1. Which is LARGER: 1 over 4 of 20, or 1 over 5 of 20?
ICAS Mathematics Paper B (Year 4)
Paper B is sat by Year 4 students. Same shape as Paper A — forty questions in 45 minutes, mostly multiple choice, across the same five areas — but the content moves on, and one topic in particular starts doing the damage.
Last updated: 5 October 2026
What changes from Paper A
Multiplication stops being repeated addition and starts being expected as fact. Division questions begin to involve remainders that mean something in the context. Fractions move from "shade a third of this shape" to comparing and finding equivalents, and decimals appear for the first time as tenths and hundredths.
Measurement adds area by counting squares, and angles turn up as amounts of turn rather than as things to measure. Chance appears as language — likely, unlikely, certain — rather than as numbers.
The topic to watch
Equivalent fractions. Year 4 is where a child either builds a picture of what a fraction is or starts memorising rules that will not hold up. ICAS tends to ask it in a form school worksheets do not: which of these is not equal to the others, or where a fraction sits between two other numbers.
Multi-step word problems are the other one to watch, where step one is right and step two is rushed. That pattern starts here and does not go away for the rest of the series.
What the mark will look like
ICAS marks run lower than school tests by design. The paper keeps stretching students well past year level, so a result that looks disappointing on a school scale can be a strong ICAS result — read it against the distribution rather than as a percentage.
How to prepare for Paper B
Practise fractions with something physical before practising them on paper — folding, cutting, sharing. A child who can see why two quarters and one half are the same thing will answer the ICAS version of the question; a child who memorised "multiply top and bottom" often will not.
For everything else, full-length timed papers are the most useful preparation. Forty questions in 45 minutes is a little over a minute each, and pacing is a skill in itself at this age.
Common questions
Which year level sits ICAS Paper B?
Year 4. ICAS names its papers by letter rather than by year — Paper A is Year 3 and Paper F is Year 8 — so a Year 4 student sits Paper B.
How long is Maths Paper B?
40 questions in 45 minutes.
How far past Year 4 does Paper B go?
The paper starts at about year level and keeps climbing, so the last questions are meant to stretch students well beyond Year 4. Not finishing comfortably is the normal experience, not a warning sign.
Year 4 also sits: English Paper B · Spelling Paper B · Science Paper B
Sample questions
Try each one first, then open the answer and worked solution under it.
Answer and worked solution
Correct answer: C
A quarter of 20 means sharing 20 into 4 equal groups, which gives 5 in each group.
A fifth of 20 means sharing the same 20 into 5 equal groups, which gives 4 in each group.
5 is more than 4, so a quarter of 20 is larger. Sharing among fewer groups leaves more in each one.
1 over 4 of 20 is larger, because 5 is more than 4.
2. Mia flips TWO coins at the same time. Which list shows ALL the different results she could get?
Answer and worked solution
Correct answer: A
Go coin by coin: the first coin can be heads or tails, and so can the second.
That gives the pairs: head-head, head-tail, tail-head, tail-tail.
As results, that is: two heads, one of each (which happens two ways), or two tails — three different results.
Two heads, two tails, or one of each — those are all the possibilities.
3. The picture graph shows the goals scored by three players. The coach wants Ali and Kiri each to reach Ben's number of goals. How many MORE goals do Ali and Kiri need between them?
Answer and worked solution
Correct answer: C
Read the three rows: Ali has 6 goals, Ben has 9 and Kiri has 4.
Work out each shortfall against Ben's 9. Ali is 3 short, and Kiri is 5 short.
The question asks for the two of them together, so three and five make 8 more goals.
Ali and Kiri need 8 more goals between them.
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More ICAS maths papers: Paper A (Year 3) · Paper C (Year 5)
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