Mathematics Knowledge
What to know
Mathematics Knowledge is straight math without a story. Expect fractions and decimals, order of operations, exponents and roots, solving equations and inequalities, factoring, systems of equations, and geometry: angles, triangles, circles, perimeter, area, and volume.
Memorize the core formulas: area of a triangle ½bh, circle area πr² and circumference 2πr, rectangle area lw, box volume lwh, triangle angles sum to 180°, Pythagorean theorem a² + b² = c², and slope = rise ÷ run.
Traps
- Order of operations, especially dividing before subtracting.
- Distributing a negative: −(x − 3) becomes −x + 3, not −x − 3.
- Squaring a binomial: (x + 3)² = x² + 6x + 9, never x² + 9.
- Negative exponents: x⁻² = 1/x².
- Being handed a diameter when the formula needs a radius.
- Mixing up perimeter and area, or forgetting to convert units first.
Rule of thumb
Substitute your answer back into the original equation. On multiple choice, you can also plug each answer choice in from the start, which is often faster than solving.
Worked example
Solve 3(x − 4) = 2x + 5. Distribute: 3x − 12 = 2x + 5. Subtract 2x from both sides: x − 12 = 5. Add 12: x = 17. Check: 3(17 − 4) = 39 and 2(17) + 5 = 39. Both sides agree, so 17 is correct.