Algebra

How f(x) + k, f(x − h), −f(x), f(−x) and a·f(x) move a graph, why horizontal shifts look backwards, and how to combine transformations in order.

The nth-term and sum formulas for arithmetic and geometric sequences, how to tell them apart, infinite geometric series, and worked examples.

A complete fraction refresher: simplifying, common denominators, mixed numbers, multiplying, dividing, comparing and converting, with worked problems.

The product, quotient, power, zero, negative and fractional exponent rules, how to combine them, scientific notation, and the mistakes that cost points.

The three kinds of percent problem, percent increase and decrease, discounts and tax, undoing a percent change, and simple and compound interest.

Find slope from two points, write a line in slope-intercept, point-slope or standard form, and handle parallel and perpendicular lines, with worked examples.

Solve any linear equation: one-step and multi-step, variables on both sides, fractions and decimals, no-solution cases, and word problems, with worked examples.

Solve systems of two linear equations by substitution, elimination or graphing, spot no-solution and infinite-solution systems, and set up word problems.

A reliable order for factoring: greatest common factor, trinomials, the ac method, difference of squares, cubes and grouping, with worked examples and practice.

What a logarithm means, the product, quotient, power and change-of-base rules, and how to solve exponential and log equations, with growth examples.