SAT Math Learning Map
Practice through Stages 1–4. Use Desmos to check work and build understanding when it helps.
Browse all Math practice topics →
Algebra
≈35%
Linear equations and formulas
- ALG-01 Solve a linear equation Stage 1
ax+b=c
Practise this topic → - ALG-02 Equations with fractions or decimals Stage 1
Clear denominators first
Practise this topic → - ALG-03 No solution or infinitely many solutions Stage 2
ax+b=ax+c
Desmos: Solve/check: graph both lines; parallel means no solution, overlap means infinitely many.
Practise this topic → - ALG-04 Rearrange a formula Stage 2
Isolate the requested variable
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Linear functions and graphs
- ALG-05 Slope and rate of change Stage 1
m=(y₂-y₁)/(x₂-x₁)
Desmos: Check: plot two points and inspect the slope.
Practise this topic → - ALG-06 Equation of a line from data Stage 2
y=mx+b
Desmos: Check/solve: enter two points or the line and inspect slope/intercept.
Practise this topic → - ALG-07 Parallel and perpendicular lines Stage 2
m₁=m₂; m₁m₂=-1
Desmos: Check: graph both lines; same slope means parallel, product of slopes -1 means perpendicular.
Practise this topic → - ALG-08 Linear word-problem model Stage 2
total = rate·quantity + initial
Desmos: Solve/check: use a table or regression only when several data points or model comparisons are given.
Practise this topic → - ALG-15 Connect linear equations, tables, and graphs Stage 2
Ax+By=C ↔ y=mx+b
Desmos: Check: graph the equation and compare intercepts or points with the table.
Practise this topic → - ALG-16 Interpret slope, intercept, and parameters Stage 3
y=mx+b in context
Desmos: Explore: add sliders for m and b to see how the model changes.
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Systems of linear equations
- ALG-09 Solve a two-variable linear system Stage 2
Substitute or eliminate
Desmos: Solve: graph both equations and click the intersection.
Practise this topic → - ALG-10 Classify a linear system Stage 3
Compare coefficient ratios
Desmos: Check: graph both lines; crossing, overlap, and parallel lines show 1, infinitely many, and 0 solutions.
Practise this topic → - ALG-11 System model in context Stage 3
Two quantities, two constraints
Desmos: Solve/check: graph the two constraints and inspect the intersection; use a table for integer context.
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Linear inequalities
- ALG-12 One-variable and compound inequalities Stage 2
Reverse sign when multiplying by a negative
Desmos: Check: enter the inequality on a number line and verify the interval and endpoint.
Practise this topic → - ALG-13 Two-variable inequality region Stage 3
Ax+By≤C
Desmos: Solve/check: enter the inequality directly to see the shaded side and test a point.
Practise this topic → - ALG-14 Constraint and optimization setup Stage 3
Feasible region
Desmos: Solve/check: graph all constraints, inspect feasible-region vertices, and compare objective values.
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Advanced Math
≈35%
Equivalent expressions
- ADM-01 Exponents, radicals, and rational exponents Stage 1
a^(m/n)=ⁿ√(a^m)
Desmos: Check only: graph original and candidate expressions when a variable is present; numeric items do not need Desmos.
Practise this topic → - ADM-02 Factor, expand, and complete the square Stage 2
(a+b)²=a²+2ab+b²
Desmos: Check: graph the original and candidate expressions; overlap confirms equivalence on the valid domain.
Practise this topic → - ADM-03 Rational expressions and restrictions Stage 3
Denominator ≠ 0
Desmos: Check: graph both forms and inspect holes or asymptotes; verify excluded x-values algebraically.
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Quadratics and polynomials
- ADM-04 Solve a quadratic equation Stage 2
ax²+bx+c=0
Desmos: Solve: graph the quadratic and click the x-intercepts.
Practise this topic → - ADM-05 Discriminant and number of roots Stage 3
b²−4ac
Desmos: Solve/check: count x-intercepts; one, two, or none correspond to the real-root count.
Practise this topic → - ADM-06 Vertex, maximum, and minimum Stage 3
x=−b/(2a)
Desmos: Solve: click the vertex to read the maximum or minimum.
Practise this topic → - ADM-07 Polynomial factors, roots, and remainder Stage 3
P(c)=0 for factor x−c
Desmos: Check: graph the polynomial and inspect x-intercepts or roots.
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Nonlinear equations and systems
- ADM-08 Absolute-value and radical equations Stage 3
|x−a|=b
Desmos: Solve/check: graph both sides and click intersections; check domain and extraneous roots algebraically.
Practise this topic → - ADM-09 Line–curve or nonlinear system Stage 4
Set expressions equal
Desmos: Solve: graph both equations and inspect intersections.
Practise this topic → - ADM-15 Rational equations Stage 3
Clear denominators; reject excluded values
Desmos: Check: graph both sides and inspect intersections, holes, and asymptotes; reject excluded values.
Practise this topic → - ADM-16 Exponential equations Stage 3
Rewrite with a common base or use logs
Desmos: Solve/check: graph both sides or use a table to locate the intersection.
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Functions and exponentials
- ADM-10 Function notation, evaluation, and composition Stage 2
f(g(x))
Practise this topic → - ADM-11 Function transformations Stage 3
f(x−h)+k
Desmos: Explore/check: graph f(x) and the transformed form; use sliders for shifts, reflections, and stretches.
Practise this topic → - ADM-12 Domain, range, and inverse functions Stage 3
f⁻¹ swaps x and y
Desmos: Check: graph f, its inverse, and y=x; inspect domain and range restrictions.
Practise this topic → - ADM-13 Exponential growth and decay Stage 3
P(1±r)^t
Desmos: Solve/check: use a table for growth or decay; use exponential regression only when data points are given.
Practise this topic → - ADM-14 Nonlinear model interpretation Stage 4
Model parameters in context
Desmos: Check: compare candidate models in a table or graph, then interpret parameters from the context.
Practise this topic → - ADM-17 Features of quadratic and polynomial functions Stage 3
Zeros, intercepts, end behavior, extrema
Desmos: Check: graph the function to inspect zeros, extrema, and end behavior.
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Problem-Solving and Data Analysis
≈15%
Ratios, rates, units, and percentages
- PSD-01 Ratios and proportional relationships Stage 1
a/b=c/d
Practise this topic → - PSD-02 Rates, density, and unit conversion Stage 2
rate=quantity/time
Practise this topic → - PSD-03 Percent increase, decrease, and reverse percent Stage 2
new=old(1±r)
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One-variable data
- PSD-04 Mean, median, and weighted mean Stage 1
mean=sum/n
Desmos: Check: enter a long data set as a list and use mean or median; skip for a few easy values.
Practise this topic → - PSD-05 Spread and distribution Stage 2
range, IQR, standard deviation
Desmos: Check: use lists or box plots to compare spread when the data set is long.
Practise this topic → - PSD-12 Frequency and relative-frequency tables Stage 2
relative frequency=count/total
Desmos: Check: enter counts in a table and calculate relative frequencies.
Practise this topic → - PSD-15 Read tables, bar graphs, line graphs, and dot plots Stage 1
Read the scale, labels, and requested category
Desmos: Check only: redraw the display when the supplied table or graph is difficult to read.
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Two-variable data and models
- PSD-06 Scatterplots and association Stage 2
Positive/negative association
Desmos: Solve/check: plot the data and inspect the direction and strength of the association.
Practise this topic → - PSD-07 Linear regression and prediction Stage 3
y=mx+b
Desmos: Solve: enter data and use y1~mx1+b for linear regression and prediction.
Practise this topic → - PSD-08 Residuals and model fit Stage 3
residual=actual−predicted
Desmos: Check: use the regression model, then compute residuals in a list.
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Probability and inference
- PSD-09 Probability and sample spaces Stage 2
P=favorable/total
Practise this topic → - PSD-10 Conditional probability and two-way tables Stage 3
P(A|B)=P(A∩B)/P(B)
Desmos: Check: organize counts in a two-way table and calculate conditional proportions.
Practise this topic → - PSD-11 Sampling, margin of error, and claims Stage 3
Sample statistic estimates population
Practise this topic → - PSD-13 Margin of error and confidence intervals Stage 3
estimate ± margin of error
Practise this topic → - PSD-14 Statistical claims and study design Stage 4
Random sampling supports generalization; random assignment supports causation
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Geometry and Trigonometry
≈15%
Area, volume, and coordinate geometry
- GEO-01 Perimeter and area Stage 1
A=bh, ½bh, πr²
Practise this topic → - GEO-02 Volume and surface area Stage 2
V=Bh; cylinder=πr²h
Practise this topic → - GEO-03 Scale, similarity, and dimensional change Stage 2
length k, area k², volume k³
Practise this topic → - GEO-04 Distance, midpoint, and coordinate geometry Stage 2
d=√((Δx)²+(Δy)²)
Desmos: Check: plot the points and inspect distance or midpoint; use formulas for the official calculation.
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Lines, angles, and triangles
- GEO-05 Lines, angles, and polygons Stage 1
triangle 180°; polygon (n−2)180°
Practise this topic → - GEO-06 Similar and congruent triangles Stage 2
Corresponding sides proportional
Practise this topic → - GEO-07 Pythagorean theorem and right triangles Stage 2
a²+b²=c²
Desmos: Check only: plot a right triangle to verify the length; the Pythagorean theorem is usually faster.
Practise this topic → - GEO-08 Special right triangles Stage 3
45-45-90; 30-60-90 ratios
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Circles and trigonometry
- GEO-09 Circle equation and center/radius Stage 3
(x−h)²+(y−k)²=r²
Desmos: Solve/check: enter the circle equation and inspect center and radius.
Practise this topic → - GEO-10 Arcs and sectors Stage 3
θ/360 of circumference/area
Practise this topic → - GEO-11 Right-triangle trigonometry Stage 3
sin, cos, tan
Desmos: Check only: use sin, cos, or tan in degree mode; a standard calculator is usually faster.
Practise this topic → - GEO-12 Radians and trigonometric relationships Stage 4
180°=π radians
Desmos: Check: switch deliberately between degree and radian mode and verify the trigonometric relationship.
Practise this topic → - GEO-13 Circle theorems, tangents, chords, and inscribed angles Stage 4
Inscribed angle = ½ intercepted arc
Desmos: Check: graph the circle and inspect tangent, chord, or intersection relationships; do not infer proof from the picture.
Practise this topic → - GEO-14 Unit-circle trigonometry Stage 4
(cos θ, sin θ)
Desmos: Check: graph a unit circle in radian mode and inspect (cos(theta), sin(theta)).
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