Mathematics Knowledge
What the questions test
Mathematics Knowledge covers school mathematics through beginning algebra and geometry: order of operations, fractions and decimals, exponents and roots, algebraic expressions, linear equations and inequalities, factoring, quadratics, ratios, percent, angles, triangles, circles, area and volume, coordinate geometry, and basic probability. The test rewards precision more than speed.
Traps
- Order of operations: exponents before multiplication; multiplication and division left to right.
- Negative signs: -3^2 = -9, while (-3)^2 = 9. Distribute a negative across every term.
- Dividing by a variable: x^2 = 5x gives x = 0 or x = 5; do not divide away a possible zero solution.
- Geometry labels: radius versus diameter, complementary (90 degrees) versus supplementary (180 degrees), and slant height versus perpendicular height.
- Inequalities: multiplying or dividing by a negative flips the sign.
Worked example
Solve 2(x - 3) = 5x + 6. Distribute: 2x - 6 = 5x + 6. Subtract 2x from both sides: -6 = 3x + 6. Subtract 6: -12 = 3x. Divide by 3: x = -4. Check: left side 2(-7) = -14; right side 5(-4) + 6 = -14.
Rule of thumb
After solving, substitute your answer into the original equation. This catches sign errors and distribution mistakes faster than re-reading your work.