Timed modules and full-length Math rehearsals
Use the guidance first, attempt each worked example, then open its solution. Practice sets and timed rehearsals keep their original boundaries.
Reading position saved on this browser; this is not a completion record.
3.1 What the timing is based on
Under standard timing, SAT Math has 44 questions in two 35-minute modules. The second module is selected using performance on the first. The 10-minute scheduled break is between Reading and Writing and Math, not between the two Math modules. [1]
Each rehearsal here has two fixed 22-question modules. Each contains 15 Algebra, 15 Advanced Math, 7 Problem-Solving and Data Analysis, and 7 Geometry and Trigonometry questions overall, with all four domains represented in each module. Each uses 33 multiple-choice and 11 numeric-response items. The actual SAT uses both formats; approximately one-quarter of Math questions are student-produced responses. [2] [8]
The essential limitation These are full-length Math-section rehearsals, not full SAT exams. Everyone sees the same second module. No routing decision, scaled-score table, score ceiling, or predicted score is supplied. All 44 items count in this rehearsal’s raw review, regardless of how operational and pretest items are handled on the actual SAT.
3.2 Rehearsal setup
Use fresh questions, scratch paper, and the calculator you expect to use. Use only the standard formulas available from the runner’s Reference control, not the additional study reference. Set a separate timer for each module. If you have approved accommodations, rehearse the timing and breaks specified for you rather than automatically using standard timing.
The embedded Desmos calculator is available during Math, with scientific and graphing options. Current policy prohibits CAS calculators and certain stored algebra functionality; check the official policy for any personal calculator rather than relying on an old approved-model list. [7]
3.3 Keep the measurement clean
Record your response before moving on. At the end of the first module, stop and do not revisit it while working on the second. Do not pause for hints or check the explanations between modules. A technology interruption or outside help should be recorded, not hidden in an apparently standard result.
3.4 Make a pacing plan that can bend
A short early item and a multi-step final item need not receive equal time. Monitor whether you are making useful progress. If not, record what you know, the next useful step, and any condition you must preserve. A correct response entered before moving on matters more than a perfect-looking page of scratch work.
Reserve time to locate unanswered questions and correct specific entry risks. Review a known sign or target concern before repeatedly rechecking an answer you have already verified independently. A flag is a navigation tool, not a substitute for an entered response. Bluebook provides a timer, Mark for Review, an option eliminator, and a question menu. [6]
3.5 Numeric responses in this book
Enter only the requested number. Do not include a unit, percent sign, dollar sign, comma, or algebraic variable in a simulated response. Use a fraction such as 4/3 when it fits, or a suitable decimal. Mixed numbers should be written as improper fractions or decimals. In a problem asking for k when an area is kπ, enter k, not an approximation to the area. [9]
All numeric-response items in the two rehearsals have an exact integer, terminating decimal, or short fraction answer. Their keys show one exact form. Equivalent valid numeric forms are accepted when the response-entry rules permit them. On the actual test, follow the on-screen entry and precision directions.
3.6 What to do with guesses and post-time discoveries
Keep the original timed response. Mark a guess as a guess even if it turns out to be correct. Solve a missed or unfinished item afterward in a separate column; this helps distinguish knowledge from execution under time pressure.
For most students trying their best, College Board recommends a guess rather than a blank, especially after eliminating choices. That guidance does not create a reason to intentionally miss questions or to chase an imagined adaptive route. [3]
Save the fresh test for the right job Read the execution examples first, then take one rehearsal with solutions closed. Finish its review before taking the second on a later day. For software navigation, adaptive delivery, and scored practice, use Bluebook; this fixed rehearsal does not reproduce those features. [4]
15 worked examples
3.01. Spend time on the target, not every variable
If 5a + 2b = 43 and a − 2b = 5, what is a?
Show worked solutionHide worked solution for example 3.01
Work. Addition gives 6a
Answer: 8
Check. b
Key takeaway. Method selection is part of solving. Look for an already-aligned elimination before opening a tool.
3.02. Use a numerical check to verify a sign
Solve −3(2x − 5) = 27.
Show worked solutionHide worked solution for example 3.02
Work. Distribute carefully: −6x + 15
Answer: −2
Check. −3(2(−2) − 5) = −3(−9) = 27.
Key takeaway. Protect signs at the moment they become risky. Do not postpone every check to the end of a module.
3.03. Avoid unnecessary radical approximation
A square has diagonal 14. What is its area?
Show worked solutionHide worked solution for example 3.03
Work. For a square of side s, the diagonal is s. Thus s
Answer: 196
Check. The diagonal is longer than the side; both exact methods agree.
Key takeaway. Keep exact values when a radical cancels. Decimal approximations add work and risk without helping.
3.04. Use roots without fully solving
The roots of 3x2 − 15x + 7 = 0 are r and s. What is r + s?
Show worked solutionHide worked solution for example 3.04
Work. For a quadratic ax2 + bx + c
Answer: 5
Check. Factoring symbolically as 3(x − r)(x − s) gives the x coefficient −3(r + s)
Key takeaway. Read the requested symmetric expression before choosing the quadratic formula.
3.05. Recognize a useful graphing job
The functions are f(x) = x2 − 5x + 3 and g(x) = 2x − 7. What is the smaller x-coordinate where their graphs intersect?
Show worked solutionHide worked solution for example 3.05
Work. Graphing both functions and inspecting intersections is a reasonable tool choice. Algebra gives x2 − 7x + 10 = (x − 2)(x − 5) = 0, so the smaller input is 2. The corresponding output is −3.
Answer: 2
Check. f(2) = g(2) = −3. Read the input coordinate, not the output.
Key takeaway. For a graph-assisted solution, know in advance which coordinate and which intersection the question requests.
Alternative. In Desmos graphing mode, enter the two equations separately. Use a window showing both x
3.06. Estimate before calculating
What is 19.8% of 405, to the nearest whole number?
Show worked solutionHide worked solution for example 3.06
Work. Estimate with 20% of 400, which is 80. Then calculate 0.198(405)
Answer: 80
Check. 20% of 405 is 81. Reducing the rate by 0.2 percentage points subtracts 0.002(405)
Key takeaway. Use an estimate as an independent magnitude check, not as a substitute for requested precision.
3.07. Settle an inequality endpoint
What is the least integer n such that 7n + 4 > 60?
Show worked solutionHide worked solution for example 3.07
Work. Subtract 4 and divide by 7: n > 8. Because the inequality is strict, 8 is excluded; the least integer is 9.
Answer: 9
Check. At 8, the left side is 60, not greater than 60. At 9, it is 67.
Key takeaway. An adjacent-integer check is especially efficient when a question asks for a least or greatest whole number.
3.08. Use a change of variable to simplify notation
If (x + 2)2 − 5(x + 2) + 6 = 0, what is the sum of all solutions for x?
Show worked solutionHide worked solution for example 3.08
Work. Let u
Answer: 1
Check. Direct substitution of 0 and 1 makes the original expression zero.
Key takeaway. A substitution saves time only if you return to the original variable before answering.
3.09. Check whether squaring actually saved time
Solve = x − 1.
Show worked solutionHide worked solution for example 3.09
Work. The right side requires x ≥ 1. Squaring gives 2x + 7
Answer: 2 +
Check. The accepted root is greater than 1. Since it satisfies the squared equation and both original sides are nonnegative, equality in the original equation follows.
Key takeaway. A domain check can reject a candidate immediately; do not spend time evaluating both radicals numerically.
3.10. Distinguish an equality threshold from a strict requirement
A population is modeled by P(t) = 160 · 2t/4 for t ≥ 0 measured in years. What is the least integer t for which P(t) > 1280?
Show worked solutionHide worked solution for example 3.10
Work. The threshold ratio is 1280/160 = 8 = 23. Thus 2t/4 > 23, which requires t/4 > 3, or t > 12. The least integer is 13.
Answer: 13
Check. P(12)
Key takeaway. The model may be exponential, but the final decision can still be an integer-boundary check.
3.11. Build a flexible time budget
Workflow scenario: a 35-minute practice module has 22 questions. You reserve the last 3 minutes for checking unanswered and flagged items. What is the average first-pass budget per question, and how should you use it?
Show worked solutionHide worked solution for example 3.11
Work. The first pass has 32 minutes, so the average is 32/22 ≈ 1.45 minutes, or about 87 seconds. This is a planning average, not a command to spend 87 seconds on every item. Quick items can fund longer, productive work elsewhere.
Answer: About 87 seconds per question on average; use flexible allocation.
Check. 22(32/22)
Key takeaway. A pacing plan is editorial and adjustable. Replace a rigid stopwatch rule with a check on whether your next step is useful.
3.12. Leave a restart note that saves work
Workflow scenario: you have reduced a problem to x2 − 9x + 14 = 0 with x > 4, but have spent too long on it. What should a useful restart note contain?
Show worked solutionHide worked solution for example 3.12
Work. Write: Solve (x − 2)(x − 7)
Answer: The remaining mathematical answer is 7; preserve the condition in the note.
Check. The other root 2 fails x > 4. A note containing only quadratic would lose the decisive restriction.
Key takeaway. Moving on is not useful when completion is one short, certain step away. Notes should preserve the next action, not narrate frustration.
3.13. Review the wrong risk first
Workflow scenario: with 90 seconds remaining, you have one unanswered multiple-choice item, a flagged answer you already checked twice, and a numeric response copied as 0.75 after calculating 3/8. What should you prioritize?
Show worked solutionHide worked solution for example 3.13
Work. Correct the known transcription error to 3/8 or 0.375, then give the unanswered item your best remaining effort. Rechecking a twice-verified answer has lower immediate value. This is a prioritization example, not a guarantee about scoring.
Answer: Repair the known wrong entry and address the blank before repetitive rechecking.
Check. 3/8
Key takeaway. Rank review tasks by concrete evidence of risk. A flag is only a reminder; it is not proof that an answer is wrong.
3.14. Keep module boundaries real during practice
Workflow scenario: after finishing Module 2 in a rehearsal, you realize that a Module 1 answer should have been 24 rather than 12. How should you record this?
Show worked solutionHide worked solution for example 3.14
Work. Keep 12 as the timed Module 1 response and score it as originally entered. Record 24 separately as a post-time correction. The correction is useful learning evidence, but changing the original record would overstate timed performance.
Answer: Preserve the timed result; record the correction in the review column.
Check. The timed score answers What did I produce under these conditions? The correction answers What can I repair afterward?
Key takeaway. Separate performance measurement from learning. Both matter, but they are not interchangeable.
3.15. Interpret a fixed-practice result honestly
Workflow scenario: you answer 38 of 44 questions correctly on an original practice rehearsal on this site. Can this be converted to a reliable SAT Math score?
Show worked solutionHide worked solution for example 3.15
Work. No. The raw accuracy is 38/44 ≈ 86.4%, but this fixed set is not calibrated to the SAT scoring model and does not adapt. Record missed skills, guesses, slow correct answers, and timing. Use official scored Bluebook practice for score-oriented feedback.
Answer: 86.4% raw accuracy, not a supported scaled-score estimate.
Check. Two sets with 44 questions can have very different difficulty and skill coverage.
Key takeaway. A precise-looking conversion table is not evidence of calibration. Do not invent one.
3.8 Rehearsal 1: setup and answer record
44 questions / 70 minutes / two fixed 22-question modules. Use 35 minutes per module for standard-time practice. Use your approved timing and break conditions when rehearsing accommodations; this practice site does not determine eligibility.
Use permitted calculator features, scratch paper, and only the standard formulas available from the runner’s Reference control. Do not use the additional study reference, old solutions, or external answer tools. This is a Math-only, nonadaptive rehearsal, not an official SAT form.
The runner records every response and keeps the two modules separate. Use Flag for Review for uncertain questions, then review the complete result after both modules are submitted.
Use the result as a diagnosis, not a score prediction Count correct out of 44 and classify misses by skill and error type. Compare with a later attempt only after noting differences in timing, prior exposure, and difficulty. For a digital, adaptive practice score, use official Bluebook practice. [4]
3.9 Rehearsal 1 / Module 1
Stay within this module. A page turn does not reset the timer.
3.10 Rehearsal 1 / Module 2
Stay within this module. A page turn does not reset the timer.
3.11 Rehearsal 2: setup and answer record
44 questions / 70 minutes / two fixed 22-question modules. Use 35 minutes per module for standard-time practice. Use your approved timing and break conditions when rehearsing accommodations; this practice site does not determine eligibility.
Use permitted calculator features, scratch paper, and only the standard formulas available from the runner’s Reference control. Do not use the additional study reference, old solutions, or external answer tools. This is a Math-only, nonadaptive rehearsal, not an official SAT form.
The runner records every response and keeps the two modules separate. Use Flag for Review for uncertain questions, then review the complete result after both modules are submitted.
Use the result as a diagnosis, not a score prediction Count correct out of 44 and classify misses by skill and error type. Compare with a later attempt only after noting differences in timing, prior exposure, and difficulty. For a digital, adaptive practice score, use official Bluebook practice. [4]
3.12 Rehearsal 2 / Module 1
Stay within this module. A page turn does not reset the timer.
3.13 Rehearsal 2 / Module 2
Stay within this module. A page turn does not reset the timer.