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Cheat sheet

CLEP College Algebra cheat sheet

A condensed reference for the formulas, graph-reading rules, and must-know facts most worth reviewing before exam day.

Function and graph essentials

  • Slope: m = (y2 - y1) / (x2 - x1). A positive slope rises left to right; a negative slope falls.
  • Slope-intercept form: y = mx + b. The y-intercept is b, and m controls steepness.
  • Average rate of change: [f(b) - f(a)] / (b - a). Use it whenever a question asks for change over an interval.
  • Domain means allowed x-values; range means possible y-values. Check denominators, square roots, and graph endpoints first.
  • For inverse functions, swap x and y, then solve for y. The graph reflects across y = x.

Equation patterns to know cold

  • Quadratic formula: x = [-b +/- sqrt(b^2 - 4ac)] / 2a for ax^2 + bx + c = 0.
  • Discriminant: b^2 - 4ac. Positive means two real roots, zero means one repeated root, negative means complex roots.
  • Difference of squares: a^2 - b^2 = (a - b)(a + b).
  • Perfect-square trinomials: a^2 + 2ab + b^2 = (a + b)^2 and a^2 - 2ab + b^2 = (a - b)^2.
  • Absolute value equations split into two cases: |A| = k means A = k or A = -k, with k >= 0.

Exponents, logs, and rational expressions

  • Exponent product: a^m * a^n = a^(m+n). Quotient: a^m / a^n = a^(m-n). Power: (a^m)^n = a^(mn).
  • Negative exponent: a^-n = 1 / a^n. Fractional exponent: a^(m/n) = nth-root(a^m).
  • Log definition: log_b(x) = y means b^y = x. Convert logs to exponent form when stuck.
  • Log rules: log(ab) = log a + log b; log(a/b) = log a - log b; log(a^k) = k log a.
  • Rational expressions: factor first, cancel common factors, then state excluded denominator values if asked.

Practice this first: Functions and graphs - This is the biggest share of the exam and the fastest place to lose points if graph reading is weak.

Now put it to work - practice CLEP College Algebra free

Reviewing the sheet is step one. Passers are usually hitting about 70-80% on realistic practice before test day, so the fastest way to know you are ready is to start answering real questions.