Question 1 of 3 · Calculator allowed
Simplify 4a × 3b.
Multiply the numerical coefficients and then write the variables together: 4 × 3 × a × b = 12ab.
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Question 2 of 3 · Calculator allowed
Write y = x² - 8x + 11 in completed-square form.
x² - 8x = (x - 4)² - 16. Adding 11 gives y = (x - 4)² - 5, so the turning point is (4, -5).
Question 3 of 3 · Calculator allowed
Solve 2x² - 3x - 4 = 0. Give the exact solutions.
Using x = [-b ± √(b² - 4ac)]/(2a) with a = 2, b = -3 and c = -4 gives x = [3 ± √(9 + 32)]/4 = (3 ± √41)/4.
These tiles show your answers to three questions. They are a starting point, not a mastery score or grade prediction.
Equivalent expressions
Correct answer: 12ab
Multiply the numerical coefficients and then write the variables together: 4 × 3 × a × b = 12ab.
Nonlinear functions
Correct answer: y = (x - 4)² - 5
x² - 8x = (x - 4)² - 16. Adding 11 gives y = (x - 4)² - 5, so the turning point is (4, -5).
Nonlinear equations in one variable
Correct answer: x = (3 ± √41)/4
Using x = [-b ± √(b² - 4ac)]/(2a) with a = 2, b = -3 and c = -4 gives x = [3 ± √(9 + 32)]/4 = (3 ± √41)/4.
For parents: look at the explanation together. A correct answer is encouraging; a missed answer gives you something specific to work on. Broader practice over time is needed to understand progress.
YOUR TOPIC MAP
20 areasFind your starting point.
01Equivalent expressions
Specification reference: Advanced Math: Equivalent expressions
Equivalent expressions requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Equivalent expressions requires. Keep exact values until the final step and check signs, units and reasonableness.
02Nonlinear equations in one variable
Specification reference: Advanced Math: Nonlinear equations in one variable
Nonlinear equations in one variable requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Nonlinear equations in one variable requires. Keep exact values until the final step and check signs, units and reasonableness.
03Nonlinear functions
Specification reference: Advanced Math: Nonlinear functions
Nonlinear functions requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Nonlinear functions requires. Keep exact values until the final step and check signs, units and reasonableness.
04Systems of equations in two variables
Specification reference: Advanced Math: Systems of equations in two variables
Systems of equations in two variables requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Systems of equations in two variables requires. Keep exact values until the final step and check signs, units and reasonableness.
05Linear equations in one variable
Specification reference: Algebra: Linear equations in one variable
Linear equations in one variable requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Linear equations in one variable requires. Keep exact values until the final step and check signs, units and reasonableness.
06Linear equations in two variables
Specification reference: Algebra: Linear equations in two variables
Linear equations in two variables requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Linear equations in two variables requires. Keep exact values until the final step and check signs, units and reasonableness.
07Linear functions
Specification reference: Algebra: Linear functions
Linear functions requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Linear functions requires. Keep exact values until the final step and check signs, units and reasonableness.
08Linear inequalities in one or two variables
Specification reference: Algebra: Linear inequalities in one or two variables
Linear inequalities in one or two variables requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Linear inequalities in one or two variables requires. Keep exact values until the final step and check signs, units and reasonableness.
09Systems of two linear equations in two variables
Specification reference: Algebra: Systems of two linear equations in two variables
Systems of two linear equations in two variables requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Systems of two linear equations in two variables requires. Keep exact values until the final step and check signs, units and reasonableness.
10Area and volume
Specification reference: Geometry and Trigonometry: Area and volume
Area and volume requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Area and volume requires. Keep exact values until the final step and check signs, units and reasonableness.
11Circles
Specification reference: Geometry and Trigonometry: Circles
Circles requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Circles requires. Keep exact values until the final step and check signs, units and reasonableness.
12Lines, angles, and triangles
Specification reference: Geometry and Trigonometry: Lines, angles, and triangles
Lines, angles, and triangles requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Lines, angles, and triangles requires. Keep exact values until the final step and check signs, units and reasonableness.
13Right triangles and trigonometry
Specification reference: Geometry and Trigonometry: Right triangles and trigonometry
Right triangles and trigonometry requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Right triangles and trigonometry requires. Keep exact values until the final step and check signs, units and reasonableness.
14Evaluating statistical claims: observational studies and experiments
Specification reference: Problem-Solving and Data Analysis: Evaluating statistical claims
Evaluating statistical claims: observational studies and experiments requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Evaluating statistical claims: observational studies and experiments requires. Keep exact values until the final step and check signs, units and reasonableness.
15Inference from sample statistics and margin of error
Specification reference: Problem-Solving and Data Analysis: Inference from sample statistics and margin of error
Inference from sample statistics and margin of error requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Inference from sample statistics and margin of error requires. Keep exact values until the final step and check signs, units and reasonableness.
16One-variable data: distributions and measures of center and spread
Specification reference: Problem-Solving and Data Analysis: One-variable data
One-variable data: distributions and measures of center and spread requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what One-variable data: distributions and measures of center and spread requires. Keep exact values until the final step and check signs, units and reasonableness.
17Percentages
Specification reference: Problem-Solving and Data Analysis: Percentages
Percentages requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Percentages requires. Keep exact values until the final step and check signs, units and reasonableness.
18Probability and conditional probability
Specification reference: Problem-Solving and Data Analysis: Probability and conditional probability
Probability and conditional probability requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Probability and conditional probability requires. Keep exact values until the final step and check signs, units and reasonableness.
19Ratios, rates, proportional relationships, and units
Specification reference: Problem-Solving and Data Analysis: Ratios, rates, proportional relationships, and units
Ratios, rates, proportional relationships, and units requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Ratios, rates, proportional relationships, and units requires. Keep exact values until the final step and check signs, units and reasonableness.
20Two-variable data: models and scatterplots
Specification reference: Problem-Solving and Data Analysis: Two-variable data
Two-variable data: models and scatterplots requires the correct mathematical rule, exact working and a final check that the result satisfies the conditions in the question.
Watch for: Do not select a familiar formula before identifying what Two-variable data: models and scatterplots requires. Keep exact values until the final step and check signs, units and reasonableness.
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College Board · SAT · Mathematics · digital-sat
current digital SAT structure checked 2026-08-27
Source checked: 2026-08-27. The current official specification controls assessment requirements and option choices.
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It shows the outcome of these three answers and gives a specific skill to discuss or practise next. It is not a full assessment, a mastery score or a grade prediction. Broader practice over time is needed to understand progress.
What does the College Board SAT Mathematics route cover?
LearningP currently maps 20 assessed areas for specification digital-sat. The visible topic map below is derived from the verified route; the current official specification remains controlling.
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The verified source bank contains 200 original LearningP question records for this route. Every mapped area meets the current publication minimum and passed the latest blocker and review audit.
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