Algebra and Functions
What to know
Candidates must translate words into expressions and equations, simplify expressions by combining like terms and applying the distributive property, and solve linear equations and inequalities. Know how to solve proportions, work with exponents (product, quotient, and power rules), and interpret slope and intercepts in y = mx + b. Function notation and recognizing linear versus nonlinear patterns are also fair game.
Traps to watch
- Multiplying an inequality by a negative number reverses the inequality sign.
- Distribute to every term: 3(x + 4) = 3x + 12, not 3x + 4.
- Like terms must share the same variable and exponent; 2x and 2x² do not combine.
- Slope is rise over run: (y₂ − y₁)/(x₂ − x₁). Keep the order consistent in numerator and denominator.
- When substituting a negative value, use parentheses to protect signs.
Worked example
Solve 4x − 7 = 2x + 5. Subtract 2x from both sides: 2x − 7 = 5. Add 7: 2x = 12. Divide by 2: x = 6. Check: 4(6) − 7 = 17 and 2(6) + 5 = 17.
Rule of thumb
Whatever you do to one side of an equation, do to the other, and undo operations in reverse order (undo addition/subtraction before multiplication/division). Always substitute your answer back to verify.