Cheat sheet

AEPA Mathematics Cheat Sheet

Processes + Number Sense

19%of exam

EstimationRatiosLogicNumber TheoryComplex Numbers

Algebra + Functions

24%of exam

FunctionsSystemsPolynomialsExponentialsLogsAsymptotes

Geometry + Measurement

19%of exam

UnitsSimilarityAreaVolumeConicsTransformations

Trigonometry + Calculus

19%of exam

Unit CircleIdentitiesLimitsDerivativesIntegralsOptimization

Stats + Discrete Math

19%of exam

DisplaysSamplingProbabilityCountingSequencesMatrices

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

Inductive

  • Patterns
  • Likely claim
  • Needs proof

Deductive

  • Rules
  • Certain conclusion
  • Valid argument

Pattern vs proof

Problem Setup Picker

  1. About enoughEstimate(Check plausibility)
  2. Per one unitRate(Track units)
  3. Same ratioProportion(Cross multiply)
  4. Pattern onlyConjecture(Needs proof)
  5. One failureCounterexample(Disproves claim)
  6. Many casesTruth table(Logic check)
  7. Diagram fitsRepresentation(Simplify context)
  8. Answer scale oddUnits(Catch error)

Number Sense

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

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

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

Domain

  • Inputs
  • x-values
  • Restrictions

Range

  • Outputs
  • y-values
  • Possible results

Allowed in vs possible out

Function Picker

  1. Constant rateLinear(Slope)
  2. Turning pointQuadratic(Vertex)
  3. Many zerosPolynomial(Factors)
  4. Constant ratioExponential(Growth/decay)
  5. Undo exponentialLogarithm(Inverse)
  6. Vertical asymptoteRational(Restrictions)
  7. Repeating waveTrig(Period)
  8. Rules by intervalPiecewise(Check domain)

Function Basics

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

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

Similar

  • Same shape
  • Scaled lengths
  • Equal angles

Congruent

  • Same size
  • Same shape
  • Rigid motion

Scale vs exact

Geometry + Measurement

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

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

SOH CAH TOA anchors trig

SOH: sineCAH: cosineTOA: tangent

Derivative vs Integral

Derivative

  • Slope
  • Rate
  • Local change

Integral

  • Area
  • Accumulation
  • Total change

Rate vs total

Calculus Picker

  1. Approach valueLimit
  2. No jumpContinuity
  3. Instant slopeDerivative
  4. Nested expressionChain rule
  5. Max/min requestedCritical points
  6. Accumulated changeIntegral
  7. Area approximationRiemann sum
  8. Position from velocityIntegral

Trigonometry

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

All Students Take Calculus

QI: allQII: sineQIII: tangentQIV: cosine

Calculus

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

Derivative slopes; integral totals

f': rateIntegral: areaFTC: link

Counting Order

nPr arranges; nCr chooses

Permutation: orderCombination: groupsFCP: slots

Permutation vs Combination

Permutation

  • Order matters
  • Arrangements
  • nPr

Combination

  • Order ignored
  • Selections
  • nCr

Arrange vs choose

Counting Picker

  1. Order mattersPermutation
  2. Groups onlyCombination
  3. Repeated stagesFCP
  4. Not eventComplement
  5. Either eventUnion
  6. Both eventsIntersection
  7. Given conditionConditional
  8. No influenceIndependence

Statistics

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

Correlation

  • Variables move
  • Association
  • No proof

Causation

  • One causes
  • Controlled evidence
  • Mechanism

Association vs cause

Probability + Counting

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

Exclusive

  • Cannot both occur
  • No overlap

Independent

  • No probability effect
  • Can overlap

Overlap vs influence

Discrete + Matrix

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