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ALEKS Math Cheat Sheet

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Numbers + Ratios

  • 25% of exam
  • Integers Fractions Percents Ratios Units

Equations + Expressions

  • 25% of exam
  • Linear Inequalities Systems Exponents Polynomials

Functions + Graphs

  • 25% of exam
  • Slope Intercepts Domain Range Quadratics

Advanced Readiness

  • 25% of exam
  • Rationals Radicals Logs Geometry Trig

Quick Facts

  • Assessment ALEKS PPL
  • Format Adaptive open response
  • Questions 25 or fewer
  • Time About 90 minutes
  • Score Institution mapped
  • Calculator School policy
  • Goal Course placement

Order NU

  • Groups, exponents, multiply divide, add subtract.
  • Groups Exponents Multiply Divide Add Subtract

Exact vs Decimal NU

Exact

  • Fractions radicals pi
  • Preferred often

Decimal

  • Approximate value
  • Round carefully
  • Follow entry format

Number Rules NU

  • Negative minus Add opposite
  • Absolute value Distance from zero
  • Fraction sum Match denominators
  • Percent change Use original base
  • Ratio Compare same units
  • Proportion Cross multiply
  • Estimate Catch impossible answers

Expression vs Equation AL

Expression

  • Simplify only
  • No equals sign

Equation

  • Solve variable
  • Has equals sign
  • Simplify before solving

Equation Picker AL

  • Fractions appear → Clear denominators
  • Parentheses appear → Distribute first
  • Like terms appear → Combine terms
  • Variable both sides → Collect variable
  • Inequality negative → Reverse symbol
  • Quadratic equals zero → Factor first
  • Denominator has x → Check restrictions
  • Root equation → Check extraneous

Linear Tools AL

  • Distribute Multiply every term
  • Like terms Same variable power
  • One step Undo operation
  • Multi step Simplify first
  • Inequality Flip for negative
  • System Eliminate or substitute
  • Check Substitute result

Factor vs Expand AL

Factor

  • Create products
  • Helps solve

Expand

  • Remove parentheses
  • Helps combine
  • Match next step

Polynomial Rules AL

  • Degree Greatest exponent
  • GCF Factor first
  • Difference squares Two conjugates
  • Trinomial Product and sum
  • Product rule Add exponents
  • Power rule Multiply exponents
  • Zero exponent Nonzero base one

Domain Checks FU

  • No zero denominators; no negative even roots.
  • Denominator Even root Log input

Slope vs Intercept FU

Slope

  • Rate of change
  • m value

Intercept

  • Axis crossing
  • Set variable zero
  • Identify the ask

Graph Picker FU

  • Find slope → Rise over run
  • Find x-intercept → Set y zero
  • Find y-intercept → Set x zero
  • Input restricted → State domain
  • Output bounded → State range
  • Parabola asked → Find vertex
  • Parallel line → Reuse slope
  • Perpendicular line → Negative reciprocal

Graph Basics FU

  • Slope Rise over run
  • y-intercept Set x zero
  • x-intercept Set y zero
  • Parallel Same slope
  • Perpendicular Negative reciprocal
  • Vertex Parabola turning point
  • Transform Shift stretch reflect

Function Rules FU

  • f(a) Substitute a
  • Domain Allowed inputs
  • Range Possible outputs
  • Composition Inside first
  • Inverse Swap x y
  • Increasing Outputs rise
  • Decreasing Outputs fall

Trig AD

  • Sine opposite; cosine adjacent; tangent opposite.
  • SOH CAH TOA

Radical vs Exponent AD

Radical

  • Root symbol
  • Check domain

Exponent

  • Power notation
  • Use exponent rules
  • Convert if useful

Rational Rules AD

  • Restriction Denominator not zero
  • Simplify Factor then cancel
  • Multiply Cancel common factors
  • Divide Flip second fraction
  • Add Use common denominator
  • Equation Clear denominators
  • Extraneous Reject zero denominator

Radicals + Logs AD

  • Square root Principal nonnegative root
  • Even root Radicand nonnegative
  • Rational exponent Root then power
  • Log Exponent question
  • Log product Add logs
  • Log quotient Subtract logs
  • Log power Bring exponent down

Geometry + Trig AD

  • Area rectangle length times width
  • Area triangle half base height
  • Circle area pi r squared
  • Pythagorean a2 plus b2 c2
  • SOH Sine opposite hypotenuse
  • CAH Cosine adjacent hypotenuse
  • TOA Tangent opposite adjacent

Common Traps

Sign Errors

  • Distribute negative signs ≠ Flip inequality signs

Fraction Errors

  • Use common denominator ≠ Do not cancel terms

Function Notation

  • Substitute input ≠ Not multiplication

Domain Loss

  • Track original restrictions ≠ Reject impossible inputs

Open Response

  • Practice exact entry ≠ Avoid answer recognition

Last Minute

  • 1. Memorize exponent rules
  • 2. Review slope forms
  • 3. Practice factoring patterns
  • 4. Check denominator restrictions
  • 5. Check radical domains
  • 6. Use original percent base
  • 7. Substitute final answers
  • 8. Read school score table

ALEKS Math Placement

  • Practice Questions 100 questions Study Guide 18 topics Cheat Sheet 56 facts Flashcards 50 cards Shorts 2 short s Videos 4 videos Blogs 5 blogs