Mathematics - Post-UTME Study Guide
Mathematics in the Post-UTME covers number work, algebra, geometry, trigonometry, statistics and probability. Most items reward a clean method rather than lengthy computation.
Core rules
- Follow BODMAS and convert units before calculating.
- Indices: a^m × a^n = a^(m+n); a^0 = 1; log laws mirror index laws.
- Linear equations: eliminate one variable by substitution or elimination, then check both equations.
- Circle theorems: angle at centre is twice angle at circumference; angle in a semicircle is 90°.
- Trigonometry: SOHCAHTOA for right triangles; sine and cosine rules for non-right triangles.
- Statistics: mean = sum of values ÷ number of values; probability of an event = favourable outcomes ÷ total outcomes.
Worked example
Solve 2x + 3y = 12 and x − y = 1. From the second equation, x = y + 1. Substitute: 2(y + 1) + 3y = 12, so 2y + 2 + 3y = 12, 5y = 10, y = 2. Then x = 2 + 1 = 3. Check: 2(3) + 3(2) = 6 + 6 = 12, and 3 − 2 = 1. The solution is x = 3, y = 2.
Traps
Do not drop negative signs when expanding brackets. Do not use degree mode on a calculator for radian questions, or vice versa. In probability, remember P(not A) = 1 − P(A). In mensuration, keep all lengths in the same unit before substituting. Do not assume a diagram is drawn to scale.