ACT Math Cheat Sheet

Cheat sheet ACT Math Cheat Sheet Practice Questions Study Guide Print / Save PDF

Number + Quantity 10-12% of exam Number Rules Exponents Radicals Complex Numbers Sequences

Algebra 17-20% of exam Algebra Moves Graphs + Lines Systems Quadratics Formula Picker

Functions 17-20% of exam Functions Domain Composition Transforms Logs

Geometry + Trig 17-20% of exam Geometry Basics Circles + Solids Trig SOH-CAH-TOA Scale

Stats + Probability 12-15% of exam Data + Stats Probability + Counting Regression Outliers Permutations

Essential Skills 20% of exam Rates Percents Proportions Units Strategy Picker

Quick Facts Section Math Questions 45 Scored 41 Time 50 min Pace 67 sec/item Score 1-36 Calculator Permitted Core split 80% + 20%

Number Rules NU a^m*a^n Add exponents a^m/a^n Subtract exponents a^-n Move across fraction a^(m/n) Root then power i^2 -1 Absolute value Distance from zero

Sequences + Matrices NU Arithmetic Add constant Geometric Multiply ratio Matrix product Inner dimensions match Result size Outer dimensions Vector Magnitude + direction Set Collection of values

FOIL AL First, Outer, Inner, Last Binomial products Combine like terms Check signs

Slope vs Intercept AL

Slope Rate of change m Rise/run

Intercept Axis crossing b or zero Starting value Rate vs start

Formula Picker AL Line rate → Slope ( rise/run ) Two points apart → Distance ( coordinate theorem ) Quadratic roots → Factor/formula ( fastest route ) Circle center → Standard form ( signs flip ) Right triangle → Pythagorean/trig ( angle decides ) Percent growth → Exponential ( 1+r factor )

Algebra Moves AL Linear equation Isolate variable Inequality Flip on negative System Substitute or eliminate Factoring Product and sum Quadratic formula Use when unfactorable Radical equation Check extra roots

Graphs + Lines AL Slope Rise over run y=mx+b Slope-intercept form Point-slope Use point + slope Distance Pythagorean on coordinates Midpoint Average coordinates Perpendicular Negative reciprocal slopes

Domain vs Range FU

Domain Allowed inputs x-values Check restrictions

Range Possible outputs y-values Check graph Input vs output

Functions FU f(a) Substitute input Domain Allowed inputs Range Possible outputs f(g(x)) Do g first Inverse Swap x and y Piecewise Choose interval first

Function Models FU Vertical shift f(x)+k Horizontal shift f(x-h) Exponential Repeated percent change Logarithm Exponent question Vertex form Shows turning point Zero x-intercept

SOH-CAH-TOA GE Sine opposite, cosine adjacent, tangent opposite SOH: sin O/H CAH: cos A/H TOA: tan O/A

Similar vs Congruent GE

Similar Same shape Scaled lengths Angles equal

Congruent Same size Same shape Sides equal Scaled vs identical

Geometry Basics GE Triangle sum 180 degrees Pythagorean a^2+b^2=c^2 Similarity Same shape scale Congruence Same size shape Area triangle 1/2 bh Scale area k^2 factor

Special Triangles GE 45s match; 30s double 45: x,x,xsqrt2 30: x,xsqrt3,2x Hypotenuse longest

Circumference vs Area GE

Circumference Boundary length Linear units 2*pi*r

Area Inside region Square units pi*r^2 Around vs inside

Circles + Solids GE Circumference 2*pi*r Circle area pi*r^2 Circle equation Center and radius Arc length Angle fraction circumference Cylinder volume Base area times height Scale volume k^3 factor

Trig GE Sine Opposite over hypotenuse Cosine Adjacent over hypotenuse Tangent Opposite over adjacent Radians pi rad = 180 Unit circle (cos, sin) sin^2+cos^2 Equals 1

Probability ST Either add; both multiply Or: add cases And: multiply chances Complement: 1-event

Mean vs Median ST

Mean Uses all values Outlier sensitive Sum/count

Median Middle value Outlier resistant Sort first Average vs middle

Data Picker ST Average asked → Mean ( sum/count ) Outlier present → Median ( resistant center ) Spread asked → Std dev ( distance from mean ) Trend asked → Regression ( line fit ) At least one → Complement ( 1-none ) Arrangements asked → Permutation ( order matters )

Data + Stats ST Mean Average Median Middle after sorting Mode Most frequent Range Max minus min Std dev Spread from mean Regression Best-fit line

Permutation vs Combination ST

Permutation Order matters Arrangements Lineups

Combination Order ignored Groups Committees Ordered vs unordered

Probability + Counting ST Probability Favorable over total Complement 1 minus event Independent Multiply probabilities Conditional Restrict sample space Permutation Order matters Combination Order ignored

Independent vs Dependent ST

Independent No influence Multiply directly Replacement often

Dependent Probability changes Update denominator No replacement Same odds vs changed

Strategy Picker ES Variables messy → Plug numbers ( simple values ) Choices numeric → Backsolve ( middle first ) Graph shown → Read axes ( units matter ) Long arithmetic → Calculator ( avoid keystrokes ) Geometry drawn → Estimate ( scale clues ) Stuck late → Eliminate ( keep pace )

Essential Skills ES Percent change Change over original Unit rate Per one unit Proportion Equal ratios Weighted avg Weights before divide Units Track every step Modeling Translate situation

Common Traps

Negative exponents Move factor ≠ Do not negate

Inequality signs Negative multiply flips ≠ Positive multiply stays

Radius vs diameter Area needs radius ≠ Diameter doubles radius

Squaring roots Can add solutions ≠ Check original equation

Scale factors Area uses k^2 ≠ Volume uses k^3

Order matters Permutation counts order ≠ Combination ignores order

Calculator reliance Setup comes first ≠ Units still matter

Last Minute 1 . Check domain restrictions 2 . Sort before median 3 . Label every unit 4 . Backsolve numeric choices 5 . Slope = rise/run 6 . Area uses square units 7 . Volume uses cubic units 8 . Use radius for circles 9 . Check radical solutions 10 . Estimate geometry drawings

ACT Math Practice Questions 120 questions Study Guide 18 topics Cheat Sheet 72 facts Flashcards 50 cards Shorts 4 short s

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