30 random questions |30 minutes | Questions are randomized every attempt. Good luck!
SAT Math - Problem Solving and Data Analysis Practice Test
Test your SAT Math - Problem Solving & Data Analysis skills with 30 random practice test questions. Great for students preparing for the SAT Math - Problem Solving & Data Analysis section!
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1. A student scores 75, 80, 85, 90 on 4 tests. Score needed on 5th test for mean of 84:
[M] Total needed=420. Current=330. 420-330=90.
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2. A box contains 4 red, 3 green, 2 blue balls. P(red or green) =
[M] 7/9.
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3. A jar has 5 red, 4 green, 3 blue chips. P(not red)?
[M] Not red=7. 7/12.
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4. A scatterplot shows positive correlation. As x increases, y:
[M] Positive correlation: y increases with x.
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5. A car's fuel tank holds 50 liters. It currently has 30 liters. What percent is full?
[M] 30/50=60%.
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6. Data: 2,3,5,7,11,13,17. If 100 is added to this dataset, the measure most affected is:
[H] Adding extreme outlier most affects the mean.
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7. Data shows: for each $1 increase in price, 5 fewer units sold. Type of relationship:
[M] Constant rate of decrease=linear.
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8. If two regression models have R²=0.85 and R²=0.70 for the same data, the better predictive model is:
[VH] Higher R² means the model explains more variation. R²=0.85 is better.
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9. A Poisson process has rate λ=3 events/hour. P(0 events in 1 hour)=
[VH] P(X=0)=e^(-3)×3⁰/0!=e^(-3).
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10. A survey finds 15% of people have glasses. In a sample of 200, expected number with glasses:
[M] 30.
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11. Which graph best shows relationship between two variables over time?
[M] Line graphs show trends over time.
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12. For regression with one predictor, R²=r². If r=0.9, how much of y-variation is unexplained?
[VH] Unexplained=1-R²=1-0.81=0.19=19%.
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13. A scatterplot shows data with r=0.87. What percent of variation in y is explained by x?
[H] R²=0.87²=0.7569≈75.7%.
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14. A manufacturer tests 100 items: 92 pass. 95% CI for true pass rate:
[H] Both formulas are equivalent: SE=√(0.92×0.08/100)=√0.000736≈0.027.
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15. A product costs $90 to make and is sold for $135. Profit margin (on selling price):
[M] 45/135=1/3≈33%.
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16. Two events A and B. P(A) = 0.4, P(B|A) = 0.6. P(A∩B) =
[M] 0.24.
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17. A Type II error (β) is reduced by:
[VH] Larger samples reduce Type II error (increase power).
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18. The z-score for a value x=65 in distribution μ=55, σ=5 is:
[H] z=(65-55)/5=2.
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19. In a class of 32 students, 8 got an A. Probability of selecting a student who got an A:
[M] 8/32=1/4.
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20. For a dataset, Q1=18, Q3=34. A value of 60 is:
[H] IQR=16. Upper fence=34+1.5(16)=58. 60>58. Outlier.
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21. Random variable X: P(X=0)=0.3, P(X=1)=0.5, P(X=2)=0.2. E(X²)=
[VH] 0+0.5+0.8=1.3.
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22. The Central Limit Theorem requires which assumption?
[VH] CLT: random sample, n sufficiently large (no strict rule of 30).
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23. The Cramer-Rao lower bound gives a lower bound for the variance of:
[VH] Cramer-Rao applies to unbiased estimators.
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24. A linear model predicts test score from study hours: score = 8×hours + 40. For 5 hours, predicted score:
[M] 80.
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25. A systematic sample selects every 10th person from a list of 1000. Sample size is:
[H] 1000/10=100.
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26. A factory output model: Q=50L-2L², L=workers. Output-maximizing workers:
[H] Q'=50-4L=0. L=12.5.
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27. Simpson's paradox occurs when:
[VH] Simpson's paradox: group-level trends reverse when data is aggregated.
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28. A survey of 500 shows 60% satisfied. Best estimate of satisfied in city of 80,000:
[M] 0.60×80000=48000.
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29. Two fair coins are flipped. Given that at least one head appears, P(both heads)=
[H] P(HH|at least one H)=P(HH)/P(at least one H)=(1/4)/(3/4)=1/3.
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30. A study finds students who eat breakfast score 8 points higher on tests. This is an observational study. This means:
[H] Observational studies show association, not causation.
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