Reading & Writing — Interactive Quiz
Click Start Test to begin. You may submit at any time. Time expiry auto-submits. Results show: correct/total, SAT-style score (12.5 per correct, rounded) /800, and time taken.
Results: —
Correct answers are highlighted in green. Your incorrect selections (if any) are highlighted in red. Explanations are shown under each question.
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📘 SAT Practice Test – Section 2: Math (44 Questions)
General Detail
- Total Questions: 44
- Time: 70 minutes
- Calculator allowed for all questions
- Covers: Algebra, Advanced Math, Problem Solving/Data, Geometry/Trig.
Instructions
- Each question has one correct answer.
- For grid-in (student-produced response) questions, enter numbers/decimals/fractions.
- Use scratch paper for solving.
- You may use a calculator.
Algebra – Linear Equations (Q1–6)
Q1. Solve for x:
\(3x – 7 = 11\)
A) \(4\)
B) \(5\)
C) \(6\)
D) \(7\)
Q2. A phone company charges $25 monthly plus $0.10 per text. If Maria’s bill was $43, how many texts did she send?
A) \(120\)
B)\( 150\)
C) \(160\)
D) \(180\)
Q3. If \(2x + y = 12\) and \(y=4\), what is \(x\)?
A) \(2\)
B) \(3\)
C) \(4\)
D)\( 5\)
Q4. The line passes through \((0, 2)\) and \((4, 10)\). What is its slope?
A) \(2\)
B) \(4\)
C) \(6\)
D)\( 8\)
Q5. Solve for y:
\(5y + 2 = 22\)
A) \(3\)
B)\( 4\)
C) \(5\)
D) \(6\)
Q6. Which is the solution to the system? $$x + y = 10 \\ x – y = 2$$
A)\( (4, 6)\)
B) \((6, 4)\)
C)\( (5, 5)\)
D)\( (8, 2)\)
Advanced Math – Quadratics/Exponents (Q7–12)
Q7. Solve:
\(x^2 – 9 = 0\)
A) \(±3\)
B)\( ±9\)
C) \(0, 9\)
D) \(3 only\)
Q8. Which is equivalent to \((2x^3)(3x^2)\)?
A) \(5x^5\)
B) \(6x^5\)
C) \(6x^6\)
D) \(5x^6\)
Q9. Solve for x:
\((x – 4)(x + 4) = 0\)
A)\( ±4\)
B) \(0\)
C) \(16\)
D) \(8\)
Q10. Which graph represents \(y = (x – 2)^2\)?
A) Parabola opening upward, vertex \((2,0)\)
B) Parabola opening upward, vertex \((0,2)\)
C) Parabola opening downward, vertex \((2,0)\)
D) Parabola opening downward, vertex \((0,2)\)
Q11. If \(3^x = 81\), then x = ?
A)\( 2\)
B)\( 3\)
C)\( 4\)
D)\( 5\)
Q12. Solve:
\(x^2 + 2x – 15 = 0\)
A)\(–5, 3\)
B)\( –3, 5\)
C)\( –1, 15\)
D)\( –15, 1\)
Problem Solving/Data Analysis (Q13–21)
Q13. A car rental company charges $50 plus $0.20 per mile. If Sarah paid $74, how many miles did she drive?
A)\( 100\)
B)\( 120\)
C)\( 150\)
D) \(170\)
Q14. A survey shows 60% prefer online, 25% in-person, rest undecided. If 200 students were surveyed, how many undecided?
A) \(20\)
B) \(30\)
C) \(40\)
D) \(50\)
Q15. A bag has 3 red, 2 blue, 5 green balls. Probability of choosing green?
A)\( 1/2\)
B) \(1/3\)
C) \(5/10\)
D) \(5/7\)
Q16. A recipe requires 2 cups sugar for 5 servings. How many cups for 15 servings?
A)\( 4\)
B) \(5\)
C) \(6\)
D)\( 7\)
Q17. In a class of 40, ratio of boys:girls = \(3:5\). How many girls?
A) \(15\)
B)\( 20\)
C) \(25\)
D) \(30\)
Q18. A stock price increases 20% from $100, then decreases 10%. Final price?
A) \($108\)
B)\( $110\)
C)\( $112\)
D)\( $120\)
Q19. Mean of \(4, 8, 12, 16?\)
A) \(10\)
B) \(11\)
C) \(12\)
D) \(13\)
Q20. Median of \(7, 9, 3, 11, 15?\)
A)\( 9\)
B) \(11\)
C)\( 7\)
D)\( 15\)
Q21. If \(40%\) of a number is 80, what is the number?
A)\( 100\)
B)\( 150\)
C) \(180\)
D)\( 200\)
Geometry/Trig (Q22–30)
Q22. Area of a triangle with base 10 and height 8?
A)\( 20\)
B)\( 30\)
C) \(40\)
D)\( 80\)
Q23. Circumference of a circle with radius 7 (use \( π ≈ 3.14\))?
A) \(22\)
B)\( 33\)
C)\( 44\)
D) \(50\)
Q24. A right triangle has legs 3 and 4. Hypotenuse?
A)\(5\)
B)\( 6\)
C)\(7\)
D)\( 8\)
Q25. Volume of a rectangular prism: \(5 × 4 × 3?\)
A)\( 60\)
B) \(50\)
C)\( 40\)
D)\( 70\)
Q26. Slope of line through \((2, 3)\) and\( (6, 7)?\)
A) \(1\)
B)\( 2\)
C)\( 3/2\)
D)\( 4\)
Q27. Interior angles of a triangle sum to:
A)\( 90°\)
B) \(120°\)
C) \(180°\)
D) \(360°\)
Q28. \(sin(30°) = ?\)
A) \(0.25\)
B)\( 0.5\)
C)\( √2/2\)
D)\( √3/2\)
Q29. A square has perimeter 36. Area?
A) \(81\)
B) \(100\)
C)\( 121\)
D) \(144\)
Q30. A cylinder has radius 3 and height 10. Volume? (Use \( π = 3.14\))
A)\(282.6\)
B)\( 300\)
C)\( 314\)
D)\( 500\)
Mixed Challenge (Q31–44)
Q31. Solve:
\(2x – 5 = 11\)
A)\(6\)
B)\( 7\)
C) \(8\)
D) \(9\)
Q32. If 5 pencils cost $2.50, how much do 12 cost?
A) \($5.00\)
B) \($6.00\)
C)\( $6.50\)
D) \($7.00\)
Q33. The equation of a line parallel to \(y = 2x + 3\) is:
A) \(y = 2x + 1\)
B) \(y = –2x + 1\)
C)\( y = 3x + 2\)
D) \(y = x + 2\)
Q34. Simplify:
\((x + 2)(x – 2)\)
A)\( x² – 2\)
B)\( x² + 4\)
C) \(x² – 4\)
D) \(x² + 2\)
Q35. If \(a = 3, b = 4\), find \(a^2 + b^2\).
A) \(12\)
B) \(18\)
C) \(25\)
D)\( 49\)
Q36. What is slope of line \(y = –3x + 5?\)
A) \(–5\)
B) \(–3\)
C)\( 3\)
D) \(5\)
Q37. Solve: \(4x = 20\).
A) \(4\)
B)\( 5\)
C) \(6\)
D)\( 7\)
Q38. A train travels 60 miles in 1.5 hours. Average speed?
A) \(30 mph\)
B) \(40 mph\)
C) \(50 mph\)
D) \(60 mph\)
Q39. Which inequality solution set matches:
\(2x + 3 < 7\) ?
A)\( x < 2\)
B) \(x > 2\)
C) \(x < 3\)
D)\( x > 3\)
Q40. Distance between \((1, 2)\) and\( (4, 6)\)?
A)\( 3\)
B) \(4\)
C) \(5\)
D) \(6\)
Q41. Factor: \(x^2 + 7x + 10\).
A) \((x + 2)(x + 5)\)
B)\((x – 2)(x + 5)\)
C) \((x – 5)(x + 2)\)
D) \(Prime\)
Q42. If \( f(x) = 2x + 1\), find\( f(4)\).
A) \(7\)
B) \(8\)
C) \(9\)
D) \(10\)
Q43. Which is solution to inequality \(x – 3 > 5?\)
A) \(x > 2\)
B) \(x > 5\)
C) \(x > 6\)
D) \(x > 8\)
Q44. A fair die is rolled. Probability of rolling an even number?
A) \(1/3\)
B)\( 1/2\)
C) \(2/3\)
D)\( 5/6\)
📘 SAT Answer Key + Explanations English
Q. No. Ans Explanation
Q1 A Scientists valued proof of theory, not aesthetic appeal.
Q2 A Mechanical time imposed discipline but limited freedom.
Q3 D Focuses on academic skepticism toward new findings.
Q4 B Poet accepts exile as reflective and freeing.
Q5 A Shows difference between outward charm and inner ambition.
Q6 C Modern talk favors visibility/performance over meaning.
Q7 A Tone mixes urgency and mourning for ecological loss.
Q8 C She values flawed, authentic portrayals of humanity.
Q9 A Highlights human-centered, sustainable city planning.
Q10 B Emphasizes that revolutions grow slowly before erupting.
Q11 C Shows that language shapes how humans perceive and think.
Q12 A Persistence through failure led to scientific success.
Q13 C Ruins are seen as living, changing environments.
Q14 B Describes climate change as gradual yet inevitable if ignored.
Q15 A Comedy used as covert political protest.
Q16 C Nostalgia used by marketers for profit.
Q17 B More knowledge reveals greater uncertainty.
Q18 A Adaptation keeps tradition alive.
Q19 C Footnotes are treated with respect and introspection.
Q20 A Creativity may look chaotic but reflects deep thought.
Q21 B Even precise maps still contain hidden distortions.
Q22 A The finding overturned the view of snow as pure nature.
Q23 C She values patience and natural light over digital shortcuts.
Q24 B Imitation may blur genuine human qualities.
Q25 C Insight arises through grappling with imperfection.
Q26 A History often portrays doubtful leaders as certain.
Q27 D Information overload can obscure true meaning.
Q28 B Author warns against overconfidence in controlling nature.
Q29 A Play questions moral accountability within systems.
Q30 B Astronauts shift from national to planetary perspective.
Q31 B Economic models fail because human emotion skews prediction.
Q32 B Shows early humans possessed sophisticated language.
Q33 C Public taste conflicted with environmental innovation.
Q34 A Empires decline internally before outside conquest.
Q35 B Her restraint revealed artistic depth, not despair.
Q36 B Debate signals respect for scientific inquiry.
Q37 C Trade reflected symbolic, social connection.
Q38 C Ease of translation endangers linguistic diversity.
Q39 A Nostalgia beautifies the past by selective memory.
Q40 B Life adapts even in extreme, unexpected conditions.
Q41 C – Science now embraces uncertainty as fundamental, not accidental.
Q42 B – Technology changes what humans do rather than removing them entirely.
Q43 C – Solitude enables self-reflection and deeper awareness.
Q44 B – The passage stresses that trust underpins economic strength.
Q45 C – Language both reflects and shapes the way people think.
Q46 C – Events echo the past, but with new circumstances and choices.
Q47 B – Ecological health relies on periodic disturbance and renewal.
Q48 B – Emotion enhances decision-making and supports reason.
Q49 C – Observing the stars reminds us of our small place in vast time.
Q50 B – AI lacks conscience and ethical reasoning.
51 A – Technology weakens our ability to focus and sustain attention..
52 B – The artist’s creativity, not the medium, determines artistic value.
53 D – Hope is essential for motivating action, not naïve optimism.
54 C – The fall of journalism results from eroded credibility, not missing facts.
Summary Section 1: Reading & Writing
- Total Questions: 54
- If you got 42+ correct (≈78%), that’s around 650–680 score level.
- If you got 47+ correct (≈87%), that’s around 700–740.
- If you got 50+ correct (≈92%), you’re pushing 750–780.
📘 SAT Math Answer Key + Explanations (Q1–54)
Q1. C — 6
Work: \(3x-7=11 \Rightarrow 3x=11+7=18 \) \(\Rightarrow x=18/3=6.\)
Q2. D — 180 texts
Work: \(25 + 0.10t = 43 \Rightarrow 0.10t = 43-25 = 18 \)
\( \Rightarrow t = 18/0.10 = 180.\)Q3. C — 4
\(2x + y = 12,\; y=4 \Rightarrow 2x = 12-4 = 8 \) \(\Rightarrow x=8/2=4.\)
Q4. A — 2
Slope = \((10-2)/(4-0) = 8/4 = 2.\)
Q5. B — 4
Work: \(5y + 2 = 22 \Rightarrow 5y = 20 \Rightarrow y = 20/5 = 4.\)
Q6. B — (6, 4)
Work: Add the two equations: \((x+y) + (x-y) = 10+2 \Rightarrow 2x=12 \) \(\Rightarrow x=6. \)
Then \(y = 10 – x = 4\)
Q7. A — ±3
Work: \(x^2 – 9 = 0 \Rightarrow x^2 = 9 \Rightarrow x = \pm 3.\)
Q8. B — \(6x^5\)
Work: Multiply coefficients and add exponents: \((2x^3)(3x^2)=2\cdot3 \cdot x^{3+2}=6x^5.\)
Q9. A — ±4
Work: Zero-product property: \(x-4=0 \Rightarrow x=4;\; x+4=0\) \( \Rightarrow x=-4\)
Q10. A — Parabola opening upward, vertex\( (2,0)\)
Reason: \(y=(x-2)^2\) is a standard upward parabola with vertex at
\(x=2,y=0\).
Q11. C \(— 4\)
Work: \(3^x = 81\). Since \(81 = 3^4\), \(x=4\).
Q12. A — \( –5 \)and \(3\)
Work: Factor:\(x^2+2x-15=(x+5)(x-3)\) \(\Rightarrow x=-5,\;3.\)
Q13. A — 120 miles
Work: \(50 + 0.20m = 74 \Rightarrow 0.20m = 24 \) \(\Rightarrow m = 24/0.20 = 120.\)
Q14. B — 30 students
Work: Undecided% = \(100 – (60+25) = 15\%\). \(15\% \) of \( 200 = 0.15 \times 200 = 30\).
Q15. A — 1/2
Work: Total balls = \(3+2+5=10\). Green = \(5 → probability =5/10=1/2.\)
Q16. C — 6 cups
Work: Sugar per serving =\( 2/5=0.4\) cups. For 15 servings: \(0.4 \times 15 = 6.\)
Q17. C — 25 girls
Work: Ratio parts = \(3+5=8\). Girls \(= 5/8\) of 40\( = (5/8)\times40 = 5\times5 = 25.\)
Q18. A — $108
Work: Increase 20%: \(100\times1.20 = 120\). Then decrease 10%: \(120\times0.90 = 108\).
Q19. A — 10
Work: Mean = sum/count =\( (4+8+12+16)/4=40/4=10.\)
Q20. A — 9
Work: Sort: \(3,7,9,11,15\). Median = middle value = 9.
Q21. D — 200
Work: \(0.40 \times N = 80 \Rightarrow N = 80/0.40 = 200\).
Q22. C — 40
Work: Area =\( 1/2×base×height\) = \(0.5\times10\times8 = 40.\)
Q23. C — 44 (approx)
Work: Circumference =\( 2\pi r = 2\times 3.14 \times 7 = 6.28\times7 = 43.96 \approx 44.\)
Q24. A — 5
Work: Classic \( 3\mbox{-}4\mbox{-}5 \) right triangle: hypotenuse =5.
Q25. A — 60
Work: Volume = \(5\times4\times3 = 60 \).
Q26. A — 1
Work: Slope = \((7-3)/(6-2)=4/4=1. \)
Q27. C — \(180^\circ. \)
Triangle interior angles sum = \(180^\circ. \)
Q28. B — 0.5
Recall: \(sin 30^\circ = \frac{1}{2} = 0.5.\)
Q29. A — 81
Work: Side =\( 36/4 = 9\). Area \(=9^2=81.\)
Q30. A — 282.6
Work: Volume =\(\pi r^2 h = 3.14\times 3^2 \times 10 = 3.14\times9\times10 \) \(= 3.14\times90 = 282.6.\)
Q31. C — 8
Work: \(2x-5=11 \Rightarrow 2x=16 \Rightarrow x=8.\)
Q32. B — $6.00
Work: Unit price \(=2.50/5=0.50\). For 12 pencils: \(12\times0.50 = 6.00.\)
Q33. A —\( y=2x+1\)
Reason: Parallel lines share slope 2; only choice with slope 2 is \(y=2x+1.\)
Q34. C — \( x^2 – 4 \)
Work: \((x+2)(x-2) = x^2 – 4.\)
Q35. C — 25
Work: \(a^2 + b^2 = 3^2 + 4^2 = 9 + 16 = 25.\)
Q36. B — –3
From \(y=−3x+5\), slope = coefficient of \(x = −3.\)
Q37. B — 5
Work: \(4x = 20 \Rightarrow x = 20/4 = 5.\)
Q38. B — 40 mph
Work: Speed = distance/time = \(60 \div 1.5\). Compute: \(1.5\times40 = 60\), so speed \(= 40 mph.\)
Q39. A — x < 2
Work: \(2x+3 < 7 \Rightarrow 2x < 4 \Rightarrow x < 2.\)
Q40. C — 5
Work: Distance =\(=\sqrt{(4-1)^2 + (6-2)^2} = \sqrt{3^2 + 4^2} = \sqrt{9+16} \) \(= \sqrt{25}=5.\)
Q41. A — (x + 2)(x + 5)
Check: \((x+2)(x+5) = x^2 +7x +10.\)
Q42. C — 9
Work: \(f(4)=2(4)+1=8+1=9.\)
Q43. D — x > 8
Work: \(x-3>5 \Rightarrow x>5+3 = 8.\)
Q44. B — 1/2
Work: Even faces on a die are {2,4,6} → 3 outcomes out of \( 6 → 3/6=1/2\)
Important — read this before using the table
- The digital SAT is still scored 400–1600 (two section scores 200–800 each).
- Raw score = number of questions you answered correctly in a section (no question penalty). Count only operational/scored items. (The College Board sometimes includes unscored “pretest” items; official practice PDFs show how to count scored items.)
- Official raw→scaled conversion varies by test form (College Board uses form-specific conversion tables). The only perfectly accurate conversion is the table released with the exact form — this means your actual scaled score can differ from these estimates. The College Board posts conversion tables in its scoring guides / practice-test PDFs.
What I’m giving you here is a simple, transparent linear estimate you can use to get a quick, consistent score approximation. It assumes a linear mapping from raw→section-score:
- Section score ≈ 200 + (raw / max_raw) × 600
- Reading & Writing max_raw = 54 (section score range 200–800)
- Math max_raw = 44 (section score range 200–800)
Use the table below to convert raw → estimated section score, then add the two section scores to get the estimated total (400–1600).
1) Reading & Writing (54 questions) — approximate conversion (raw → estimated section score)
| Raw correct | Est. section score |
|---|---|
| 0 | 200 |
| 1 | 211 |
| 2 | 222 |
| 3 | 233 |
| 4 | 244 |
| 5 | 256 |
| 6 | 267 |
| 7 | 278 |
| 8 | 289 |
| 9 | 300 |
| 10 | 311 |
| 11 | 322 |
| 12 | 333 |
| 13 | 344 |
| 14 | 356 |
| 15 | 367 |
| 16 | 378 |
| 17 | 389 |
| 18 | 400 |
| 19 | 411 |
| 20 | 422 |
| 21 | 433 |
| 22 | 444 |
| 23 | 456 |
| 24 | 467 |
| 25 | 478 |
| 26 | 489 |
| 27 | 500 |
| 28 | 511 |
| 29 | 522 |
| 30 | 533 |
| 31 | 544 |
| 32 | 556 |
| 33 | 567 |
| 34 | 578 |
| 35 | 589 |
| 36 | 600 |
| 37 | 611 |
| 38 | 622 |
| 39 | 633 |
| 40 | 644 |
| 41 | 656 |
| 42 | 667 |
| 43 | 678 |
| 44 | 689 |
| 45 | 700 |
| 46 | 711 |
| 47 | 722 |
| 48 | 733 |
| 49 | 744 |
| 50 | 756 |
| 51 | 767 |
| 52 | 778 |
| 53 | 789 |
| 54 | 800 |
(Values rounded to nearest whole number; calculated with 200 + 600(raw/54).)*
2) Math (44 questions) — approximate conversion (raw → estimated section score)
| Raw correct | Est. section score |
|---|---|
| 0 | 200 |
| 1 | 214 |
| 2 | 227 |
| 3 | 241 |
| 4 | 255 |
| 5 | 268 |
| 6 | 282 |
| 7 | 295 |
| 8 | 309 |
| 9 | 323 |
| 10 | 336 |
| 11 | 350 |
| 12 | 364 |
| 13 | 377 |
| 14 | 391 |
| 15 | 405 |
| 16 | 418 |
| 17 | 432 |
| 18 | 446 |
| 19 | 459 |
| 20 | 473 |
| 21 | 486 |
| 22 | 500 |
| 23 | 514 |
| 24 | 527 |
| 25 | 541 |
| 26 | 555 |
| 27 | 568 |
| 28 | 582 |
| 29 | 595 |
| 30 | 609 |
| 31 | 623 |
| 32 | 636 |
| 33 | 650 |
| 34 | 664 |
| 35 | 677 |
| 36 | 691 |
| 37 | 705 |
| 38 | 718 |
| 39 | 732 |
| 40 | 746 |
| 41 | 759 |
| 42 | 773 |
| 43 | 786 |
| 44 | 800 |
(Values rounded; calculated with 200 + 600(raw/44).)*Z