TSI math practice test: all four TSIA2 math categories, free

The TSIA2 math College Readiness Classification test is 20 multiple-choice questions across four reporting categories: Quantitative Reasoning, Algebraic Reasoning, Geometric and Spatial Reasoning, and Probabilistic and Statistical Reasoning. You need 950 to be college ready. Each free drill below is 12 original questions in one category, with every answer explained.

20
math questions on the real CRC: 4
reporting categories: 950
the college-ready score: 12
questions in each free drill

Last checked 22 October 2026 · Test facts from the Texas Education Agency and Texas college testing centers

Free math drills: pick a category. 12 original TSI-style questions each at an 18-minute practice pace, then every answer explained. No sign-up.

12
questions
18 min
time limit
Free
every answer explained

By the LifeScore Editorial Team · Updated 22 October 2026 · How we check facts · How this is scored

What is on the TSI math test?

Four categories of roughly equal weight: Quantitative Reasoning (numbers, percents and ratios), Algebraic Reasoning (equations and functions), Geometric and Spatial Reasoning (shapes and coordinates) and Probabilistic and Statistical Reasoning (data and chance).

The TSIA2 math reporting categories, from Texas college test guides
Category	What it covers
Quantitative Reasoning	Number sense, fractions, decimals and percents, ratios, rates and proportions, exponents, roots and scientific notation, and money problems.
Algebraic Reasoning	Linear equations and inequalities, expressions, functions and function notation, slope and lines, systems of equations, and simple quadratics.
Geometric and Spatial Reasoning	Area, perimeter and volume, angles, the Pythagorean theorem, coordinates (distance and midpoint), similar figures and transformations.
Probabilistic and Statistical Reasoning	Mean, median, mode and range, reading tables and two-way tables, and the probability of single and combined events.

Because the test is adaptive, the categories are mixed and the difficulty moves with your answers. A student who answers the first algebra questions well will see harder algebra, including quadratics and systems, so review beyond the basics if you are aiming for College Algebra or calculus.

What is TSI Quantitative Reasoning?

Arithmetic with a purpose: fractions, decimals and percents, ratios and rates, unit prices, exponents and scientific notation, mostly set in short everyday problems.

Quantitative Reasoning questions are rarely hard one at a time, but they are designed to catch the slips people make after years without doing arithmetic by hand: taking a percent of the wrong number, adding the parts of a ratio wrongly, or misplacing a decimal point when converting units.

The rules that cover most of them: part = percent × whole; percent change = change ÷ original; a ratio a:b splits a total into a + b parts; a unit rate is total ÷ quantity; and when you multiply powers of ten, you add the exponents. Estimate before you calculate, so an answer ten times too large stands out.

What is TSI Algebraic Reasoning?

Linear equations and inequalities, expressions, function notation, slope and the equation of a line, systems of two equations and simple quadratics, often wrapped in a word problem.

Algebra is the category most students worry about and the one that rewards review fastest. The questions return to a small set of skills: solving for a variable in a few steps, reading f(x) notation, finding the slope between two points, writing a line in y = mx + b form, and setting up one equation from a sentence such as "a gym charges $25 to join and $12 a month".

The biggest point-losers are sign errors when moving terms across the equals sign and stopping one step early, for example answering 3x = 15 with 15. Both are fixed by the same habit: check your answer in the original equation before you choose it.

What is TSI Geometric and Spatial Reasoning?

Perimeter, area and volume, angle facts, the Pythagorean theorem, similar figures, transformations such as slides and reflections, and distance and midpoints on the coordinate plane.

Geometry questions are where a quick sketch earns the most points. Draw the figure, label what you know, and write the formula before you put numbers in. Most mistakes come from mixing up area and perimeter, using a diameter where the radius belongs, or forgetting that the longest side of a right triangle is the one opposite the right angle.

Coordinate questions blend geometry with algebra: the midpoint is the average of the coordinates, the distance is the Pythagorean theorem on the horizontal and vertical changes, and a reflection over the x-axis changes the sign of y.

What is TSI Probabilistic and Statistical Reasoning?

Mean, median, mode and range, reading tables, charts and two-way tables, and the probability of single, combined and conditional events.

The statistics questions are mostly about reading carefully. A two-way table can answer "what fraction of the students who walk to school are juniors?" or "what fraction of juniors walk to school?", and the numbers differ. Before you divide, say out loud which group is the whole.

For probability, independent events multiply ("heads and a 6" is 1/2 × 1/6), and a "not" question is 1 minus the probability of the event. For a missing value in a mean, always go through the total: mean × count gives the sum.

What do TSI math questions look like?

Short problems with four options, two from each category below; the first, third, fifth and seventh are worked in full and the others open when you tap.

TSI-style question 1 · Percent increase
A bus pass costs $45. Its price goes up by 12%. What is the new price of the pass?
1. A$50.40
2. B$57.00
3. C$45.12
4. D$5.40
Worked answer
A: $50.40. A 12% rise multiplies the price by 1.12: 45 × 1.12 = 50.40.
1. The new price is 100% + 12% = 112% of the old one.
2. 112% as a decimal is 1.12.
3. 45 × 1.12 = 50.40, so the new price is $50.40.
The trap: $5.40 is the increase, not the new price. Read whether the question asks for the change or the result.
TSI-style question 2 · Ratio
A mix uses flour and sugar in the ratio 5:2. A baker uses 21 cups of flour and sugar together. How many cups of sugar does she use?
1. A6
2. B8.4
3. C15
4. D10.5
Show the worked answer
A: 6. The ratio has 5 + 2 = 7 parts, so one part is 21 ÷ 7 = 3 cups and sugar is 2 × 3 = 6 cups.
1. Add the parts of the ratio: 5 + 2 = 7.
2. One part is 21 ÷ 7 = 3 cups.
3. Sugar is 2 parts: 2 × 3 = 6 cups.
The trap: Dividing 21 by 2 or by 5 skips the step of adding the parts. A ratio of 5:2 splits a total into 7 shares.
TSI-style question 3 · System of equations
If x + y = 14 and x − y = 4, what is the value of x?
1. A9
2. B5
3. C10
4. D18
Worked answer
A: 9. Add the equations: 2x = 18, so x = 9 (and y = 5).
1. Adding the two equations cancels y: (x + y) + (x − y) = 14 + 4.
2. 2x = 18, so x = 9.
3. Check: 9 + 5 = 14 and 9 − 5 = 4, with y = 5.
The trap: Choosing 5, which is y, or 18, which is 2x. Finish the step and answer the variable the question names.
TSI-style question 4 · Function notation
If f(x) = 3x² − 2x, what is f(−2)?
1. A16
2. B8
3. C−8
4. D10
Show the worked answer
A: 16. Replace every x with (−2): 3(−2)² − 2(−2) = 3(4) + 4 = 16.
1. Write the substitution with brackets: 3(−2)² − 2(−2).
2. Square first: (−2)² = 4, so the first term is 12.
3. −2 × −2 = +4, and 12 + 4 = 16.
The trap: Getting 8 by treating −2(−2) as −4. Two negatives multiply to a positive, so the second term adds 4.
TSI-style question 5 · Pythagorean theorem
A 13-foot ladder leans against a wall and touches it 12 feet above the ground. How far from the wall is the foot of the ladder?
1. A5 feet
2. B1 foot
3. C17.7 feet
4. D25 feet
Worked answer
A: 5 feet. The ladder is the hypotenuse: 12² + d² = 13², so d² = 169 − 144 = 25 and d = 5 feet.
1. Sketch it: the wall and the ground make a right angle, and the ladder is the longest side.
2. 12² + d² = 13², so 144 + d² = 169.
3. d² = 25, so d = 5 feet.
The trap: Adding the squares (144 + 169) treats the ladder as a leg. The longest side, opposite the right angle, is always c.
TSI-style question 6 · Distance on a grid
What is the distance between the points (1, 2) and (7, 10)?
1. A10
2. B14
3. C8
4. D6
Show the worked answer
A: 10. The horizontal change is 6 and the vertical change is 8, so the distance is √(6² + 8²) = √100 = 10.
1. Horizontal change: 7 − 1 = 6. Vertical change: 10 − 2 = 8.
2. These are the legs of a right triangle: 6² + 8² = 36 + 64 = 100.
3. √100 = 10.
The trap: 14 adds the two changes. The straight-line distance is the hypotenuse, which is shorter than walking across and then up.
TSI-style question 7 · Mean
The mean of five quiz scores is 82. Four of the scores are 78, 85, 90 and 74. What is the fifth score?
1. A83
2. B82
3. C81.75
4. D76
Worked answer
A: 83. Five scores with a mean of 82 total 5 × 82 = 410. The four known scores total 327, so the fifth is 410 − 327 = 83.
1. Total of all five: 5 × 82 = 410.
2. Total of the four you know: 78 + 85 + 90 + 74 = 327.
3. Fifth score: 410 − 327 = 83.
The trap: 81.75 is the mean of the four known scores. A missing-value mean question always goes through the total.
TSI-style question 8 · Conditional probability
In a class of 30 students, 18 play a sport, and 12 of those 18 also play an instrument. A student who plays a sport is chosen at random. What is the probability that the student plays an instrument?
1. A2/3
2. B2/5
3. C3/5
4. D1/3
Show the worked answer
A: 2/3. The choice is only among the 18 who play a sport, and 12 of them play an instrument: 12/18 = 2/3.
1. Name the whole: "a student who plays a sport", so the whole is 18, not 30.
2. The part: 12 of those 18 play an instrument.
3. 12/18 = 2/3.
The trap: 2/5 is 12/30, which divides by the whole class. The words after "chosen at random" tell you which group is the whole.

Make math your college-ready subject

One drill shows the gap. Four drills in every category and eight full mocks close it.

The TSI Pass Pack gives you 8 full mocks on the real clock, 24 drills of 12 questions for the sections that cost you points, and a predictor that turns your mocks into the odds of reaching your target. One payment, no subscription, and your free score stays free.

Prep courses for these tests usually cost $19 to $129. The TSI Pass Pack is US$39 (£29), once.

See the TSI Pass Pack How our questions are built and checked

8
timed mocks: 24
topic drills: 1
score predictor

What formulas do I need for TSI math?

There is no formula sheet you can rely on, so know these by heart: percent and percent change, slope and the line, the Pythagorean theorem, distance and midpoint, the area and volume formulas, mean, and the probability rules.

Our study list, with the category each formula matters most in
Formula	What it says	Category
Percent	part = percent × whole	Quantitative
Percent change	(new − old) ÷ old	Quantitative
Slope	(y₂ − y₁) ÷ (x₂ − x₁)	Algebraic
Line	y = mx + b (m is slope, b is the y-intercept)	Algebraic
Pythagorean theorem	a² + b² = c²	Geometric
Distance	√((x₂ − x₁)² + (y₂ − y₁)²)	Geometric
Midpoint	((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)	Geometric
Circle	area = πr², circumference = 2πr	Geometric
Volume of a box	length × width × height	Geometric
Mean	sum of values ÷ number of values	Statistical
Independent events	P(A and B) = P(A) × P(B)	Statistical

Can I use a calculator on the TSI math test?

Only the calculator the test shows on some questions; you cannot bring your own. Practise without one.

The on-screen calculator appears where the arithmetic is not the point of the question. Everywhere else you work by hand on the scratch paper the center gives you, which is why fractions, negatives and exponents by hand are worth an evening of review even for strong students. Our drills assume no calculator.

How should I study for TSI math in a week?

Spend the first day finding your weakest category, the next four on one category a day starting with the weakest, and the last two on a full practice test and the questions you missed.

Our plan, about 40 minutes a day

Day 1
40 min
Take one free drill in each of two categories. Write down every question type you missed.
Day 2
40 min
Your weakest category: redo the drill, then 15 problems of the type you missed most.
Day 3
40 min
Algebra: linear equations, slope and one-equation word problems. Check every answer by substituting.
Day 4
40 min
Quantitative: percents, ratios and unit rates by hand, estimating first.
Day 5
40 min
Geometry and statistics: make the formula card above and use it on two drills.
Day 6
60 min
Take the full [TSI practice test](/tsi-practice-test) and review every miss.
Day 7
30 min
Redo the questions you missed, then rest. Sleep matters more than one more hour.

The broader plan, with ELAR and the essay, is in how to pass the TSI. If you are also comparing other placement tests, the ACCUPLACER math practice test covers very similar skills.

Frequently asked questions

How many math questions are on the TSI?

The math College Readiness Classification test has 20 questions. If you score below 950, a 48-question diagnostic test follows.

What score do I need on TSI math?

950 or higher on the math CRC, or a diagnostic level of 6. See TSI scores.

Is TSI math hard?

It runs from percents and ratios to quadratics and probability. The adaptive format means strong students meet harder questions, so review beyond the basics if you want College Algebra.

Is there geometry on the TSI?

Yes, a full reporting category: area, volume, angles, right triangles, similar figures, transformations and coordinates.

Which category should I study first?

The one with your lowest drill score. If they are close, start with algebra: its skills appear in the other three categories too.

Clear the 950 math benchmark

Four drills for each math category, eight full TSI-style mocks and every answer worked step by step, in one payment.