Section A
Multiple-choice — Questions 1 to 15
(+2)
1
number-sense
easy
Which of the following is the greatest even number?
Answer: 1
Even numbers among the choices: 730 and 698. 821 and 299 are odd. The greater of 730 and 698 is 730.
2
multiplication
easy
The result of 6 × 3 is not the same as _________________.
Answer: 3
6 × 3 = 18. Option 1: 6+6+6=18 (same). Option 2: 6 groups of 3 = 18 (same). Option 3: 6×6×6=216 (different — this is the answer). Option 4: 3+3+3+3+3+3=18 (same).
3
fractions
easy
What fraction of the figure below is shaded?
Answer: 3
The figure has 10 equal cells in total, and 4 of them are shaded, so the shaded fraction is 4/10.
4
mass
medium
What is the mass of two such identical chickens as shown below?
Answer: 4
The scale needle points to 330 g for one chicken (the tick 3 small marks past the 300 g mark, at 10 g per tick). Two identical chickens: 330 × 2 = 660 g.
5
money
easy
Alvin had some notes and coins as shown below. How much did Alvin have in total?
Answer: 4
Notes: $5 + $50 + $2 = $57. Coins: 50c + 10c + 5c + 20c = 85c. Total = $57 + $0.85 = $57.85.
6
addition
easy
Mdm Wong sold 272 fishballs in the morning. She sold 129 fishballs in the afternoon. How many fishballs did she sell altogether?
Answer: 4
272 + 129 = 401 fishballs.
7
time
medium
Ravi did his homework during the times as shown below. How long did Ravi take to do his homework?
Answer: 2
Start clock shows 3:30 (hour hand between 3 and 4, minute hand at 6). End clock shows 5:00 (hour hand at 5, minute hand at 12). From 3:30 to 5:00 is 1 h 30 min.
8
multiplication
easy
3 boys and 5 girls went shopping. Each child spent $4. How much money did they spend altogether?
Answer: 3
3 + 5 = 8 children. 8 × $4 = $32.
9
picture-graph
medium
The following picture graph shows the favourite sports of all students in Primary 2G class. Some information was covered by an ink spillage. Study the picture graph carefully and answer the question. There are 9 more students who like Soccer than Softball. How many students are in Primary 2G altogether?
Answer: 4
Each circle stands for 3 students. Badminton = 2 circles = 6. Basketball = 4 circles = 12. Soccer = 5 circles = 15. Soccer has 9 more than Softball, so Softball = 15 − 9 = 6. Total = 6 + 12 + 15 + 6 = 39.
10
measurement
easy
Look at the diagram below. How far is Siti's house from the school?
Answer: 4
150 m + 280 m + 120 m = 550 m.
11
measurement
easy
Look at the diagram below carefully. The pencil is ___ cm longer than the eraser. What is the missing number in the box?
Answer: 3
The pencil runs from 0 cm to 24 cm (24 cm long). The eraser runs from 6 cm to 12 cm (6 cm long). The pencil is 24 − 6 = 18 cm longer than the eraser.
12
fractions
medium
Arrange the following fractions in order, beginning with the greatest fraction: 1/8, 1/3, 1/11, 1/5.
Answer: 4
For unit fractions, a smaller denominator means a larger fraction. Ordering the denominators from smallest to largest: 3, 5, 8, 11. So greatest to least: 1/3, 1/5, 1/8, 1/11.
13
number-patterns
medium
Study the number pattern shown below. There are 2 missing numbers in the pattern (X and Y). What is the sum of the 2 missing numbers?
Answer: 3
Each pentagon's top number is the sum of its two bottom numbers: 10+14=24 ✓, 26+16=42 ✓. So 33+X=50 → X=17, and Y=32+20=52. X+Y = 17+52 = 69.
14
shape-patterns
medium
Look at the pattern below. What is the missing solid figure (the next two shapes)?
Answer: 1
The pattern repeats every 5 shapes: rectangular prism, cylinder, cube, thin prism, oval cylinder. After the 11th shape (rectangular prism, the start of a new cycle), the next two are position 12 (cylinder) and position 13 (cube).
15
number-patterns
medium
Look at the number pattern below. What is the value of the letter M?
Answer: 2
The rule is: center = (top × right) + (left × bottom). Check: 8×3 + 4×9 = 24+36 = 60 ✓. 10×5 + 2×7 = 50+14 = 64 ✓. For the third cross: 6×4 + 2×M = 34 → 24 + 2M = 34 → M = 5.
Section B
Free-response — Questions 16 to 25
(+4)
16
addition-subtraction
easy
Jane baked some cookies. She gave 85 cookies to her mother. Then she gave 290 cookies to her friends. She had 128 cookies left. How many cookies did Jane bake at first?
Answer: 503
85 + 290 + 128 = 503 cookies.
17
figure-counting
medium
Jamie had some identical sticks. She used 4 sticks to make a square. After making 8 identical squares, Jamie had 3 sticks left. How many sticks did Jamie have altogether?
Answer: 35
The diagram shows the 8 squares touching only at their corners (no shared sides), so each square uses its own 4 sticks: 8 × 4 = 32 sticks used. Plus the 3 sticks left over: 32 + 3 = 35 sticks altogether.
18
money
easy
In a café, an ice-cream cone cost $2 and a hotdog bun cost $3.50. Mary bought 2 hotdog buns and 4 ice-cream cones. How much change did she receive after she had given the cashier a fifty-dollar note?
Answer: 35
Cost = 2 × $3.50 + 4 × $2 = $7 + $8 = $15. Change from $50 = $50 − $15 = $35.
19
ratio
medium
2 mugs of water are needed to fill a beaker completely. 8 mugs of water are needed to fill a pail completely. How many beakers of water will be needed to fill up 5 such identical pails completely?
Answer: 20
1 pail = 8 mugs = 4 beakers (since 1 beaker = 2 mugs). 5 pails = 5 × 4 = 20 beakers.
20
picture-graph
medium
The picture graph shows the favourite food of some children in a club. There were 80 children in the club altogether. How many children did not choose any of these food as their favourite food?
Answer: 12
Each square stands for 4 children, each half-square for 2. Noodles: 3.5 squares = 14. Sandwich: 3 squares = 12. Nuggets: 5 squares = 20. Fish balls: 1.5 squares = 6. Fries: 4 squares = 16. Total who chose = 14+12+20+6+16 = 68. Did not choose = 80 − 68 = 12.
21
age-problems
medium
3 years ago, Wendy was 6 years old. This year, Wendy's father is 5 times as old as she is. How old will her father be in 8 years' time?
Answer: 53
Wendy is now 6+3=9 years old. Her father is now 9×5=45. In 8 years, he will be 45+8=53.
22
word-problems
medium
During a sale, 1 free box of tissue papers is given for every 3 boxes of tissue papers bought. Miss Lim needs 28 boxes of tissue papers altogether. How many boxes of tissue papers does Miss Lim need to buy?
Answer: 21
Every 4 boxes obtained = 3 bought + 1 free. 28 ÷ 4 = 7 groups. Boxes bought = 7 × 3 = 21 (and free = 7, giving 21+7=28 total).
23
word-problems
easy
Mr Lim has 10 bottles of orange juice. Each bottle contains 2 ℓ of orange juice. He shares 3 bottles of the orange juice with his children. How many litres of orange juice is left?
Answer: 14
Bottles left = 10 − 3 = 7. Litres left = 7 × 2 = 14 ℓ.
24
word-problems
medium
Belle had 212 stickers. Mandy had 176 stickers. Belle then bought some more stickers. In the end, Mandy had 64 fewer stickers than Belle. How many stickers did Belle buy?
Answer: 28
Let Belle buy x stickers. (212+x) − 176 = 64 → 212+x = 240 → x = 28.
25
number-sense
hard
Annie wrote a 3-digit odd number on a piece of paper. The number was less than 500. All the digits were different. The digit in the ones place was 1 more than the digit in the tens place. The sum of the 3 digits was 21. What number did Annie write?
Answer: 489
Let the hundreds digit be H, tens digit T, ones digit T+1. H + T + (T+1) = 21 → H + 2T = 20. Since the number is < 500, H is 1–4. Testing H=1,2,3,4 for an integer T: only H=4 gives T=8 (an integer), so ones = 9. Number = 489. Check: 489 < 500, odd, digits 4,8,9 all different, ones(9)=tens(8)+1, sum=4+8+9=21. All conditions satisfied.
Section C
Free-response — Questions 26 to 31
(+5)
26
word-problems
medium
Ribbon A is 42 cm long. It is 16 cm longer than Ribbon B. Ribbon C is twice as long as Ribbon B. What is the total length of the 3 ribbons? Give your answer in cm.
Answer: 120
Ribbon B = 42 − 16 = 26 cm. Ribbon C = 2 × 26 = 52 cm. Total = 42 + 26 + 52 = 120 cm.
27
number-patterns
hard
There were 26 children in a group. All the children were lined up in a row. Every 2nd child held a book and every 3rd child carried a bag. The first 6 children lining in the row were shown below. How many children were not holding any item?
Answer: 9
Children holding a book: multiples of 2 up to 26 → 13 children. Children carrying a bag: multiples of 3 up to 26 → 8 children (3,6,...,24). Children holding both (multiples of 6): 4 children (6,12,18,24). Holding at least one item = 13+8−4 = 17. Not holding any item = 26 − 17 = 9.
28
number-sense
medium
Alicia had a book with a total of 100 pages. She flipped the pages and counted the number of times the digit '1' appeared in the book. How many times did the digit '1' appear from Page 1 to 100?
Answer: 21
Digit '1' in the ones place: 1,11,21,...,91 → 10 times. Digit '1' in the tens place: 10–19 → 10 times. Page 100 contributes one more '1' (hundreds place). Total = 10 + 10 + 1 = 21.
29
word-problems
hard
There were 34 students in a class. All the students were seated in a circle and the teacher stood in the middle of the circle. A teacher gave each student 1 book and she moved in the circular direction. She repeated the movement until she ran out of books. In the end, only 5 students received 3 books. How many books did the teacher give in total?
Answer: 73
After 2 full rounds, all 34 students have 2 books each: 34×2=68 books given. She then starts a 3rd round but runs out after giving a 3rd book to only 5 students: +5 books. Total = 68 + 5 = 73 books.
30
number-patterns
medium
Bernice likes to do number coding. This is one number coding pattern that she has created: 2★3 = 2+3+4 = 9; 5★4 = 5+6+7+8 = 26; 3★6 = 3+4+5+6+7+8 = 33. Following the same pattern, 8★5 = ?. What is the missing value?
Answer: 50
A★B means the sum of B consecutive integers starting from A. So 8★5 = 8+9+10+11+12 = 50.
31
measurement
hard
The diagram below shows 3 identical strings, each measuring 90 cm. The strings are lined up as shown below. Find the value of the missing length in the box. Give your answer in cm.
Answer: 65
Both rows span the same total distance from the same left edge. Bottom row total = 90 (string B) + 23 (gap) + 90 (string C) = 203 cm. Top row total = 48 + 90 (string A) + ? = 138 + ?. Setting them equal: 138 + ? = 203 → ? = 65 cm.