Section A
MCQs — 15 Questions
(+2 / -1)
1
place-value
easy
Find the value of 4 thousands + 3 tens + 8 ones.
Answer: 1
4 thousands + 3 tens + 8 ones = 4000 + 30 + 8 = 4038.
2
fractions
easy
Which fraction is smaller than 1/2?
Answer: 2
2/5 = 0.4, which is less than 1/2 = 0.5. 2/3 ≈ 0.67, 3/6 = 0.5 (equal, not smaller), and 3/4 = 0.75 are all not smaller than 1/2.
3
measurement
medium
What is the mass of the watermelon?
Answer: 1
The dial goes from 0 to 4 kg, with each of the 4 marked divisions (0, 1, 2, 3) 90° apart, so each small tick is 0.2 kg. The needle stops 3 small ticks before the 2 kg mark, i.e. at 1.7 kg = 1700 g.
4
place-value
easy
The digit 5 of a number is in the hundreds place. Which one of the following is the number?
Answer: 4
1385 → 5 is in the tens place. 3851 → 5 is in the tens place. 5813 → 5 is in the thousands place. 8531 → 5 is in the hundreds place. Only 8531 has 5 in the hundreds place.
5
money
easy
A file cost 16.75 dollars. A T-shirt cost 67.50 dollars more than the file. How much did the T-shirt cost?
Answer: 2
T-shirt cost = 16.75 + 67.50 = 84.25 dollars.
6
area
medium
Look at the figure below. What is the area of the figure?
Answer: 3
The figure is a kite shape whose diagonals measure 6 units and 4 units. Area = (6 × 4) ÷ 2 = 12 square units.
7
data-analysis
medium
The bar graph shows the number of points scored by four classes in a Math competition. Which class scored the highest points in total?
Answer: 2
Totals: 3K = 12 + 5 = 17, 3L = 9 + 13 = 22, 3M = 4 + 15 = 19, 3N = 13 + 8 = 21. 3L has the highest total.
8
time
easy
Monica started watching a movie at 4.15 p.m. and ended at 6.05 p.m. What is the duration of the movie?
Answer: 3
From 4:15 p.m. to 6:05 p.m. is 1 hour 50 minutes (4:15 → 5:15 is 1 hour, 5:15 → 6:05 is 50 minutes).
9
geometry
medium
Which figure has perpendicular lines?
Answer: 1
Figure 1 has two line segments meeting at a right angle (90°) at its lowest point, so it contains perpendicular lines. The other figures have no right angles.
10
measurement
medium
Lingli had 4 m of ribbon. She cut the ribbon into as many strips of 9 cm as she could and had some ribbon left. How much ribbon was left?
Answer: 4
4 m = 400 cm. 400 ÷ 9 = 44 remainder 4, since 44 × 9 = 396. So 400 − 396 = 4 cm of ribbon was left.
11
time
medium
What is the time shown on the clock?
Answer: 1
The minute hand points to 8 (40 minutes) and the hour hand is between 10 and 11, closer to 11. This is 10:40, which is the same as 20 minutes to 11.
12
patterns
medium
Study the pattern below. The figure is made up of sticks. How many sticks are there in Figure 7?
Answer: 2
The number of sticks increases by 3 each time: 4, 7, 10, 13, 16, 19, 22. Figure 7 has 22 sticks.
13
fractions
easy
What fraction of the figure is shaded?
Answer: 3
4 out of the 10 equal parts of the figure are shaded, which is 4/10 = 2/5.
14
perimeter
hard
The figure is made up of 2 identical rectangles. Find the perimeter of the figure.
Answer: 2
Tracing the outline of the step-shaped figure: 15 + 4 + 9 + 4 + 15 + 4 + 9 + 4 = 64 cm.
15
measurement
medium
The figure below shows the amount of water in a measuring cup. What is the total amount of water in 2 such measuring cups?
Answer: 4
The measuring cup contains 260 ml of water. 2 cups contain 260 × 2 = 520 ml.
Section B
Free-response — 10 Questions
(+4)
16
fractions
medium
Liam picked 240 apples. He sold 3/8 of them at the market. How many apples does he still have? [Enter your answer only between 0 and 9999]
Answer: 150
Apples sold = 3/8 × 240 = 90. Apples left = 240 − 90 = 150.
17
perimeter
hard
Figure A is made up of four identical rectangles. The breadth of one rectangle is 3 cm and its length is 3 times of its breadth. Find the perimeter of Figure A. Give your answer in cm. [Enter your answer only between 0 and 9999]
Answer: 42
Each rectangle is 3 cm × 9 cm (length = 3 × 3 = 9 cm). Figure A is formed by one rectangle standing on its side (3 cm wide, 9 cm tall) next to three rectangles stacked on top of each other (9 cm wide, 3 cm tall each, 9 cm tall together), forming one solid rectangle 12 cm wide by 9 cm tall. Perimeter = 2 × (12 + 9) = 42 cm.
18
ratio
medium
Mei Ling, Sarah and Diya had 270 beads.
Mei Ling had 3 times as many beads as Sarah.
Diya had twice as many beads as Sarah.
How many beads did Diya have? [Enter your answer only between 0 and 9999]
Answer: 90
Let Sarah = x. Mei Ling = 3x, Diya = 2x. Total: x + 3x + 2x = 6x = 270, so x = 45. Diya had 2 × 45 = 90 beads.
19
data-analysis
hard
The bar graph shows the number of footballs sold in a shop from Monday to Friday.
Each football was sold for 9 dollars.
How much more money in dollars did the shop collect on Tuesday compared to Monday? [Enter your answer only between 0 and 9999]
Answer: 144
Monday: 18 footballs sold = 18 × 9 = 162 dollars. Tuesday: 34 footballs sold = 34 × 9 = 306 dollars. Difference = 306 − 162 = 144 dollars.
20
patterns
hard
Mr Tan puts some sticks at equal distance on a straight line. The distance between the 1st and 5th stick is 20 cm.
If the total distance between the 1st stick and the last stick is 40 m. How many sticks are there altogether? [Enter your answer only between 0 and 9999]
Answer: 801
From the 1st to the 5th stick there are 4 equal gaps covering 20 cm, so each gap = 5 cm = 0.05 m. The total distance of 40 m contains 40 ÷ 0.05 = 800 gaps, so there are 800 + 1 = 801 sticks in total.
21
place-value
medium
What is the smallest four-digit even number that can be formed with the given digits below? [Enter your answer only between 0 and 9999]
Answer: 2054
For the smallest number, use the smallest non-zero digit (2) as the thousands digit, then the remaining digits in ascending order (0, 4, 5) for the rest, but the number must be even, so it must end in 0 or 4. Using 2054: it starts with the smallest possible leading digit (2), and ends in the even digit 4, with the remaining digits (0, 5) placed in ascending order in between — giving the smallest valid even number, 2054.
22
arithmetic
medium
A bus left a bus interchange with 47 people onboard. When it reached the first bus stop, 12 people boarded the bus and some people alighted the bus. There were 23 people on the bus when it left the first bus stop.
How many people alighted the bus at the first bus stop? [Enter your answer only between 0 and 9999]
Answer: 36
After boarding: 47 + 12 = 59 people. Since 23 people remained, the number who alighted = 59 − 23 = 36.
23
time
medium
Samantha watched two movies continuously at the cinema.
The first movie lasted for 2 h 15 min. The second movie lasted for 1 h 50 min.
She started watching the first movie at 14 25. What time did she finish watching the second movie? (Write the time in 24-hour format without the colon. For example, 15:45 → 1545.) [Enter your answer only between 0 and 9999]
Answer: 1830
14:25 + 2 h 15 min = 16:40 (end of first movie). 16:40 + 1 h 50 min = 18:30. Written without the colon: 1830.
24
algebra
medium
Dash and Luke had the same number of marbles at first. After Luke gave 12 marbles to Dash, Dash had four times as many marbles as Luke.
How many marbles did Luke have in the end? [Enter your answer only between 0 and 9999]
Answer: 8
Let each start with x marbles. After the transfer: Dash = x + 12, Luke = x − 12. Since Dash = 4 × Luke: x + 12 = 4(x − 12) → x + 12 = 4x − 48 → 3x = 60 → x = 20. Luke ended with x − 12 = 8 marbles.
25
patterns
hard
The figures below are made up of identical squares. The figures follow a pattern.
Study Figures 1, 2 and 3 above and the table below. Which figure will have a total of 52 shaded squares? [Enter your answer only between 0 and 9999]
Answer: 12
Figure n is an (n+2) by (n+2) grid of squares with an n by n unshaded square in the middle. So shaded squares = (n+2)² − n² = 4n + 4. Figure 1: 4(1)+4 = 8 shaded (matches the 3×3 grid with 1 unshaded). Figure 2: 4(2)+4 = 12 shaded (4×4 grid with 4 unshaded). Figure 3: 4(3)+4 = 16 shaded (5×5 grid with 9 unshaded). Setting 4n + 4 = 52 gives n = 12, so Figure 12 has 52 shaded squares.
Section C
Free-response — 6 Questions
(+5)
26
money
medium
Mary had 29 coins. She had 15 one-dollar coins and the rest were fifty-cents and ten-cents coins. She had 20.80 dollars altogether.
How many fifty-cents coins did Mary have? [Enter your answer only between 0 and 9999]
Answer: 11
The 15 one-dollar coins total $15, leaving 29 − 15 = 14 coins worth $20.80 − $15 = $5.80. Let f = number of fifty-cent coins and t = number of ten-cent coins: f + t = 14 and 0.5f + 0.1t = 5.80. Multiplying the second equation by 10: 5f + t = 58. Subtracting the first equation: 4f = 44, so f = 11.
27
area
hard
The figure is made up of 3 identical rectangles and 1 square. The perimeter of the square is 36 cm. The length of one rectangle is 4 cm longer than its breadth.
Find the area of the shaded rectangle. Answer in cm². [Enter your answer only between 0 and 9999]
Answer: 21
The square has perimeter 36 cm, so its side = 36 ÷ 4 = 9 cm. The 3 identical rectangles sit side by side directly below the square, so their combined width equals the square's side: 3 × breadth = 9 cm, giving breadth = 3 cm. The length is 4 cm longer than the breadth: length = 3 + 4 = 7 cm. Area of the shaded rectangle = 3 × 7 = 21 cm².
28
algebra
medium
Adam, Ben and Clare had 2659 stickers altogether.
Ben had 162 more stickers than Adam.
Clare had 137 fewer stickers than Adam.
How many stickers did Adam have? [Enter your answer only between 0 and 9999]
Answer: 878
Let Adam = A. Ben = A + 162, Clare = A − 137. Total: A + (A + 162) + (A − 137) = 2659 → 3A + 25 = 2659 → 3A = 2634 → A = 878.
29
algebra
medium
There are 24 cars and motorcycles altogether. There is a total number of 76 wheels. Each car has 4 wheels and each motorcycle has 2 wheels.
How many cars are there? [Enter your answer only between 0 and 9999]
Answer: 14
Let c = cars, m = motorcycles. c + m = 24 and 4c + 2m = 76. Dividing the second equation by 2: 2c + m = 38. Subtracting the first equation: c = 14.
30
money
hard
Yilin went to a cake shop to buy some muffins. What was the maximum number of muffins that Yilin can buy with 50 dollars? [Enter your answer only between 0 and 9999]
Answer: 28
The 4-for-$7.00 bundle costs $1.75 per muffin, cheaper than buying singly at $1.80, so buy as many bundles as possible. $50 ÷ $7 = 7 bundles with $1 left over (7 × $7 = $49). 7 bundles = 28 muffins, and the remaining $1 is not enough for another single muffin ($1.80). So the maximum is 28 muffins.
31
algebra
medium
There were 4 times as many adults as children in a mall. After 132 adults and 9 children went home, there was an equal number of adults and children in the mall. How many children were in the mall at first? [Enter your answer only between 0 and 9999]
Answer: 41
Let children = c, so adults = 4c. After some left: adults = 4c − 132, children = c − 9. These are equal: 4c − 132 = c − 9 → 3c = 123 → c = 41.