Mathematics Knowledge
Mathematics Knowledge tests algebra, geometry, and number properties without a calculator. Expect linear equations, inequalities, exponent rules, factoring, angle relationships, perimeter, area, volume, and coordinate geometry.
Algebra essentials
Distribute carefully, combine like terms, then undo operations in reverse order. Whatever is done to one side must be done to the other. Multiplying or dividing an inequality by a negative number reverses the inequality sign. Know exponent rules: x^a · x^b = x^(a+b), (x^a)^b = x^(ab), x^0 = 1 for x ≠ 0, and x^−a = 1/x^a.
Geometry essentials
A straight line is 180°, a triangle's interior angles sum to 180°, and vertical angles are equal. For right triangles, a² + b² = c², where c is the hypotenuse. Circle circumference is 2πr and area is πr². Rectangle area is length × width; triangle area is 1/2 × base × height; prism volume is base area × height.
Worked example
Solve 5 − 2x ≥ 11. Subtract 5 from both sides: −2x ≥ 6. Divide by −2 and reverse the sign: x ≤ −3. Check x = −4: 5 − 2(−4) = 13, and 13 ≥ 11 is true. Check x = 0: 5 ≥ 11 is false. The solution is x ≤ −3.
Traps
Watch negative signs when distributing, especially −(x − 4). Do not confuse radius with diameter. Keep area in square units and volume in cubic units. When factoring, verify by multiplying back. Do not assume a figure is drawn to scale; use stated values and properties.