Mathematics Knowledge
Content map
Mathematics Knowledge is straight computation: fractions and decimals, percents, exponents and roots, order of operations, factoring, linear equations and inequalities, systems of equations, quadratics, and geometry covering angles, triangles, the Pythagorean theorem, circles, area, and volume.
Traps
- Order of operations: exponents before multiplication, multiplication before addition; work parentheses from the inside out.
- Negative signs. Minus 3 squared is minus 9, but negative 3 in parentheses squared is positive 9. Subtracting a negative adds.
- Distribution: 3(x - 4) = 3x - 12, not 3x - 4.
- Percent change = (new - old) divided by old, times 100. A 25 percent increase means multiplying by 1.25.
- Geometry: know radius versus diameter, and remember triangle area is one half base times height, where the height is perpendicular to the base.
- Dividing an inequality by a negative number flips the sign.
- Angle facts: angles in a triangle sum to 180 degrees, a straight line is 180, and vertical angles are equal.
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 by substituting: 3(13) = 39 and 2(17) + 5 = 39. Substituting back is the fastest way to catch a sign slip or a distribution error.