Mathematics Knowledge
Scope
Mathematics Knowledge is direct computation and symbol manipulation: arithmetic, fractions and decimals, exponents and radicals, algebra, geometry, and basic probability. There is no story to decode, but there is also no partial credit, so check each step.
Must-know rules
- Order of operations: parentheses, exponents, multiply/divide left to right, add/subtract left to right.
- Exponent rules: x^a times x^b = x^(a+b); (x^a)^b = x^(ab); x^0 = 1; negative exponents give reciprocals.
- Distributive property and factoring; the quadratic formula for ax^2 + bx + c = 0.
- Geometry: triangle area (1/2)bh, circle area pi r^2 and circumference 2 pi r, Pythagorean theorem a^2 + b^2 = c^2, rectangular solid volume lwh.
- Slope = (y2 - y1)/(x2 - x1); parallel lines share a slope, perpendicular slopes are negative reciprocals.
Traps
- Dropping a negative sign when distributing: 3 - (x - 4) becomes 3 - x + 4.
- Using diameter where radius belongs, or forgetting to square the radius.
- Reporting only one root of a quadratic and forgetting the second.
- Cancelling terms across a plus sign instead of cancelling factors.
- Mixing perimeter and area, or forgetting that area uses square units.
Worked example
Solve 3(x - 2) = 2x + 5. Distribute: 3x - 6 = 2x + 5. Subtract 2x: x - 6 = 5. Add 6: x = 11. Check: 3(9) = 27 and 2(11) + 5 = 27.
Rule of thumb
Substitute your answer back into the original equation, and keep units on every geometry result - squared for area, cubed for volume.