Mathematics
Mathematics
The PMA entrance exam's Mathematics subtest checks computational fluency and multi-step reasoning without a calculator: arithmetic, algebra, geometry, and introductory trigonometry, usually as five-option multiple-choice items.
Core rules to have automatic
- Order of operations (PEMDAS), fraction–decimal–percent conversions, ratio and proportion, averages.
- Linear equations and systems; inequalities (flip the sign when multiplying or dividing by a negative); exponent laws; factoring and the quadratic formula.
- Geometry: angle relationships, triangle inequality, Pythagorean theorem, 30-60-90 and 45-45-90 triangles, area and perimeter, circle circumference and area, volume of prisms, cylinders, cones, and spheres.
- Trigonometry: SOH-CAH-TOA and exact values at 0°, 30°, 45°, 60°, 90°.
- Word problems: define the variable, translate each clause into an equation, solve, then check units and reasonableness.
Worked example
A rectangle's length is 3 cm more than twice its width, and its perimeter is 36 cm. Find its area. Let width = w, so length = 2w + 3. Perimeter: 2(w + 2w + 3) = 36, so 6w + 6 = 36 and w = 5. Length = 13. Area = 5 × 13 = 65 cm². The trap is stopping at 5 or 13; the question asks for area.
Traps that cost marks
- Answering perimeter when area is requested, or giving a radius when the diameter is asked.
- Dropping a negative sign when distributing: −(x − 4) = −x + 4, not −x − 4.
- Mixing degrees and radians, or selecting the wrong trig ratio.
- Rounding too early in multi-step items; keep exact values until the final step.
- For "greatest/least" items, compare fractions by cross-multiplying instead of eyeballing denominators.