Mathematical Problem Solving
What this section measures
These items go beyond arithmetic into algebra, geometry, exponents, inequalities, and number properties. The content is standard high-school level; the scoring difference is careful setup and answering precisely what is asked.
Algebra. Solve linear equations by isolating the variable, and systems by substitution or elimination. For quadratics, try factoring first (x^2 - 5x + 6 = (x-2)(x-3)). Express the quantity the question names - if it asks for 2x + 3, do not stop at x.
Geometry. Memorize area and perimeter formulas, the Pythagorean theorem and the 3-4-5 / 5-12-13 triples, angle rules (straight line 180, triangle 180, vertical angles equal), and similar-triangle proportionality. Circle basics: circumference 2 pi r, area pi r squared.
Exponents and roots. Add exponents when multiplying like bases, subtract when dividing, multiply when raising a power to a power. A negative exponent means reciprocal.
Inequalities. Flip the sign when multiplying or dividing by a negative.
Traps that appear
- Solving correctly but answering the wrong quantity.
- Dividing by a variable that could be zero, losing a solution.
- Ignoring constraints such as integer or positive that eliminate an otherwise valid root.
- Using diameter where radius is required, or forgetting a unit conversion.
Rule of thumb
Write down what the question asks for as a symbol before starting, and check your result by substituting it back into the original equation.
Worked example. If 3x - 7 = 2x + 5, what is 5x? Subtracting 2x gives x - 7 = 5, so x = 12 and 5x = 60. Choosing 12 is the trap: the item asked for 5x.