Algebra
35%of exam
Linear EquationsSystemsInequalitiesSlope & Intercepts
Advanced Math
35%of exam
Problem-Solving & Data Analysis
15%of exam
Ratios & RatesPercentagesStatisticsScatterplots
Geometry & Trigonometry
15%of exam
Area & VolumeTrianglesCirclesTrig Ratios
Quick Facts
- Exam
- Digital SAT Math
- Owner
- College Board
- Questions
- 44 (2x22)
- Time
- 70 min (35/module)
- Score range
- 200-800
- Calculator
- Allowed throughout (Desmos)
- Format
- 75% MC, 25% grid-in
- Level
- High school / college admissions
- Blueprint
- Digital SAT since March 2024
Order of Operations
PEMDAS: Parentheses, Exponents, Multiply/Divide, Add/Subtract
P: Parentheses firstE: Exponents nextMD: left to rightAS: left to right
Slope vs Y-Intercept
Slope
- Rate of change
- Rise over run
Y-intercept
- Starting value
- Where line crosses y-axis
Steepness vs starting point
Problem Approach Picker
- Two linear equations given→Substitution or elimination(Systems)
- Equation has x²→Quadratic formula or factor(Advanced Math)
- Ratio or rate given→Set up proportion(PSDA)
- Percent change asked→(new-old)/old(PSDA)
- Right triangle sides→Pythagorean theorem(Geometry)
- Angle and one side known→SOH-CAH-TOA(Trig)
Linear Equations & Slope
- Slope formula
- (y2-y1)/(x2-x1)
- Slope-intercept form
- y=mx+b
- Point-slope form
- y-y1=m(x-x1)
- Standard form
- Ax+By=C
- Parallel lines
- Equal slopes
- Perpendicular lines
- Negative reciprocal slopes
- x-intercept
- Set y=0
- y-intercept
- Set x=0
Systems & Inequalities
- Substitution method
- Solve one, sub in
- Elimination method
- Add or subtract equations
- No solution
- Same slope, different intercept
- Infinite solutions
- Equations are identical
- One solution
- Different slopes
- Flip inequality sign
- Multiply or divide by negative
- Compound inequality
- Two bounds, one variable
- Absolute value equation
- x=a or x=-a
FOIL for Binomial Multiplication
First, Outer, Inner, Last term products
First: multiply first termsOuter: multiply outer termsInner: multiply inner termsLast: multiply last terms
Factoring vs Quadratic Formula
Factoring
- Fast for nice numbers
- Whole-number roots
Quadratic formula
- Always works
- Handles messy roots
Try factor first
Function & Graph Picker
- Need vertex of parabola→-b/2a for x
- Need number of roots→Check discriminant
- Growth over time→Exponential model
- Need x-intercepts→Factor or quadratic formula
- Graph shifts up/down→Add constant outside f(x)
- Graph shifts left/right→Add constant inside f(x)
Quadratics
- Standard quadratic form
- ax²+bx+c=0
- Quadratic formula
- x=(-b±√(b²-4ac))/2a
- Discriminant formula
- b²-4ac
- Discriminant > 0
- Two real roots
- Discriminant = 0
- One repeated root
- Discriminant < 0
- No real roots
- Vertex form
- a(x-h)²+k
- Vertex x-coordinate
- -b/2a
- Factoring trinomials
- Find two binomial factors
- Completing the square
- Convert to vertex form
Exponential vs Linear Growth
Linear growth
- Adds constant amount
- Straight-line graph
Exponential growth
- Multiplies by factor
- Curved graph
Add vs multiply
Exponents & Transformations
- Exponential growth
- a(1+r)^t
- Exponential decay
- a(1-r)^t
- x^a · x^b
- Add exponents
- x^a ÷ x^b
- Subtract exponents
- (x^a)^b
- Multiply exponents
- x^-a
- 1/x^a
- x^0
- Equals 1
- x^(1/n)
- nth root of x
- f(x)+k
- Shifts graph up k
- f(x-h)
- Shifts graph right h
Polynomials & Radicals
- Difference of squares
- a²-b²=(a+b)(a-b)
- (a+b)²
- a²+2ab+b²
- (a-b)²
- a²-2ab+b²
- a³+b³
- (a+b)(a²-ab+b²)
- Radical equations
- Check for extraneous roots
- √(x²)
- Equals |x|
- Polynomial degree
- Highest exponent value
- End behavior
- Determined by leading term
Mean vs Median
Mean
- Average of all values
- Skewed by outliers
Median
- Middle value sorted
- Resistant to outliers
Outliers affect mean more
Data & Geometry Picker
- Two categorical variables→Two-way frequency table
- Trend between two variables→Scatterplot and line of fit
- Spread of data asked→Standard deviation or IQR
- Missing side, right triangle→Pythagorean or trig ratio
- Angle in radians→Convert using π/180
- Circle arc length→Use radius and central angle
Ratios, Rates & Percentages
- Unit rate
- Ratio per one unit
- Percent increase
- (new-old)/old×100
- Percent decrease
- (old-new)/old×100
- x% of n
- (x/100)×n
- Direct variation
- y=kx
- Inverse variation
- y=k/x
- Cross multiplication
- a/b=c/d→ad=bc
Statistics & Data Interpretation
- Mean
- Sum divided by count
- Median
- Middle value when sorted
- Mode
- Most frequent value
- Range
- Maximum minus minimum
- Standard deviation
- Spread of data around mean
- IQR
- Q3 minus Q1
- Scatterplot association
- Positive, negative, or none
- Line of best fit
- Models the overall trend
- Margin of error
- Range of sampling uncertainty
- Two-way table
- Joint and marginal frequencies
SOH-CAH-TOA Trig Ratios
SOH sin, CAH cos, TOA tan
SOH: opposite over hypotenuseCAH: adjacent over hypotenuseTOA: opposite over adjacent
Area vs Perimeter
Area
- Space inside shape
- Squared units
Perimeter
- Distance around shape
- Linear units
Inside vs boundary
Area & Volume Formulas
- Circle area
- πr²
- Circumference
- 2πr
- Triangle area
- ½×base×height
- Rectangle area
- length×width
- Trapezoid area
- ½(b1+b2)×height
- Cylinder volume
- πr²h
- Sphere volume
- (4/3)πr³
- Cone volume
- ⅓πr²h
- Prism volume
- length×width×height
Common Pythagorean Triples
3-4-5, 5-12-13, 8-15-17 scale to any multiple
3-4-5 triangle5-12-13 triangle8-15-17 triangle6-8-10 also works
Sine vs Cosine
Sine
- Opposite over hypotenuse
- Rises from 0
Cosine
- Adjacent over hypotenuse
- Starts at maximum
Opposite vs adjacent side
Triangles & Trigonometry
- Pythagorean theorem
- a²+b²=c²
- 3-4-5 triple
- Common right triangle
- 5-12-13 triple
- Common right triangle
- 45-45-90 triangle
- Legs x, hyp x√2
- 30-60-90 triangle
- Sides x, x√3, 2x
- SOH-CAH-TOA
- sin cos tan ratios
- sin θ
- Opposite ÷ hypotenuse
- cos θ
- Adjacent ÷ hypotenuse
- tan θ
- Opposite ÷ adjacent
- Triangle angle sum
- 180 degrees total
- Similar triangles
- Proportional sides, equal angles
Special Right Triangle Ratios
Two special right triangles to memorize
45-45-90: legs x, hyp x√230-60-90: sides x, x√3, 2xMemorize both ratio setsFaster than trig on these
Common Traps
Percent Change Base Trap
Always divide by original value ≠ Not the new value
Vertex Form Hidden Sign
(x+3)² means h = -3 ≠ Flip sign to find h
Radians vs Degrees Trap
π radians equals 180 degrees ≠ Watch calculator angle mode
Squaring Creates Extraneous Roots
Check answers in original equation ≠ Squaring can add fake roots
Area vs Perimeter Units
Area is squared units ≠ Perimeter is a single length
Mean vs Median Skew
Outliers pull the mean ≠ Median ignores extreme values
x-intercept vs y-intercept
x-intercept sets y to zero ≠ y-intercept sets x to zero
Last Minute
- 1.44 questions across two modules
- 2.70 minutes total, 35 per module
- 3.Calculator allowed on every question
- 4.Desmos graphing calculator built in
- 5.Algebra & Advanced Math: 35% each
- 6.Geometry & Data domains: 15% each
- 7.Score range is 200 to 800
- 8.75% multiple choice, 25% grid-in
- 9.Module 1 routes to Module 2
- 10.Vertex x = -b/(2a)
- 11.Check for extraneous radical roots
- 12.Know triples: 3-4-5 and 5-12-13
- 13.SOH-CAH-TOA gives sin cos tan
- 14.Outliers skew mean, not median
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