Every Exam PrepFREE EXAM PREP
Ask AI
CHEAT SHEET · ALEKS MATH PLACEMENT

ALEKS Math Placement Cheat Sheet.
The night-before summary, built like the exam.

Download the PDF
Weighted to the current exam outline·15-minute scanVerified against the official content outline
By Vincent Ruan, EA, CFP®Published August 14, 2026
Drill weak spots →

Percents & Proportions

  • Percent change: (new - old) / old × 100. Always divide by the original value.
  • Percent of a number: rate as a decimal × base. 35% of 240 = 0.35 × 240 = 84.
  • Original price after discount: original = final ÷ (1 - rate). Paid 68 after 20% off: 68 ÷ 0.80 = 85.
  • Proportion: a/b = c/d means ad = bc. Pair each numerator with the opposite denominator.
  • Successive percents multiply: 12% off then 8% tax = × 0.88 × 1.08, never a flat -4%.

Geometry

  • Rectangle: A = lw, P = 2(l + w). Triangle: A = (1/2)bh, angles sum to 180.
  • Circle: A = πr^2, C = πd = 2πr. Square the radius, not the diameter.
  • Box: V = lwh. Cylinder: V = πr^2h.
  • Pythagorean theorem: a^2 + b^2 = c^2. Triples: 3-4-5, 5-12-13, 8-15-17.
  • Complementary angles sum to 90; supplementary to 180.

Linear Equations & Lines

  • Slope: m = (y2 - y1)/(x2 - x1). Slope-intercept: y = mx + b. Point-slope: y - y1 = m(x - x1).
  • Parallel: equal slopes. Perpendicular: slopes multiply to -1 (negative reciprocals).
  • Intercepts: x-intercept sets y = 0; y-intercept sets x = 0.
  • Inequality flip: reverse the sign only when multiplying or dividing by a negative.
  • Absolute value: |X| = k (k > 0) splits into X = k or X = -k.

Exponent Laws

  • x^a · x^b = x^(a+b); x^a ÷ x^b = x^(a-b); (x^a)^b = x^(ab).
  • x^0 = 1 (x ≠ 0); x^(-n) = 1/x^n; x^(m/n) = (nth root of x)^m. 16^(3/4) = 8.
  • (2a^3)^4 = 16a^12: raise every factor, multiply the exponents.

Factoring Patterns

  • Difference of squares: a^2 - b^2 = (a - b)(a + b).
  • Perfect square: (a ± b)^2 = a^2 ± 2ab + b^2. Never drop the middle term.
  • Trinomial x^2 + bx + c: find two numbers with product c and sum b.
  • Always pull the GCF first: 2x^2 + 10x + 12 = 2(x + 2)(x + 3).

Quadratics, Exponentials & Logs

  • Quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a).
  • Discriminant b^2 - 4ac: positive → 2 real roots; zero → 1; negative → none.
  • Vertex: x = -b/(2a); substitute back for y.
  • Log meaning: log_b(x) = y means b^y = x.
  • Log rules: log(ab) = log a + log b; log(a/b) = log a - log b; log(a^n) = n log a.
  • Same-base equations: b^m = b^n forces m = n. Check log arguments stay positive.

Trigonometry

  • SOH-CAH-TOA: sin = opp/hyp, cos = adj/hyp, tan = opp/adj.
  • Special values: sin 30 = 1/2, cos 30 = √3/2, sin 45 = cos 45 = √2/2, tan 45 = 1, sin 60 = √3/2, cos 60 = 1/2.
  • Radians: degrees × π/180; 180° = π; 150° = 5π/6.
  • Identity: sin^2 θ + cos^2 θ = 1, so 1 - cos^2 θ = sin^2 θ.
  • Quadrant signs: all positive in QI; sin in QII; tan in QIII; cos in QIV.

Frequently asked questions

What is the best way to use this formula sheet?

Use it for active recall, not passive reading. Cover a section, write every formula from memory, then check what you missed and drill only those. In the final week, recreate the whole sheet blank-page style once a day; whatever will not come out of your pen is what you review that evening.

Can I bring a formula sheet into the actual ALEKS assessment?

Plan on no. ALEKS supplies an on-screen calculator only when a specific problem allows one, and proctored placement attempts are run under your school's rules, which treat outside references as aids you cannot use. Every formula on the sheet needs to live in your memory by test day.

Which formulas on the sheet earn the most points?

The workhorses are the quadratic formula, the exponent laws, percent change, slope and the line forms, and the SOH-CAH-TOA ratios. They appear across multiple topic bands, so each one you automate pays off repeatedly. The factoring patterns are close behind because they unlock both the algebra and the quadratics sections.

How do I memorize the special trig values without mixing them up?

Derive them once instead of memorizing a table. Cut an equilateral triangle in half for the 30-60-90 sides 1, root 3, and 2, and cut a square diagonally for the 45-45-90 sides 1, 1, root 2. Sketching those two triangles in the margin takes ten seconds and regenerates every special sine, cosine, and tangent value on demand.

Sources

  1. 1.ALEKS PPL Mathematics Assessment Exam — University of Illinois Urbana-Champaign Department of Mathematics (accessed Aug 14, 2026)
  2. 2.Taking the Placement Assessment (ALEKS Math Placement) — University of Kansas Department of Mathematics (accessed Aug 14, 2026)

Official sources

Every exam fact on this page traces to a primary document published by the body that administers the exam.

Last verified against the official exam content outline: