Mathematics: Arithmetic, Algebra, and Geometry
Core skills
Mathematics questions cover arithmetic, ratios and percentages, algebra, geometry, and word problems. Master order of operations, fraction and decimal operations, proportional reasoning, linear equations, exponent rules, triangle properties, circle formulas, and coordinate geometry. In word problems, translate each phrase into a mathematical relationship before calculating.
Common traps
Percentage changes are not symmetric: a 20% increase followed by a 20% decrease gives 96% of the original, not 100%. When distributing a negative sign, apply it to every term. Area and perimeter are often confused, as are radius and diameter. For similar figures, lengths scale by the factor but areas scale by its square. Check units and convert them before combining quantities. Do not round early; keep precision until the final step.
Rule of thumb
Write an equation, solve it, then substitute the answer back into the original wording to see whether it makes sense. For percent problems, identify the base: “of” usually signals the base. For geometry, sketch and label known values before choosing a formula.
Worked example
Solve 3x + 5 = 20. Subtract 5: 3x = 15. Divide by 3: x = 5. Check: 3(5) + 5 = 20, which is correct.