1. The shape below is a quadrilateral. Its corner angles are marked rather than drawn accurately, and three of the four are given. Work out angle x.
ICAS Mathematics Paper F (Year 8)
Paper F is sat by Year 8 students. Format matches Papers D and E — 35 multiple-choice questions plus five that ask for a number typed in — over 60 minutes.
This is the hardest paper in the range, and the gap between a comfortable result and a struggle is wider here than anywhere below it.
Last updated: 5 October 2026
What Year 8 brings
Linear equations become routine, including ones with the unknown on both sides and ones involving fractions. Pythagoras arrives, and with it the first questions where a diagram has to be interpreted before it can be used. Rates and ratios move beyond the introductory form. Percentage change — increase, decrease, and working backwards to the original — turns up often. Surface area and volume extend to composite solids. Congruence appears. Probability starts handling two events rather than one.
What makes Paper F hard
Not the content. Most Year 8 students have met most of it.
What separates results is how far the question sits from the method. A school question tells you it is about Pythagoras. A Paper F question gives you a situation, and recognising that it is a Pythagoras problem is most of the work. The same applies to percentage change, where the difficulty is almost always identifying what the original amount was.
The integer-answer questions at the end compound this: no options to test against, and by then the clock is real.
Where marks go
- Questions needing a diagram to be read before it can be used — the figure is given, but which lengths matter is not
- Working backwards on percentage change — finding the original after an increase is a different operation from finding the increase, and the two get swapped
- Multi-stage problems where each stage is easy and the sequence is not
- Pacing into the integer tail, the same trap as Papers D and E
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 F
Do fewer questions, more slowly, and spend the time on the first thirty seconds of each one — deciding what kind of problem it is. That decision is what the paper tests. Students who practise by doing many questions of a known type get faster at something Paper F does not ask for.
Then sit full 60-minute papers, because the end of the paper is where the difference shows.
Common questions
Which year level sits ICAS Paper F?
Year 8. ICAS names its papers by letter rather than by year — Paper A is Year 3 and Paper F is Year 8 — so a Year 8 student sits Paper F.
How long is Maths Paper F?
40 questions in 60 minutes.
How should a Year 8 student practise for Paper F?
Fewer questions, more slowly, with the time spent on the first thirty seconds of each one — deciding what kind of problem it is. That decision is what the paper tests, and doing many questions of a known type does not rehearse it.
Year 8 also sits: English Paper F · Science Paper F
Sample questions
Try each one first, then open the answer and worked solution under it.
Answer and worked solution
Correct answer: A
The interior angles of any quadrilateral add to 360°.
80 + 95 + 110 = 285.
x = 360 − 285 = 75°.
x = 75°.
2. Solve: x ÷ 2 + x ÷ 4 = 9. x =
Answer and worked solution
Correct answer: 12
Both terms are parts of the same x, so combine them. Rewrite x ÷ 2 as 2x ÷ 4 so the two shares have the same name.
Two quarters of x plus one quarter of x is three quarters of x, so 3x ÷ 4 = 9.
Multiply both sides by 4 and then divide by 3: x = 12. Checking: half of 12 is 6, a quarter is 3, and 6 plus 3 does make 9.
x = 12.
3. A ferry crossing takes 7 hours 35 minutes. The ferry leaves at 22:45. At what time does it dock?
Answer and worked solution
Correct answer: C
Bridge midnight first: 22:45 + 1 h 15 min reaches 24:00 (midnight).
That leaves 7 h 35 min − 1 h 15 min = 6 h 20 min to travel after midnight.
Midnight + 6:20 = 06:20.
The ferry docks at 06:20.
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More ICAS maths papers: Paper E (Year 7)
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