Mathematics and Mental Ability: Algebra, Probability and Reasoning
Mathematics and Mental Ability on KUUMAT tests algebra, trigonometry, coordinate geometry, calculus, vectors, probability and statistics, plus reasoning items such as series, coding, blood relations, direction sense, and syllogisms. Numerical accuracy matters, but many reasoning questions are solved faster by writing a small table or diagram than by inspecting options.
Core rules
- Algebra: state domain restrictions before cancelling; a quadratic ax²+bx+c=0 has roots [−b±√(b²−4ac)]/2a.
- Trigonometry: sin²θ+cos²θ=1; check the quadrant before choosing a sign.
- Coordinate geometry: distance √((x₂−x₁)²+(y₂−y₁)²); slope (y₂−y₁)/(x₂−x₁).
- Probability: P(A and B)=P(A)P(B|A); “without replacement” changes the denominator.
- Mental ability: in a series, test first differences, then ratios; in blood relations, draw a family tree; in syllogisms, accept only what the premises force.
Worked example
A bag has 3 red and 5 blue balls. Two are drawn without replacement. P(both red) = (3/8)×(2/7) = 6/56 = 3/28. The second denominator is 7 because one ball has already been removed; using 8 would be sampling with replacement.
Traps
- Squaring an equation and keeping extraneous roots.
- Forgetting that tanθ is undefined at 90° and 270°.
- Mixing percentage points with percent change.
- In reasoning, assuming real-world knowledge instead of the stated premises.
- Rounding too early in multi-step calculations.