Number + Quantity
10-12%of exam
Algebra
17-20%of exam
Functions
17-20%of exam
Geometry + Trig
17-20%of exam
Stats + Probability
12-15%of exam
Essential Skills
20%of exam
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
- 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
- Arithmetic
- Add constant
- Geometric
- Multiply ratio
- Matrix product
- Inner dimensions match
- Result size
- Outer dimensions
- Vector
- Magnitude + direction
- Set
- Collection of values
FOIL
First, Outer, Inner, Last
Binomial productsCombine like termsCheck signs
Slope vs Intercept
Slope
- Rate of change
- m
- Rise/run
Intercept
- Axis crossing
- b or zero
- Starting value
Rate vs start
Formula Picker
- 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
- 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
- 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
Domain
- Allowed inputs
- x-values
- Check restrictions
Range
- Possible outputs
- y-values
- Check graph
Input vs output
Functions
- 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
- 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
Sine opposite, cosine adjacent, tangent opposite
SOH: sin O/HCAH: cos A/HTOA: tan O/A
Similar vs Congruent
Similar
- Same shape
- Scaled lengths
- Angles equal
Congruent
- Same size
- Same shape
- Sides equal
Scaled vs identical
Geometry Basics
- 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
45s match; 30s double
45: x,x,xsqrt230: x,xsqrt3,2xHypotenuse longest
Circumference vs Area
Circumference
- Boundary length
- Linear units
- 2*pi*r
Area
- Inside region
- Square units
- pi*r^2
Around vs inside
Circles + Solids
- 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
- 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
Either add; both multiply
Or: add casesAnd: multiply chancesComplement: 1-event
Mean vs Median
Mean
- Uses all values
- Outlier sensitive
- Sum/count
Median
- Middle value
- Outlier resistant
- Sort first
Average vs middle
Data Picker
- 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
- 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
Permutation
- Order matters
- Arrangements
- Lineups
Combination
- Order ignored
- Groups
- Committees
Ordered vs unordered
Probability + Counting
- Probability
- Favorable over total
- Complement
- 1 minus event
- Independent
- Multiply probabilities
- Conditional
- Restrict sample space
- Permutation
- Order matters
- Combination
- Order ignored
Independent vs Dependent
Independent
- No influence
- Multiply directly
- Replacement often
Dependent
- Probability changes
- Update denominator
- No replacement
Same odds vs changed
Strategy Picker
- 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
- 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
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