CCAT math questions: the 7 types, shortcuts and worked examples
CCAT math questions are short word problems and number questions that you solve without a calculator in about 18 seconds each. There are seven recurring types: percentages, ratios, averages, rates, probability, comparing numbers and simple algebra. The maths is easy; the clock isn't. Knowing the type on sight and using the right shortcut is what makes the difference. Math sits in the CCAT's "math and logic" area alongside logic questions.
- 7 types: percentages, ratios, averages, rates, probability, comparisons, algebra word problems.
- No calculator, about 18 seconds per question.
- Most traps are wrong-base percentages, total vs remainder and odds vs probability.
- On forge's free numerical tests, percentage and ratio questions are answered correctly only 59% of the time.
- forge's CCAT-style bank has 160 math questions across 10 timed drills and 10 simulations.
Free sample question
CCAT math question
Rates, averages, probability, discounts and age problems. No calculator: that's the point.
One question in the real format, with the worked solution · no signup
Quick summary
- CCAT math covers seven familiar problem types, all at secondary school level.
- You get no calculator and roughly 18 seconds per question.
- Shortcuts (10% first, cancel before multiplying, decimals for comparisons) save the most time.
- Watch for the wrong base in percentages and "how many more" versus "how many in total".
- Skip long word problems early and return if there's time.
The seven types of CCAT math question
| Type | Example | Fast method |
|---|---|---|
| Percentages | A $40 item after a 20% discount | Find 10%, then scale; for reverse %, divide by 0.8 |
| Ratios | Split 60 in the ratio 2:3 | Total parts (5), one part (12), multiply |
| Averages | The average of five numbers is 18; find the missing one | Average × count = total |
| Rates | 6 litres per 100 km: fuel for 350 km? | Scale the unit: 3.5 × 6 |
| Probability | 7 red and 9 blue counters: P(red)? | Favourable ÷ total = 7/16 |
| Comparisons | Largest of 3/5, 0.58, 62%, 5/8 | Convert everything to decimals |
| Algebra word problems | Mia is 3 times her brother's age… | Call the unknown x, write one equation |
forge's CCAT-style question bank reflects the same mix: percentages and unit rates are the most common math subtypes, followed by averages, probability and algebra.
$96 is 80% of the original. 96 ÷ 0.8 = 120, so the original was $120.
Shortcut: 96 ÷ 8 = 12 (that's 10%), × 10 = $120. Adding 20% to $96 gives $115.20, the trap answer.
Total work = 4 × 6 = 24 worker-hours. With 3 workers: 24 ÷ 3 = 8 hours.
Trap: fewer workers take longer, so any answer under 6 hours can be ruled out immediately.
Current total = 4 × 70 = 280. Target total = 5 × 72 = 360. Fifth score = 360 − 280 = 80.
No-calculator shortcuts worth learning
- Percentages from 10%: 10% of 340 is 34, so 15% is 34 + 17 = 51.
- Cancel before multiplying: 36 × 25 ÷ 9 = 4 × 25 = 100.
- Fractions to decimals: know 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, 1/6 ≈ 0.167.
- Estimate, then match: if the options are far apart, a rough answer is enough.
- Work backwards: for age or algebra problems, test the options in the equation.
Our mental maths guide and percentage shortcuts go further.
Drill CCAT math on forge
10 timed CCAT-style math drills (10 questions in 3 minutes) with worked answers, plus full simulations.
Start CCAT mathRelated guides
- CCAT test: format and scoring
- Free CCAT practice test
- CCAT logic questions
- Ratio questions
- Numerical reasoning tests
Source notes
Pace and the no-calculator rule come from Criteria's candidate CCAT page (checked 2 October 2026). Subtype frequencies describe forge's CCAT-style question bank; the 59% figure comes from answers on forge's free numerical tests (re-graded 30 September 2026). All questions are written by forge. CCAT is a trademark of Criteria Corp; forge is independent and not affiliated with Criteria.
Frequently asked questions
What kind of math is on the CCAT?
Everyday arithmetic and word problems: percentages and discounts, ratios, averages, unit rates such as speed or fuel use, simple probability, comparing fractions and decimals, and short algebra word problems. Nothing beyond secondary school level.
Can I use a calculator for CCAT math questions?
No. Criteria doesn't allow calculators on the CCAT. The numbers are chosen so the sums work mentally or with a line of rough working.
How long should a CCAT math question take?
The whole test averages 18 seconds per question. Simple math items should take 10 to 20 seconds; skip multi-step word problems that take longer and come back if time allows.
How do I get faster at CCAT math?
Learn a few shortcuts (10% then adjust for percentages, cancelling before multiplying, converting fractions to decimals), recognise the common problem types, and practise at 18 seconds per question without a calculator.
Is CCAT math harder than SHL numerical reasoning?
The maths itself is simpler, but you have far less time and no calculator. SHL numerical tests use data tables and allow a calculator; the CCAT uses short standalone problems at speed.
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