SAT / PSAT math foundations
Work with proportions, data and geometry through short lessons and focused practice.
Independent skill practice, not endorsed by College Board. This program does not cover the full math syllabus or Reading and Writing, and does not reproduce exam timing, adaptive modules or question formats. Use official Bluebook practice alongside it.
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Your path
Read the method, then put it to work.
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Work with proportions
Find a percentage and divide a total into proportional parts.
Lessons & practices
LessonFind a percentage in your head 3 min readPracticeLessonDivide in a ratio 3 min readPractice -
Turn a situation into an equation
Keep units consistent and identify the quantity that stays the same.
Lessons & practices
LessonUse time units 3 min readPracticeLessonSet up the equation 4 min readPracticeThese mixtures, journeys and work rates introduce equations. Systems, inequalities and advanced algebra need additional study.
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Read and summarize data
Read the labels before calculating, then choose a useful summary.
Lessons & practices
LessonRead data before calculating 6 min readPracticeLessonChoose a useful center 4 min readPractice -
Reason about chance and samples
Choose the right denominator and distinguish chance variation from selection bias.
Lessons & practices
LessonCondition on information 5 min readPracticeLessonQuestion the sample 4 min readPractice -
Read lines and angles
Use coordinate differences and angle totals instead of judging the drawing.
Lessons & practices
LessonRead rise over run 4 min readPracticeLessonComplete the angle sum 4 min readPracticeSome geometry rounds ask you to compare quantities and explore a diagram. SAT and PSAT use different answer formats.
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Compare area and volume
Use perpendicular height and keep length, area and volume scale factors separate.
Lessons & practices
LessonUse base and height 4 min readPracticeLessonScale length, area and volume 4 min readPractice -
Connect triangles and circles
Choose the right triangle ratio, then use an angle to find a fraction of a circle.
Lessons & practices
LessonChoose a triangle ratio 4 min readPracticeLessonMeasure a circle sector 4 min readPracticeThis introduces right-triangle ratios and circle sectors; additional geometry topics remain outside this program.
Go further
Try a harder setting, apply the method in another practice, then review what changed.
Optional practice. Your rounds appear in Progress; your completed modules stay complete.
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Choose a model before solving
Define the unknowns and their units. Match each condition to an equation, including fixed charges, equal costs or two linked totals.
Lessons & practices
LessonPracticeAfter your round
Substitute the solved values into every original condition. Explain which relationship a tempting wrong equation changes. -
Track the amount of solute
Separate total mixture mass from solute mass. When replacing liquid, subtract what leaves before adding what enters, then find the new concentration.
Lessons & practices
LessonPracticeAfter your round
Check the final mass and solute separately. After repeated replacement, use the updated concentration rather than the original one. -
Distinguish a rate from its change
Compare the percentage-point difference with the percentage change from the original rate. Then find what percentage one amount is of another.
Lessons & practices
PracticeAfter your round
Name the denominator before dividing. To check an unknown percentage, multiply the whole by your percentage and compare with the given part. -
Recover a missing group average
Turn each average into a total using its group size. Combine totals or subtract the known group, then divide by the appropriate count.
Lessons & practices
LessonPracticeAfter your round
Check the reconstructed overall average. Explain why taking the simple mean of two group averages fails when their sizes differ.