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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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.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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