TSI Math Practice Test
This free TSI math practice test has 15 questions written by the StudyPDF team in the style of the TSIA2 Mathematics test. It covers all four areas the real test reports on: quantitative reasoning, algebraic reasoning, geometric and spatial reasoning, and probabilistic and statistical reasoning, weighted roughly the way the real test weights them. Answer all 15, then check your score and read the explanation for every question.
Which of these numbers is the greatest?
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All 15 questions at a glance
Prefer to read before you play? Every question in the sampler is listed below. Answers and explanations stay collapsed until you open them.
1. Which of these numbers is the greatest?
- A. 7.2
- B. 22/3
- C. 2π
- D. The square root of 50
Show answer and explanation
Answer: B. 22/3
Turn each one into a decimal: 22/3 is about 7.33, the square root of 50 is about 7.07 because 7 squared is 49, and 2π is about 6.28. So 22/3 beats 7.2 by a small margin. Estimating a root from the nearest perfect square is the fastest way through this kind of comparison.
2. On a map, 1 inch represents 15 miles. Two towns are 3.5 inches apart on the map. How far apart are they in real life?
- A. 18.5 miles
- B. 45 miles
- C. 52.5 miles
- D. 60 miles
Show answer and explanation
Answer: C. 52.5 miles
Multiply the map distance by the scale: 3.5 times 15 is 52.5 miles. Adding 3.5 and 15 gives 18.5, which ignores what a scale means, and 45 or 60 come from rounding 3.5 down to 3 or up to 4 before multiplying.
3. Which expressions are equivalent to 3(2x - 4) + x? Select all that apply.
Select all that apply.
- A. 7x - 12
- B. 6x - 4 + x
- C. x + 6x - 12
- D. 7x - 4
- E. 6x - 12 + x
Show answer and explanation
Answer: A. 7x - 12, C. x + 6x - 12, E. 6x - 12 + x
Distribute the 3 to both terms in the parentheses: 6x - 12, then add x to get 7x - 12. Reordering the same terms does not change the value, so x + 6x - 12 and 6x - 12 + x are equivalent too. The two options with -4 forgot to multiply the 4 by 3.
4. A phone plan costs C = 25 + 0.10t dollars per month, where t is the number of text messages sent. What does 0.10 represent?
- A. The cost of each text message
- B. The monthly base fee
- C. The total bill for t messages
- D. The number of texts included in the plan
Show answer and explanation
Answer: A. The cost of each text message
In a linear model, the number multiplied by the variable is the rate of change, so each extra text adds $0.10 to the bill. The 25 is the fixed starting amount you pay even with zero texts, and the whole expression C is the total bill.
5. Solve the inequality: -3x + 5 > 14
- A. x > 3
- B. x < 3
- C. x > -3
- D. x < -3
Show answer and explanation
Answer: D. x < -3
Subtract 5 to get -3x > 9, then divide by -3. Dividing or multiplying an inequality by a negative number flips the sign, so the answer is x < -3. Forgetting the flip gives x > -3, the most common wrong answer here. Test a value like x = -4 to check: 12 + 5 = 17, which is greater than 14.
6. What are the solutions of x^2 + 2x - 15 = 0?
- A. x = -5 or x = 3
- B. x = 5 or x = -3
- C. x = 15 or x = -1
- D. x = -2 or x = 15
Show answer and explanation
Answer: A. x = -5 or x = 3
Find two numbers that multiply to -15 and add to 2: 5 and -3. That factors the equation as (x + 5)(x - 3) = 0, and each factor equals zero at a different x, so x = -5 or x = 3. The second option has the right numbers with the signs reversed, which happens when you copy the numbers from the factors instead of solving x + 5 = 0 and x - 3 = 0.
7. Complete the sentence.
A town of 2,000 people doubles in population every 5 years. If that pattern continues, after 15 years it will have _____ people.
Options for blank 1: 6,000, 8,000, 12,000, 16,000
Show answer and explanation
Answer: 16,000
Fifteen years is three doubling periods, so the population is 2,000 times 2 times 2 times 2, which is 2,000 times 8, or 16,000. The answer 6,000 treats doubling as adding 2,000 each time, which is linear growth, not exponential.
8. Which of these equations describe exponential decay? Select all that apply.
Select all that apply.
- A. y = 500(0.8)^t
- B. y = 500(1.2)^t
- C. y = 500 - 0.8t
- D. y = 300(1/2)^t
- E. y = 0.8t^2
Show answer and explanation
Answer: A. y = 500(0.8)^t, D. y = 300(1/2)^t
Exponential decay has the variable in the exponent and a base between 0 and 1, so the amount shrinks by the same factor each step, as in 0.8 and 1/2. A base of 1.2 is growth, 500 - 0.8t loses the same amount each step, which is linear, and 0.8t^2 is a quadratic.
9. If g(x) = x^2 - 3x, what is g(-2)?
- A. -10
- B. -2
- C. 2
- D. 10
Show answer and explanation
Answer: D. 10
Substitute -2 for every x: (-2)^2 is 4, and -3 times -2 is +6, so g(-2) = 4 + 6 = 10. Writing (-2)^2 as -4 or losing the sign on the second term gives the wrong answers, so put negative inputs in parentheses before you square them.
10. A 10-foot ladder leans against a wall and makes a 60 degree angle with the ground. How far is the foot of the ladder from the wall? (cos 60 degrees = 0.5, sin 60 degrees is about 0.87)
- A. 8.7 feet
- B. 5 feet
- C. 10 feet
- D. 20 feet
Show answer and explanation
Answer: B. 5 feet
The ladder is the hypotenuse, and the distance along the ground is the side next to the 60 degree angle, so use cosine: 10 times 0.5 is 5 feet. Using sine gives 8.7 feet, which is how high the ladder reaches up the wall, so label the sides relative to the angle before choosing a ratio.
11. Complete the sentence.
A closed box is 4 cm long, 3 cm wide and 2 cm tall. Its volume is _____ cubic cm, and its surface area is _____ square cm.
Options for blank 1: 9, 24, 26, 52
Options for blank 2: 9, 24, 26, 52
Show answer and explanation
Answer: 24, 52
Volume is length times width times height, 4 times 3 times 2, which is 24. Surface area adds up all six faces, and they come in pairs: 2 times (12 + 8 + 6) is 52. Forgetting that each face has a twin on the opposite side gives 26.
12. The point (3, -2) is reflected across the y-axis. What are the coordinates of its image?
- A. (3, 2)
- B. (-3, 2)
- C. (-3, -2)
- D. (2, 3)
Show answer and explanation
Answer: C. (-3, -2)
A reflection across the y-axis keeps the point at the same height and flips it to the other side, so only the x-coordinate changes sign: (-3, -2). Changing the y-coordinate instead, giving (3, 2), is a reflection across the x-axis.
13. A class records five things about each student. Which of them are categorical data? Select all that apply.
Select all that apply.
- A. Favorite sport
- B. Height in centimeters
- C. Number of siblings
- D. Blood type
- E. Daily high temperature in their town
Show answer and explanation
Answer: A. Favorite sport, D. Blood type
Categorical data sorts people into groups with names, like a sport or a blood type, and fits a bar chart or a pie chart. Height, sibling count and temperature are numbers you can average, so they are quantitative and belong in a histogram, dot plot or line graph instead.
14. You flip a fair coin and roll a standard six-sided die. What is the probability of getting heads and a 6?
- A. 1/12
- B. 1/8
- C. 2/3
- D. 7/12
Show answer and explanation
Answer: A. 1/12
The coin and the die do not affect each other, so multiply: 1/2 times 1/6 is 1/12. Adding the two probabilities gives 2/3, which is wrong for and, and 7/12 is the probability of heads or a 6, not both.
15. Complete the sentences.
Set A is 48, 50, 52 and set B is 20, 50, 80. Both sets have a mean of _____. The set with the greater spread is _____.
Options for blank 1: 48, 50, 52, 60
Options for blank 2: set A, set B, neither, the spread is equal
Show answer and explanation
Answer: 50, set B
Each set adds up to 150, and 150 divided by 3 is 50. The same mean can hide very different data: set B ranges over 60 points while set A ranges over only 4, so set B has the greater spread by range and by standard deviation.
What's on the TSIA2 math test
The TSIA2 is the college readiness test Texas public colleges and universities give to entering students who are not exempt, so it matters only if you are starting college in Texas. Its math part begins with the College Readiness Classification test: 20 multiple-choice questions, each with four answer choices. According to College Board's test specifications, they split into four content areas: about 6 questions of quantitative reasoning, 7 of algebraic reasoning, 3 of geometric and spatial reasoning and 4 of probabilistic and statistical reasoning.
Quantitative reasoning means comparing rational and irrational numbers, ratios, proportions and percents, and reading linear expressions and equations in context. Algebraic reasoning is the largest area: linear equations, inequalities and systems, evaluating functions, and quadratic, exponential, polynomial, rational and radical equations, including growth and decay problems. Geometric and spatial reasoning covers unit conversions, perimeter, area, surface area and volume, transformations and basic right triangle trigonometry. Probabilistic and statistical reasoning covers probability, measures of center and spread, and choosing and reading a display of data.
The test is adaptive and untimed. Handheld calculators are not allowed on the online test, but some questions come with a pop-up calculator, either a basic one, one with a square root key or a graphing calculator. Scores are reported from 910 to 990. If you land below the college readiness benchmark, you go straight on to a 48-question diagnostic test, 12 questions per area, which reports whether you are basic, proficient or advanced in each one. The benchmark is set by the Texas Higher Education Coordinating Board (THECB) and has been adjusted before, so this page does not print a number. Check College Board's TSIA2 pages, the THECB or your college's testing center for the one that applies when you test.
How to use this sampler
These 15 questions follow the real weighting in miniature: 4 quantitative, 5 algebraic, 3 geometric and 3 statistical. They also reach into the harder end of the content list, so expect a quadratic equation, exponential growth and decay, and a trigonometry ratio, not only arithmetic. If those topics feel far away, that is useful to know before test day, because the TSIA2 is aligned to Algebra II level standards.
Work without a calculator unless you really need one. On the real test only some questions offer a pop-up calculator, so you want the basic moves, like distributing, factoring and fractions, to be quick by hand. The real test has a single answer for every question. The select all that apply and fill in the blank items here are practice formats that make you check every option, which is a good habit when the wrong choices are built from common slips.
There is no time limit on the TSIA2, so practice accuracy over speed. Afterward, read every explanation, including for the questions you got right. Each one names the slip behind the most tempting wrong answer, such as dividing by the new value in a percent change or forgetting to flip an inequality, and those slips repeat across many questions.
An honest note: the StudyPDF team wrote every question here to the content areas College Board publishes for TSIA2 Mathematics. None of them are real TSIA2 items, none are copied from College Board's sample questions or a prep company's bank, and StudyPDF is not affiliated with College Board or the THECB.
How to build more practice tests from your own materials
Fifteen questions can show you which math area needs work. They cannot get you ready on their own, especially when the gap is one topic, like quadratics or right triangle trigonometry, that a short sampler only touches once.
StudyPDF works from your material instead. Upload your prep book, your algebra notes or the worksheets from your class. Then press New material, pick a practice test, choose those files as the sources and set how long it should be. You get a test written from those exact pages, and every explanation cites where the answer comes from.
Bo is the tutor for the rest. Ask him why an answer is right and he walks you through it from your own pages, with a hint first if you want one.
You do not have to upload anything to start. Name a topic instead, for example solving quadratic equations or probability of independent events, and you get practice questions on it. Starting is free.
Written by the StudyPDF team. Last updated 2026-08-19.