For a group of students, the line of best fit relating hours studied, x, to test score, y, is y = 2.4x + 61. Which is the best interpretation of the number 2.4?

Each additional hour of study is associated with an increase of about 2.4 points in test score.

A student who does not study is predicted to score 2.4 points.

Studying 2.4 hours guarantees a score of 61.

Each student studied about 2.4 hours.

TSI Math

Free TSI Math Practice Questions

10 sample questions for the TSI Math, with the correct answer and an explanation for each. No account needed. Try each one before you open the answer.

Sections covered on the exam: Quantitative Reasoning, Propertiesofexponents, Ratios,Rates,Andproportions, Linearexpressions, Interpretinglinearmodels, Algebraic Reasoning, Solvinglinearequations, Inequalities, Systemsofequations, Polynomials, Quadratics, Geometric And Spatial Reasoning, Measurementandunitconversion, Polygonsandcircles, Trianglesandsimilarity, Right-Triangletrigonometry, Three-Dimensionalfigures, Transformations, Probabilistic And Statistical Reasoning, Measuresofcenterandspread, Probability, Scatterplots,Sampling,Andthenormaldistribution, Scatterplotsandstudydesign.

Question 1 · Quantitative Reasoning
What is the value of −3² + 4(5 − 2)³ ÷ 6?
- A.18
- B.45
- C.9
- D.27
Show answer and explanation
Answer: C. 9
The exponent applies only to 3, so −3² = −9. Next, (5 − 2)³ = 3³ = 27, and 4 × 27 ÷ 6 = 108 ÷ 6 = 18 (multiplication and division left to right). Finally, −9 + 18 = 9. Treating −3² as (−3)² = 9 gives the incorrect total of 27.
Question 2 · Linearexpressions
If 4a − 6 = 10, what is the value of 6a − 9?
- A.24
- B.4
- C.15
- D.21
Show answer and explanation
Answer: C. 15
Solve for a: 4a = 16, so a = 4, and 6(4) − 9 = 15. A faster route: 4a − 6 = 2(2a − 3) = 10, so 2a − 3 = 5, and 6a − 9 = 3(2a − 3) = 15.
Question 3 · Inequalities
A delivery van can carry at most 2,000 pounds, including the driver. The driver weighs 180 pounds, and each package weighs 35 pounds. What is the greatest number of packages the van can carry?
- A.51
- B.57
- C.52
- D.53
Show answer and explanation
Answer: C. 52
180 + 35p ≤ 2,000, so 35p ≤ 1,820 and p ≤ 52. The van can carry at most 52 packages. Ignoring the driver's weight gives 2,000 ÷ 35 ≈ 57, which exceeds the limit.
Question 4 · Quantitative Reasoning
What value of x satisfies √(3x + 1) − 2 = 3?
- A.4
- B.0
- C.24
- D.8
Show answer and explanation
Answer: D. 8
Isolate the radical first: √(3x + 1) = 5. Square both sides: 3x + 1 = 25, so x = 8. Check: √25 − 2 = 3. Squaring before isolating the radical produces an incorrect result.
Question 5 · Three-Dimensionalfigures
A cone has a radius of 6 centimeters and a height of 8 centimeters. What is its volume?
- A.60π cm³
- B.96π cm³
- C.288π cm³
- D.48π cm³
Show answer and explanation
Answer: B. 96π cm³
V = (1/3)πr²h = (1/3)π(36)(8) = 96π cm³. Omitting the 1/3 gives the cylinder volume, 288π. The value 60π is the cone's lateral surface area, πrs with slant height s = 10.
Question 6 · Scatterplots,Sampling,Andthenormaldistribution
For a group of students, the line of best fit relating hours studied, x, to test score, y, is y = 2.4x + 61. Which is the best interpretation of the number 2.4?
- A.A student who does not study is predicted to score 2.4 points.
- B.Each additional hour of study is associated with an increase of about 2.4 points in test score.
- C.Studying 2.4 hours guarantees a score of 61.
- D.Each student studied about 2.4 hours.
Show answer and explanation
Answer: B. Each additional hour of study is associated with an increase of about 2.4 points in test score.
The slope, 2.4, is the predicted change in score for each 1-hour increase in study time. The intercept, 61, is the predicted score for 0 hours of study.
Question 7 · Ratios,Rates,Andproportions
A cyclist rides 18 kilometers in 40 minutes. What is the cyclist's average speed in kilometers per hour?
- A.0.45
- B.12
- C.45
- D.27
Show answer and explanation
Answer: D. 27
Convert the time to hours: 40 minutes = 2/3 hour. Speed = 18 ÷ (2/3) = 27 km/h. Dividing 18 by 40 gives kilometers per minute (0.45), not per hour.
Question 8 · Algebraic Reasoning
What value of x satisfies (2/3)(x + 6) = x − 4?
- A.24
- B.−24
- C.8
- D.0
Show answer and explanation
Answer: A. 24
Multiply both sides by 3: 2(x + 6) = 3(x − 4), so 2x + 12 = 3x − 12 and x = 24. Check: (2/3)(30) = 20 and 24 − 4 = 20.
Question 9 · Quadratics
For what value of c does the equation x² + 8x + c = 0 have exactly one real solution?
- A.4
- B.16
- C.64
- D.8
Show answer and explanation
Answer: B. 16
A quadratic has exactly one real solution when its discriminant is zero: 8² − 4(1)(c) = 0, so 64 = 4c and c = 16. Then x² + 8x + 16 = (x + 4)², whose only solution is x = −4.
Question 10 · Trianglesandsimilarity
A person who is 5.5 feet tall casts a shadow 3.3 feet long. At the same time, a flagpole casts a shadow 15 feet long. How tall is the flagpole?
- A.25 feet
- B.18 feet
- C.27.5 feet
- D.9 feet
Show answer and explanation
Answer: A. 25 feet
The sun's rays form similar triangles, so height/shadow is the same: 5.5/3.3 = h/15. Cross multiply: 3.3h = 82.5, so h = 25 feet.

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