Year 4 sits ICAS Paper B. Six practice maths questions at the Paper B level, from the opening questions to the hard end, where Distinction and High Distinction are decided.
The paperICAS Mathematics Paper B: 40 multiple-choice questions in 45 minutes. ICAS English Paper B: 45 questions in 45 minutes.
WhenSat at school, in the school's sitting window (usually August to September).
AwardsHigh Distinction, Distinction, Credit, Merit and Participation, decided by rank within the year level.
The rampThe questions get harder from start to finish; the last third decides the top awards.
Six practice questions, easy to hard
Try each one before opening the answer: the working shows the step where a wrong answer usually goes wrong.
1 · ICAS Paper B · Mathematics · Warm-up
Noah compared the masses of three things on a balance scale. Which list puts them in order from heaviest to lightest?
melon, mango, apple
mango, apple, melon
melon, apple, mango
apple, melon, mango
Show the answer and the working
Answer: C (melon, apple, mango)
On a balance the heavier side goes down. So the melon is heavier than the apple, and the apple is heavier than the mango. From heaviest: melon, apple, mango.
Fastest method: On each scale, the lower pan holds the heavier thing. The thing that is on both scales is in the middle.
The trap: thinking the higher pan is heavier, which turns the whole order round
2 · ICAS Paper B · Mathematics · Warm-up
Max buys a puzzle for $6.70 and a magazine for $1.10. He pays with a $20 note. How much change should Max get?
$7.80
$12.20
$18.90
$13.30
Show the answer and the working
Answer: B ($12.20)
Altogether the two things cost $6.70 + $1.10 = $7.80, so the change is $20 − $7.80 = $12.20.
Fastest method: Count on from the cost to the note (to the next dollar first), or subtract and check by adding back.
The trap: taking away only one of the prices, or giving the total cost instead of the change
3 · ICAS Paper B · Mathematics · Middle of the paper
A number machine uses the same rule every time. When 5 goes in, 12 comes out. When 4 goes in, 11 comes out. Which rule could the machine be using?
Double the number, then add 2
Multiply the number by 3, then take away 3
Add 7
Add 1, then double the answer
Show the answer and the working
Answer: C (Add 7)
'Add 7' turns 5 into 12 and 4 into 11. Each other rule fits the first pair but not the second.
Fastest method: Test each rule on the number that goes in, step by step, and check EVERY pair.
The trap: checking only the first pair, or doing the two steps of a rule in the wrong order
4 · ICAS Paper B · Mathematics · Middle of the paper
The marks on a number line are equally spaced. The second mark is 500 and the sixth mark is 600. What number is at the ninth mark?
700
650
675
660
Show the answer and the working
Answer: C (675)
From the second to the sixth mark there are 4 gaps covering 600 − 500 = 100, so each gap is 25. The ninth mark is 3 gaps after 600: 600 + 3 × 25 = 675.
Fastest method: Count the GAPS between the two labelled marks, find what one gap is worth, then count on.
The trap: counting the marks instead of the gaps, so each gap seems smaller
5 · ICAS Paper B · Mathematics · The hard end
Hugo joined five identical squares to make a rectangle 5 squares long and 1 square wide. The perimeter of the rectangle is 48 cm. What is the perimeter of one small square?
16 cm
4 cm
12 cm
20 cm
Show the answer and the working
Answer: A (16 cm)
Going round the outside of the rectangle you pass 12 sides of small squares. So one side is 48 ÷ 12 = 4 cm, and the perimeter of one small square is 4 × 4 = 16 cm.
Fastest method: Perimeter is the distance all the way round. Count the 1 cm edges, or find one side first and then go round.
The trap: dividing the perimeter by the number of squares, or giving the length of one side instead of the perimeter
6 · ICAS Paper B · Mathematics · The hard end
In this number sentence, each ★ stands for the same number. 52 − ★ = 10 + ★ What number does ★ stand for?
20
42
22
21
Show the answer and the working
Answer: D (21)
Try ★ = 21: 52 − 21 = 31 and 10 + 21 = 31. Both sides match. (The gap 52 − 10 = 42 is shared among the 2 stars: 42 ÷ 2 = 21.)
Fastest method: Both sides must be equal; try a value for ★ in BOTH places, then adjust.
The trap: working out the difference of the numbers and forgetting that the star is used more than once
Number: place value to tens of thousands, the four operations, simple fractions, patterns.
Measurement and space: time, length, area by counting, angles compared with a right angle, 2D and 3D shapes, maps and grids.
Data and chance: tables, graphs and simple chance. English practice runs on full reading passages, so it is not sampled here.
How the practice works
A free diagnostic first: it finds the skills not yet held and names the step behind every miss.
Then every week: a 20-question practice paper on those skills, a mock on Saturday on the real clock, and a report to you on Sunday.
Marked by code; a wrong answer is worked through step by step before the right one is shown.
Questions parents ask
Which ICAS paper does Year 4 sit?
Paper B. Year 3 sits Paper A, Year 5 Paper C and Year 6 Paper D.
Is ICAS harder than school maths?
The early questions match the year's curriculum; the last third goes further and rewards reasoning, which is where the practice here spends most of its time.
Are these real ICAS questions?
No. Each question is an original variation of a task type found on real Paper B papers; no past paper is reproduced.