AEPA Mathematics Cheat Sheet

Cheat sheet AEPA Mathematics Cheat Sheet Practice Questions Study Guide Print / Save PDF

Processes + Number Sense 19% of exam Estimation Ratios Logic Number Theory Complex Numbers

Algebra + Functions 24% of exam Functions Systems Polynomials Exponentials Logs Asymptotes

Geometry + Measurement 19% of exam Units Similarity Area Volume Conics Transformations

Trigonometry + Calculus 19% of exam Unit Circle Identities Limits Derivatives Integrals Optimization

Stats + Discrete Math 19% of exam Displays Sampling Probability Counting Sequences Matrices

Quick Facts Exam NT304 Format 150 MCQ Time 5 h Pass 220 scaled Fee $119 Calculator On-screen scientific Reference On-screen formulas Heaviest Algebra 24%

Inductive vs Deductive PR

Inductive Patterns Likely claim Needs proof

Deductive Rules Certain conclusion Valid argument Pattern vs proof

Problem Setup Picker PR About enough → Estimate ( Check plausibility ) Per one unit → Rate ( Track units ) Same ratio → Proportion ( Cross multiply ) Pattern only → Conjecture ( Needs proof ) One failure → Counterexample ( Disproves claim ) Many cases → Truth table ( Logic check ) Diagram fits → Representation ( Simplify context ) Answer scale odd → Units ( Catch error )

Number Sense PR Estimate Friendly numbers Percent Part per hundred Ratio Multiplicative comparison Proportion Equal ratios Rate Units per unit Rational Fraction form Irrational Nonrepeating decimal Complex a + bi Prime Two factors LCM Smallest shared multiple

Reasoning + Logic PR Conjecture Pattern claim Counterexample One disproof Inductive Pattern reasoning Deductive Rule reasoning Converse q -> p Inverse not p -> not q Contrapositive not q -> not p Biconditional p iff q Truth table All cases

Mathematical Practice PR Representation Model choice Units Context labels Reasonableness Plausibility check Proof Justified argument Formula page Reference tool Calculator Computation tool Distractor Trap choice Error log Miss pattern

Domain vs Range AL

Domain Inputs x-values Restrictions

Range Outputs y-values Possible results Allowed in vs possible out

Function Picker AL Constant rate → Linear ( Slope ) Turning point → Quadratic ( Vertex ) Many zeros → Polynomial ( Factors ) Constant ratio → Exponential ( Growth/decay ) Undo exponential → Logarithm ( Inverse ) Vertical asymptote → Rational ( Restrictions ) Repeating wave → Trig ( Period ) Rules by interval → Piecewise ( Check domain )

Function Basics AL Relation Input-output set Function One output Domain Allowed inputs Range Possible outputs Composition Nested functions Inverse Undo function Even y-axis symmetry Odd Origin symmetry Piecewise Rule by interval

Algebra Models AL Linear Constant slope Quadratic Parabola Polynomial Power sum Exponential Constant ratio Logarithmic Inverse exponential Rational Fraction expression Radical Root expression Absolute value Distance from zero System Shared solution

Similar vs Congruent GE

Similar Same shape Scaled lengths Equal angles

Congruent Same size Same shape Rigid motion Scale vs exact

Geometry + Measurement GE Perimeter Boundary length Circumference Circle perimeter Area Square units Surface area Outer area Volume Cubic units Similarity Same shape Scale factor Length multiplier Precision Measurement detail Error Measured difference

Coordinate + Conics GE Slope Rise over run Midpoint Average coordinates Distance Pythagorean length Circle Equal radius Parabola Quadratic conic Ellipse Two-focus oval Hyperbola Two branches Translation Slide Reflection Mirror image

Trig Ratios TR SOH CAH TOA anchors trig SOH: sine CAH: cosine TOA: tangent

Derivative vs Integral TR

Derivative Slope Rate Local change

Integral Area Accumulation Total change Rate vs total

Calculus Picker TR Approach value → Limit No jump → Continuity Instant slope → Derivative Nested expression → Chain rule Max/min requested → Critical points Accumulated change → Integral Area approximation → Riemann sum Position from velocity → Integral

Trigonometry TR Unit circle Radius one Radians Arc measure Sine y-coordinate Cosine x-coordinate Tangent sin/cos Period Cycle length Amplitude Half height Identity Always true Law of sines SSA/ASA triangles Law of cosines SAS/SSS triangles

Quadrant Signs TR All Students Take Calculus QI: all QII: sine QIII: tangent QIV: cosine

Calculus TR Limit Approach value Continuity No break Derivative Instant rate Product rule Differentiate product Chain rule Differentiate composite Critical point f' = 0 Optimization Max/min context Integral Accumulated area Riemann sum Rectangle total FTC Derivative-integral link

Calculus Core TR Derivative slopes; integral totals f': rate Integral: area FTC: link

Counting Order ST nPr arranges; nCr chooses Permutation: order Combination: groups FCP: slots

Permutation vs Combination ST

Permutation Order matters Arrangements nPr

Combination Order ignored Selections nCr Arrange vs choose

Counting Picker ST Order matters → Permutation Groups only → Combination Repeated stages → FCP Not event → Complement Either event → Union Both events → Intersection Given condition → Conditional No influence → Independence

Statistics ST Mean Balance point Median Middle value Mode Most frequent IQR Middle spread Std deviation Typical spread Outlier Unusual value Bias Systematic skew Random sample Fair selection Normal curve Bell distribution

Correlation vs Causation ST

Correlation Variables move Association No proof

Causation One causes Controlled evidence Mechanism Association vs cause

Probability + Counting ST Sample space All outcomes Complement Not event Union A or B Intersection A and B Conditional Given event Independent No effect Permutation Order matters Combination Groups only Binomial Fixed trials Expected value Long-run average

Exclusive vs Independent ST

Exclusive Cannot both occur No overlap

Independent No probability effect Can overlap Overlap vs influence

Discrete + Matrix ST Sequence Ordered list Series Sequence sum Recursive Uses previous terms Arithmetic Constant difference Geometric Constant ratio Matrix Number array Vector Magnitude + direction Determinant Square-matrix scalar Set Element collection

Common Traps

Examples vs proof Examples suggest ≠ Proof establishes

Order vs selection Permutation orders ≠ Combination groups

Area vs perimeter Area squares ≠ Perimeter lengths

Endpoint vs continuity Endpoint may exist ≠ Limit may fail

Correlation vs cause Association observed ≠ Cause proven separately

Domain restrictions Denominator not zero ≠ Even root nonnegative

Calculator traps Mode matters ≠ Units still matter

Last Minute 1 . Weights: 19/24/19/19/19 2 . Estimate before calculating 3 . Track units every step 4 . Domain before simplifying 5 . Order matters: nPr 6 . Groups only: nCr 7 . Derivative = rate 8 . Integral = accumulation 9 . Correlation is not cause 10 . One counterexample disproves

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