Mathematics Knowledge: Core Algebra and Geometry
Mathematics Knowledge tests recall and application of fundamental math rules-arithmetic properties, fractions, exponents, algebra, and geometry-usually without a word-problem story. Speed comes from knowing formulas cold.
Must-know content
- Order of operations: parentheses, exponents, multiply/divide left to right, add/subtract left to right (PEMDAS).
- Fractions: to add, find a common denominator; to divide, multiply by the reciprocal.
- Exponents: x^a · x^b = x^(a+b); x^a / x^b = x^(a−b); (x^a)^b = x^(ab); x^0 = 1; x^(−1) = 1/x.
- Algebra: solve by isolating the variable; whatever you do to one side, do to the other. Factor to solve quadratics.
- Geometry: area of triangle = ½bh; circle area = πr²; circumference = 2πr; Pythagorean theorem a² + b² = c²; angles in a triangle sum to 180°.
Traps
- Negative signs: (−3)² = 9, but −3² = −9.
- Square roots: √(a+b) is not √a + √b.
- Adding exponents incorrectly when multiplying terms with the same base.
- Forgetting units or mixing radius and diameter.
Worked example
Solve 3x − 5 = 16. Add 5 to both sides: 3x = 21. Divide by 3: x = 7. Check: 3(7) − 5 = 21 − 5 = 16. ✔
Rule of thumb
Substitute your answer back into the original equation. If it checks, you almost certainly have the right value.