What Maths Level Am I? 40-Question Placement Self-Check
This is a diagnostic self-check, not an official school-placement test. The page title states the question many learners ask; the tool answers with a readiness profile rather than a school-stage label. Work without a calculator unless a question clearly needs one. Do not look up answers.
Suggested time: 45–60 minutes. If you cannot start a question after a reasonable attempt, leave it unanswered and continue.
A. Number and Arithmetic
1. What is 48 ÷ 6?
2. Which is greatest?
3. 3,407 + 895 =
4. 15% of 240 is
5. Which number is divisible by 9?
6. 2⁵ × 2³ =
7. √144 + √25 =
8. Write 0.00072 in standard form.
B. Fractions, Ratio and Proportion
9. 3/4 + 1/6 =
10. 5/8 of 96 =
11. Simplify 18:24.
12. $80 is increased by 25%. New value?
13. If 4 notebooks cost $10, 10 notebooks cost
14. A map scale is 1:50,000. 3 cm represents
15. x is directly proportional to y. If x=18 when y=6, x when y=14 is
16. A price falls from $250 to $200. Percentage decrease?
C. Algebra and Functions
17. Solve 3x + 5 = 20.
18. Expand 4(x − 3).
19. Factorise x² + 7x + 12.
20. If f(x)=2x²−1, f(3)=
21. Solve x² − 9 = 0.
22. The gradient through (2,5) and (6,13) is
23. Simplify (x²y³)(x⁴y).
24. If 2ˣ = 32, x =
D. Geometry and Measurement
25. Angles in a triangle sum to
26. Area of a rectangle 8 cm by 5 cm?
27. A right triangle has legs 6 and 8. Hypotenuse?
28. Circumference of a circle of radius 4 is
29. Interior angle of a regular hexagon?
30. Similar figures have linear scale factor 3. Area scale factor?
31. tan θ = opposite /
32. Volume of a cylinder radius 3, height 5?
E. Data, Probability and Problem Solving
33. Mean of 4, 6, 8, 12?
34. Probability of an even number on a fair six-sided die?
35. Median of 3, 5, 7, 20, 100?
36. A bag has 3 red and 7 blue counters. P(red)=
37. If P(A)=0.4, then P(not A)=
38. A car travels 150 km in 2.5 h. Average speed?
39. A quantity doubles every 3 hours. After 9 hours it is multiplied by
40. A student says “correlation proves causation.” Best response?
World Mathematics route: return to the World Mathematics Atlas for the wider map behind this diagnostic: school levels, mathematical objects, examinations and progression routes.
Mathematics placement self-check: turn 40 questions into a diagnostic map, not a label
A placement quiz is a sample
Forty questions cannot measure every curriculum detail. Treat the result as evidence about current readiness and possible gaps, not an official school placement or ability classification.
Sample across prerequisite chains
Include number, algebra, functions, geometry, statistics and problem solving at increasing demand. A later-topic error may originate in an earlier prerequisite.
Separate accuracy from confidence
Ask students to mark whether they knew, guessed or were unsure. A correct guess and a confidently correct solution provide different diagnostic evidence.
Record working
For Mathematics, the route matters. Two students with the same wrong answer may need completely different repairs.
Use stop rules
If a learner is repeatedly unable to access a level, stop rather than force the remaining questions. Move down to prerequisites and preserve motivation.
Do not convert the score directly to a school grade
The quiz is not standardised against SEAB, Cambridge, IB or AP populations. Avoid claims such as ’32/40 means Grade A’.
Create a gap profile
Report secure domains, unstable domains and prerequisite gaps. Recommend what to learn next rather than a single rank.
Retest after repair
Use parallel questions, not the exact memorised items. Improvement should survive changed numbers and representations.
For tutors
Use the self-check before the first lesson, then validate it through conversation and observed working. It should accelerate diagnosis, not replace professional judgement.
For learners
The useful output is a route: what can I already do, what breaks next, and which prerequisite gives the highest return if repaired now?
Examination tools route: Mathematics Examination Tools & Reference → Singapore Mathematics Hub → World Mathematics Atlas.