean.

   (a)

   (b)

   (c)

4. 4

   Question 4

   Solve x + 13 − x − 24 = 1.

   Ans: x =

5. 5

   Question 5

   Evaluate (−6) × (−15) ÷ (−9) mentally without using a calculator.

   Ans:

6. 6

   Question 6

   In the diagram, AB is parallel to CD. The straight line PQ crosses AB at E and CD at F.

   The angle marked 68° is the angle between EB and EF.

   Find, stating your reason for each answer, (a) angle x, (b) angle y.

   (a) x =

   (b) y =

7. 7

   Question 7

   Factorise completely 12x²y − 27y³.

   Ans:

8. 8

   Question 8

   A trader sells a bicycle for $621, making a profit of 15% on the price he paid for it.

   Find the price he paid.

   Ans: $

9. 9

   Question 9

   The table shows the masses of 20 parcels.

   Masses of 20 parcels

   Mass, m (kg)	0 < m ≤ 10	10 < m ≤ 20	20 < m ≤ 30	30 < m ≤ 40
   Frequency	4	7	6	3

   Calculate an estimate of the mean mass of a parcel.

   Ans:kg

10. 10

    Question 10

    A rectangular sheet of metal measures 20 cm by 14 cm. A semicircle of diameter 14 cm is cut away from one end.

    Find the area of the metal that remains, correct to 3 significant figures.

    Ans:cm²

11. 11

    Question 11

    A straight line passes through P(1, −2) and Q(5, 6).

    Find the equation of the line in the form y = mx + c.

    Ans:

12. 12

    Question 12

    A cyclist rides 18 km at an average speed of 12 km/h, then rides a further 24 km at an average speed of 16 km/h.

    Find her average speed for the whole journey.

    Ans:km/h

13. 13

    Question 13

    Solve the simultaneous equations

    3x + 2y = 16,

    5x − 2y = 16.

    x =

    y =

14. 14

    Question 14

    Given that 2^{x + 3} = 8^{x − 1}, find the value of x.

    Ans: x =

15. 15

    Question 15

    In triangle ABC, the line DE is parallel to BC. AD = 6 cm, DB = 4 cm and DE = 9 cm.

    (a)Find the length of BC.

    BC =cm

    (b)Find the ratio of the area of triangle ADE to the area of trapezium DBCE.

    Ans:

16. 16

    Question 16

    A curve has equation y = x² − 6x + 5.

    (a)Find the coordinates of the two points where the curve crosses the x-axis.

    Ans:

    (b)Write down the equation of the line of symmetry of the curve.

    Ans:

    (c)Find the coordinates of the minimum point of the curve.

    Ans:

17. 17

    Question 17

    Simplify x² − 9x² + x − 12.

    Ans:

18. 18

    Question 18

    A solid cone has base radius 5 cm and slant height 13 cm.

    (a)Find its vertical height.

    Ans:cm

    (b)Find its volume, correct to 3 significant figures.

    Ans:cm³

19. 19

    Question 19

    Without using a calculator, find the exact value of

    2024² − 2023 × 2025.

    You must show how you obtained your answer.

    Ans:

20. 20

    Question 20

    Two solid spheres are made of the same material. The radius of the larger sphere is 3 times the radius of the smaller sphere. The smaller sphere has a mass of 40 g.

    (a)Find the mass of the larger sphere.

    Ans:g

    (b)The two spheres are melted down and recast as a single sphere. Find the radius of this new sphere as a multiple of the radius of the smaller sphere, correct to 3 significant figures.

    Ans:

End of paper

How close is this to the real Maths paper?

Very close in format. MOE describes the real ASEAN Scholarship Maths paper as 2 hours of multiple-choice and short-answer questions, with a calculator allowed (not graphing or programmable ones). The one big difference: in the real test, only your final answers are marked, so there are no marks for working.