Mathematics: Clean Setup, Exact Answer
Mathematics
The Mathematics portion of the PMA Cadet Entrance Test checks arithmetic fluency, algebra, geometry, trigonometry, and multi-step word problems. Questions reward a clean setup more than calculator speed.
Core rules
- Follow order of operations: parentheses, exponents, multiplication/division left to right, addition/subtraction left to right.
- For linear equations, perform the same operation on both sides; distribute signs carefully.
- Exponent rules: a^m × a^n = a^(m+n); a^m ÷ a^n = a^(m-n); (a^m)^n = a^(mn).
- Geometry: rectangle area = length × width; triangle area = ½ × base × height; circle circumference = 2πr; circle area = πr²; right triangles satisfy a² + b² = c².
- Right-triangle ratios: sin θ = opposite/hypotenuse; cos θ = adjacent/hypotenuse; tan θ = opposite/adjacent.
- Average = total ÷ number of items; weighted averages use the weights.
Worked example
Solve 3(x - 2) = 2x + 7. Distribute: 3x - 6 = 2x + 7. Subtract 2x: x - 6 = 7. Add 6: x = 13. Check: 3(11) = 33 and 2(13) + 7 = 33.
Traps
- Dropping a negative sign when distributing, e.g. -2(x - 3) = -2x + 6, not -2x - 6.
- Mixing units (minutes vs hours, cm vs m) before computing rate or area.
- Answering the wrong quantity in word problems-label what is asked.
- Using diameter instead of radius in circle formulas.