Section A
Multiple Choice — Questions 1 to 15
(+2 / -1)
1
fractions
easy
Which of the following is an equivalent fraction of 2/3?
1
3/5
2
4/9
3
8/12
4
5/8
Show answer
Answer: 3
2/3 = (2×4)/(3×4) = 8/12. None of the other options simplify to 2/3.
2
area
medium
The figure below is made up of unit squares, with one corner cut off by a diagonal line. Find the area of the figure in square units.
1
18 square units
2
20 square units
3
16 square units
4
22 square units
Show answer
Answer: 1
The full rectangle is 5 units by 4 units, giving 20 square units. The corner cut off by the diagonal is a right triangle with both legs 2 units long, so its area is (2×2)÷2 = 2 square units. Area of the figure = 20 − 2 = 18 square units.
3
division
easy
Sarah had 720 beads at first. She gave an equal number of beads to each of her 4 friends and had 24 beads left. How many beads did Sarah give to each friend?
1
204
2
183
3
174
4
156
Show answer
Answer: 3
Beads given away = 720 − 24 = 696. Each friend received 696 ÷ 4 = 174 beads.
4
time
medium
Mr Lim left the office at the time shown on the clock below. He reached home 35 minutes later. At what time did he reach home? Give your answer in 24-hour format.
1
15:25
2
16:00
3
16:25
4
16:35
Show answer
Answer: 2
The clock shows 3:25 p.m. 3:25 p.m. + 35 minutes = 4:00 p.m., which is 16:00 in 24-hour format.
5
fractions
medium
The figure below is made up of identical squares. How many more squares must be shaded so that 3/4 of the figure is shaded?
1
7
2
4
3
9
4
12
Show answer
Answer: 1
The figure has 20 squares in all, and 8 are already shaded. For 3/4 of the figure to be shaded, 3/4 × 20 = 15 squares must be shaded. So 15 − 8 = 7 more squares must be shaded.
6
money
easy
Ethan wants to buy a sandwich for $2.35, a juice for $1.10, and a muffin for 90 cents. He only has $4.00. How much more money does he need?
1
$4.35
2
$0.35
3
$0.90
4
$0.55
Show answer
Answer: 2
Total cost = $2.35 + $1.10 + $0.90 = $4.35. He needs $4.35 − $4.00 = $0.35 more.
7
place-value
easy
15 thousands and 6 tens is the same as ___.
1
156
2
1506
3
15,060
4
15,600
Show answer
Answer: 3
15 thousands = 15,000, and 6 tens = 60. Together, 15,000 + 60 = 15,060.
8
algebra
medium
Ben and Cara had some marbles each. Ben had 42 marbles. After Cara had given away 25 marbles, she had 12 fewer marbles than Ben. What was the number of marbles Cara had at first?
1
55
2
53
3
50
4
45
Show answer
Answer: 1
After giving away marbles, Cara had 12 fewer than Ben, so Cara had 42 − 12 = 30 marbles. Before giving any away, Cara had 30 + 25 = 55 marbles.
9
perimeter
medium
Study the figure below. Only four of its six sides are labelled. Find the perimeter of the figure.
1
88 cm
2
76 cm
3
96 cm
4
68 cm
Show answer
Answer: 1
The two unlabelled inner sides can be found from the outer ones: the missing horizontal side = 24 − 15 = 9 cm, and the missing vertical side = 20 − 12 = 8 cm. Adding up all six sides: 24 + 20 + 15 + 8 + 9 + 12 = 88 cm.
10
measurement
easy
A ribbon, 6 m long, is cut into 2 pieces. One piece is 2 m 45 cm long. What is the length of the other piece?
1
3 m 45 cm
2
3 m 55 cm
3
4 m 45 cm
4
4 m 55 cm
Show answer
Answer: 2
6 m = 600 cm. 600 cm − 245 cm = 355 cm = 3 m 55 cm.
11
data-handling
hard
The bar graph shows the number of stickers Mia and Zara had. Ken had some stickers too. The bar for Ken's number of stickers has not been drawn.
Mia gave Ken some stickers. Each of the three children had the same number of stickers after that. How many stickers did Ken have at first?
1
6
2
8
3
4
4
10
Show answer
Answer: 1
Only Mia gave stickers away, so Zara's amount never changed — her original 12 stickers must equal the final equal share for all three. Total stickers = 3 × 12 = 36. Ken's original amount = 36 − 18 (Mia) − 12 (Zara) = 6.
12
multiplication
medium
Ryan bought 4 packets of buttons. Sam bought 3 times as many packets of buttons as Ryan. There were 18 buttons in each packet. How many buttons did Sam buy?
1
216
2
72
3
54
4
108
Show answer
Answer: 1
Sam bought 4 × 3 = 12 packets. Sam's buttons = 12 × 18 = 216.
13
multiples
easy
The smallest two common multiples of 4 and 6 are ___.
1
1 and 2
2
2 and 4
3
6 and 12
4
12 and 24
Show answer
Answer: 4
The multiples of 4 are 4, 8, 12, 16, 20, 24, ... and the multiples of 6 are 6, 12, 18, 24, ... The smallest common multiple is 12, and the next is 24.
14
area
easy
A square tile has sides of length 9 cm. Find its area. Give your answer in cm².
1
18
2
27
3
36
4
81
Show answer
Answer: 4
Area of a square = side × side = 9 × 9 = 81 cm².
15
measurement
medium
What is the length of the twig in cm?
1
6.5 cm
2
6.7 cm
3
7.3 cm
4
7.7 cm
Show answer
Answer: 2
The twig starts at the 1.5 cm mark and ends at the 8.2 cm mark. Its length is 8.2 − 1.5 = 6.7 cm.
Section B
Open Answer — Questions 16 to 25
(+4)
16
distance
medium
16 fence posts are placed at equal distances apart along a straight path. The distance between the 1st post and the 2nd post is 5 m. What is the total distance between the 1st and the 16th post in meters? [Enter your answer only between 0 and 9999]
Show answer
Answer: 75
There are 15 equal gaps between the 1st and 16th posts, and each gap is 5 m. Total distance = 15 × 5 = 75 m.
17
algebra
hard
A store has 3 types of toys. Type X has 150 more toys than Type Y. Type Z has 4 times as many toys as Type Y. After selling 60 toys from Type Z, the number of toys in Type Z becomes equal to Type X. How many toys are there altogether at first? [Enter your answer only between 0 and 9999]
Show answer
Answer: 570
Let Type Y = y. Type X = y + 150. Type Z = 4y. After selling 60 from Type Z: 4y − 60 = y + 150, so 3y = 210 and y = 70. Type X = 220, Type Z = 280. Total = 70 + 220 + 280 = 570.
18
word-problem
medium
In a hall, 210 people were seated to watch a show at first. After the first show, 35 of them left their seats. Then, 3 times as many people as those who left came in to occupy the remaining seats. How many seats are there in the hall? [Enter your answer only between 0 and 9999]
Show answer
Answer: 280
Seats still occupied after people left = 210 − 35 = 175. New arrivals = 3 × 35 = 105. Total seats in the hall = 175 + 105 = 280.
19
division
easy
Mrs Ong had 184 stickers. She gave each pupil 7 stickers and had 2 stickers left. How many pupils did Mrs Ong give the stickers to? [Enter your answer only between 0 and 9999]
Show answer
Answer: 26
Stickers given away = 184 − 2 = 182. Number of pupils = 182 ÷ 7 = 26.
20
time
medium
Mr Kumar left his house at 9.40 a.m. for his dentist appointment. He took 55 min to travel from his house to the dentist. He arrived 10 minutes before his appointment started. What time did his appointment start? Express in 12-hour format. (Write your answer without using a colon. For example, write 530 instead of 5:30.) [Enter your answer only between 0 and 9999]
Show answer
Answer: 1045
9.40 a.m. + 55 minutes = 10.35 a.m. He arrived 10 minutes before his appointment started, so his appointment started at 10.35 a.m. + 10 minutes = 10.45 a.m., written as 1045.
21
combinatorics
medium
Liam wants to order a meal from a café. He plans to order a meal that includes 1 main dish, 1 side and 1 drink.
Menu — Main dish: Chicken Wrap, Veggie Wrap. Side: Fries, Garden Salad. Drink: Water, Juice, Lemonade.
How many different ways can Liam order his meal? [Enter your answer only between 0 and 9999]
Show answer
Answer: 12
There are 2 choices of main dish, 2 choices of side, and 3 choices of drink. Total ways = 2 × 2 × 3 = 12.
22
division
hard
Uncle Ray bought 2150 stickers. He packed 6 stickers into each pack and found that he had some stickers left. He sold each pack of stickers for $7 and the remaining stickers at $3 each. How much did he receive altogether? [Enter your answer only between 0 and 9999]
Show answer
Answer: 2512
2150 ÷ 6 = 358 packs with 2 stickers left over (358 × 6 = 2148). Money received = (358 × $7) + (2 × $3) = $2506 + $6 = $2512.
23
perimeter
medium
A piece of string, 44 cm long, was bent into the shape of a square. The same piece of string was then bent into the shape of a rectangle. The length of the rectangle was 15 cm. What was the breadth of the rectangle in cm? [Enter your answer only between 0 and 9999]
Show answer
Answer: 7
The string's length stays the same, so both shapes have a perimeter of 44 cm. For the rectangle, 2 × (15 + breadth) = 44, so 15 + breadth = 22, giving breadth = 7 cm.
24
mass
medium
Uncle Sam had 9 kg of rice at first. After using 6800 g of rice to cook a meal, he packed the remaining rice equally into 4 packets. What was the mass of rice in each packet in grams? [Enter your answer only between 0 and 9999]
Show answer
Answer: 550
9 kg = 9000 g. Rice remaining = 9000 − 6800 = 2200 g. Each packet = 2200 ÷ 4 = 550 g.
25
algebra
medium
4 storybooks and 5 bookmarks cost 120 dollars altogether. Each storybook costs 12 dollars more than each bookmark. Find the cost of each storybook in dollars. [Enter your answer only between 0 and 9999]
Show answer
Answer: 20
Let each bookmark cost p dollars, so each storybook costs (p + 12) dollars. 4(p + 12) + 5p = 120, so 9p + 48 = 120, giving 9p = 72 and p = 8. Each storybook costs 8 + 12 = 20 dollars.
Section C
Open Answer (Achievers) — Questions 26 to 31
(+5)
26
algebra
hard
5 keychains and 6 magnets cost 98 dollars. A keychain and a magnet cost 17 dollars. How much does a magnet cost in dollars? [Enter your answer only between 0 and 9999]
Show answer
Answer: 13
Let a keychain cost k dollars and a magnet cost m dollars. k + m = 17, so k = 17 − m. Substituting: 5(17 − m) + 6m = 98, so 85 + m = 98, giving m = 13.
27
data-handling
hard
The graph below shows the oranges picked by 3 farmers. There is a smudge covering part of the graph.
The total number of oranges picked by Farmer Wong and Farmer Ali was 4 times the number of oranges picked by Farmer Devi. How many oranges did Farmer Devi pick? [Enter your answer only between 0 and 9999]
Show answer
Answer: 20
Farmer Wong picked 48 oranges and Farmer Ali picked 32 oranges, so together they picked 48 + 32 = 80 oranges. Since this is 4 times Farmer Devi's amount, Farmer Devi picked 80 ÷ 4 = 20 oranges.
28
perimeter
hard
Maya draws a figure as shown below. It is made up of 2 identical squares P and 1 square Q. The length of square Q is 5 cm. What is the perimeter of the whole figure in cm? [Enter your answer only between 0 and 9999]
Show answer
Answer: 92
The total height of the figure (2 squares P plus square Q, stacked corner to corner) is 23 cm, so 2 × (side of P) + 5 = 23, giving side of P = 9 cm. Since the squares only touch at single corner points, no edges are shared, so the perimeter of the whole figure is simply the sum of the three squares' own perimeters: 2 × (4 × 9) + (4 × 5) = 72 + 20 = 92 cm.
29
number-patterns
hard
A number pattern is shown below:
4, 6, 6, 9, 4, 6, 6, 9, 4, 6, 6, 9, ...
What is the sum of the first 50 numbers of the number pattern? [Enter your answer only between 0 and 9999]
Show answer
Answer: 310
The pattern repeats every 4 numbers: 4, 6, 6, 9, with a sum of 25 per group. 50 numbers = 12 complete groups (48 numbers) plus 2 more numbers (4, 6). Sum = (12 × 25) + (4 + 6) = 300 + 10 = 310.
30
word-problem
hard
A shop sells notepads at the prices shown.
1 notepad costs $4.
1 pack of 5 notepads costs $16.
Special Offer: Buy 2 packs of notepads, get 1 notepad free.
Mia wants to buy 17 notepads. What is the least amount (in dollars) she needs to spend? [Enter your answer only between 0 and 9999]
Show answer
Answer: 52
Buying 3 packs (15 notepads) for 3 × $16 = $48 triggers the special offer once (using 2 of the 3 packs), giving 1 free notepad — so 3 packs actually give her 16 notepads for $48. She still needs 1 more notepad, bought singly for $4. Least amount spent = $48 + $4 = $52.
31
algebra
hard
Store X had 720 more toys than Store Y. Store Z had 4 times as many toys as Store Y. After 900 toys were sold from Store X, there were 3 times as many toys in Store Y as in Store X. How many more toys were there in Store Z than in Store Y? [Enter your answer only between 0 and 9999]
Show answer
Answer: 810
Let Store Y = y. Store X = y + 720. Store Z = 4y. After selling 900 from Store X, Store X has y + 720 − 900 = y − 180. Since Store Y = 3 × (new Store X): y = 3(y − 180), so y = 3y − 540, giving 2y = 540 and y = 270. Store Z = 4 × 270 = 1080. Store Z − Store Y = 1080 − 270 = 810.