TSIA2 Math

TSI Math Practice Test: 12 TSIA2 Questions Solved Step by Step

Twelve original TSIA2 math questions solved step by step, the 950 college-ready score, how the diagnostic works, and which scores exempt you.

Professor Chacha October 9, 2026 11 min read 12 views

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To be college ready in math on the TSIA2, you need a score of 950 or higher on the College Readiness Classification (CRC) test. If you score below 950, you can still be college ready by reaching Diagnostic Level 6 on the diagnostic test that follows. These benchmarks are set by the State of Texas in 19 TAC §4.57, and colleges can't change them.

This page has 12 original practice questions in the style of the TSIA2 math test, grouped by the four areas the test covers, each solved step by step. First, check whether you need to take the test at all.

Do you need to take the TSI math test?

You are exempt from the math part of TSI if you already have one of these scores. Texas rules (19 TAC §4.54) accept them for five years from the test date:

Test	Score that exempts you from TSI math
SAT (taken on or after March 5, 2016)	530 or higher on Math
ACT (taken on or after February 15, 2023)	22 or higher on Math
ACT (taken before February 15, 2023)	Composite 23 or higher, with at least 19 on Math
STAAR end-of-course	4000 or higher on Algebra II
GED	165 or higher on Mathematical Reasoning (practice with our GED math practice test)
HiSET	15 or higher on Mathematics

Other students can be exempt too, for example those who already have an associate or bachelor's degree, some military service members and veterans, and students who completed a college preparatory course in high school. Your college's testing office makes the final call, so ask them before you schedule anything.

How the TSIA2 math test works

TSIA2 is built by the College Board and delivered on the ACCUPLACER platform, so the screen will look the same as on the ACCUPLACER math test, but the scoring is different. The math section runs in up to two stages, one after the other in the same sitting:

The CRC test. Everyone starts here: 20 multiple-choice questions, adaptive, scored from 910 to 990. A score of 950 or higher ends math testing and makes you college ready.
The diagnostic test. If your CRC score is below 950, you move straight on to 48 more questions, 12 from each content area. It places you at a level from 2 to 6. Level 6 also counts as college ready. Levels 2 to 5 show which skills to build before or during your first math course.

According to the official TSIA2 Mathematics Test Specifications, the 20 CRC questions are split like this:

Content area	CRC questions	What it covers
Quantitative Reasoning	6	Comparing numbers, ratios, percents, linear relationships in money problems
Algebraic Reasoning	7	Linear equations, inequalities, and systems; exponential growth and interest; quadratic and other functions
Geometric and Spatial Reasoning	3	Unit conversions, area and volume, right triangles, basic trigonometry
Probabilistic and Statistical Reasoning	4	Probability, mean, median, spread, reading data displays

Algebra and quantitative reasoning make up 13 of the 20 questions, so that is where your study time pays off most. The practice questions below follow the same mix.

Quantitative Reasoning

For 12 more questions in this area, organized by the four official skills, see our TSIA2 Quantitative Reasoning practice.

1.Which list shows these numbers in order from least to greatest?
$\sqrt{10}$, $\pi$, 3.2, $\tfrac{10}{3}$

A$\sqrt{10},\ \pi,\ 3.2,\ \tfrac{10}{3}$
B$\pi,\ \sqrt{10},\ 3.2,\ \tfrac{10}{3}$
C$\pi,\ 3.2,\ \sqrt{10},\ \tfrac{10}{3}$
D$3.2,\ \pi,\ \sqrt{10},\ \tfrac{10}{3}$

Show solution

Turn each number into a decimal you can compare.

\[\begin{gathered}\pi \approx 3.142 \\ \sqrt{10} \approx 3.162 \\ 3.2 \\ \tfrac{10}{3} \approx 3.333\end{gathered}\]

To place $\sqrt{10}$ without a calculator: $3.1^2 = 9.61$ and $3.2^2 = 10.24$, so $\sqrt{10}$ is between 3.1 and 3.2, a little above $\pi$.

Common trap: Rounding $\sqrt{10}$ to "about 3" and putting it first. It is close to 3.16, which is more than $\pi$.

Answer: B ($\pi,\ \sqrt{10},\ 3.2,\ \tfrac{10}{3}$)

2.A phone plan went up from $45 to $54 per month. By what percent did the price increase?

A9%
B$16.\overline{6}\%$
C20%
D120%

Show solution

Percent change is the change divided by the original amount.

\[\tfrac{54 - 45}{45} = \tfrac{9}{45} = 0.20 = 20\%\]

Common trap: Dividing by the new price: $\tfrac{9}{54} \approx 16.7\%$. Percent change always compares to where you started.

Answer: C (20%)

3.A gym charges a $50 sign-up fee plus $25 per month. After how many months will a member have paid a total of $350?

Show solution

Write the total cost as an equation and solve for the number of months, $m$.

\[\begin{gathered}50 + 25m = 350 \\ \Rightarrow\; 25m = 300 \\ \Rightarrow\; m = 12\end{gathered}\]

Common trap: Dividing $350 by $25 and getting 14. The $50 fee is part of the $350, so take it out first.

Answer: A (12)

4.Maria earns $18 per hour. She needs to earn at least $630 this month. Which inequality shows the number of hours, $h$, she needs to work?

A$18h \le 630$
B$18h \ge 630$
C$h + 18 \ge 630$
D$630h \ge 18$

Show solution

Her pay is $18h$ dollars. "At least $630" means her pay must be 630 or more, so the symbol is $\ge$.

\[\begin{gathered}18h \ge 630 \\ \Rightarrow\; h \ge 35\end{gathered}\]

She needs to work 35 hours or more.

Common trap: Reading "at least" as "no more than" and writing $\le$. "At least" sets a minimum: the answer can be that number or larger.

Answer: B ($18h \ge 630$)

Algebraic Reasoning

Systems of equations and money word problems are the core of this area. If they slow you down, work through our lesson on systems of equations word problems first.

5.If $x + y = 12$ and $2x - y = 9$, what is the value of $y$?

A7
B$-5$
C3
D5

Show solution

Add the two equations so that $y$ cancels.

\[\begin{gathered}(x + y) + (2x - y) = 12 + 9 \\ \Rightarrow\; 3x = 21 \\ \Rightarrow\; x = 7\end{gathered}\]

Then substitute into the first equation: $7 + y = 12$, so $y = 5$.

Common trap: Stopping at $x = 7$. The question asks for $y$. Underline what the question asks for before you start.

Answer: D (5)

6.You put $2,000 in a savings account that earns 5% interest, compounded once a year. How much is in the account after 2 years?

A$2,200
B$2,100
C$2,205
D$2,210

Show solution

Each year the balance is multiplied by $1.05$.

\[\begin{gathered}2000 \times 1.05 = 2100 \\ 2100 \times 1.05 = 2205\end{gathered}\]

In one step: $2000(1.05)^2 = 2205$.

Common trap: Using simple interest: 5% of $2,000 is $100 per year, so $2,200. With compound interest, the second year earns interest on $2,100, not on $2,000.

Answer: C ($2,205)

7.Solve: $-3x + 7 \gt 22$

A$x \gt -5$
B$x \gt 5$
C$x \lt 5$
D$x \lt -5$

Show solution

Subtract 7, then divide by $-3$. Dividing by a negative number flips the inequality sign.

\[\begin{gathered}-3x \gt 15 \\ \Rightarrow\; x \lt -5\end{gathered}\]

Check with $x = -6$: $-3(-6) + 7 = 25$, and 25 is greater than 22.

Common trap: Forgetting to flip the sign when dividing by $-3$, which gives $x \gt -5$. Test a number from your answer in the original inequality to catch it.

Answer: D ($x \lt -5$)

8.A ball is thrown straight up. Its height in feet after $t$ seconds is $h(t) = -16t^2 + 64t$. After how many seconds does the ball hit the ground?

Show solution

The ball is on the ground when the height is 0.

\[\begin{gathered}-16t^2 + 64t = 0 \\ \Rightarrow\; -16t(t - 4) = 0 \\ \Rightarrow\; t = 0 \text{ or } t = 4\end{gathered}\]

$t = 0$ is the moment it is thrown, so it lands after 4 seconds.

Common trap: Answering 2. That is when the ball is highest ($t = -\tfrac{b}{2a} = 2$), halfway through the flight, not when it lands.

Answer: B (4)

Geometric and Spatial Reasoning

9.A room measures 12 feet by 15 feet. Carpet is sold by the square yard. How many square yards of carpet cover the floor?

A60
B540
C20
D180

Show solution

The area is $12 \times 15 = 180$ square feet. One yard is 3 feet, so one square yard is $3 \times 3 = 9$ square feet.

\[180 \div 9 = 20 \text{ square yards}\]

Common trap: Dividing by 3 instead of 9 and getting 60. Converting square units means converting both dimensions, so the factor is squared.

Answer: C (20)

10.A 13-foot ladder leans against a wall. The bottom of the ladder is 5 feet from the wall. How high up the wall does the ladder reach?

A12 feet
B8 feet
C18 feet
D13.9 feet

Show solution

The ladder is the hypotenuse of a right triangle. Use the Pythagorean theorem with the ladder as $c$.

\[\begin{gathered}5^2 + h^2 = 13^2 \\ \Rightarrow\; h^2 = 169 - 25 = 144 \\ \Rightarrow\; h = 12\end{gathered}\]

Common trap: Adding the squares as if the ladder were a leg: $\sqrt{13^2 + 5^2} \approx 13.9$. The longest side, the ladder, is always $c$.

Answer: A (12 feet)

Probabilistic and Statistical Reasoning

11.A bag has 4 red, 6 blue, and 5 green marbles. One marble is picked at random. What is the probability that it is not blue?

A$\tfrac{2}{5}$
B$\tfrac{4}{15}$
C$\tfrac{2}{3}$
D$\tfrac{3}{5}$

Show solution

There are $4 + 6 + 5 = 15$ marbles, and $4 + 5 = 9$ of them are not blue.

\[P(\text{not blue}) = \tfrac{9}{15} = \tfrac{3}{5}\]

Common trap: Answering the opposite question. $\tfrac{6}{15} = \tfrac{2}{5}$ is the probability that the marble is blue. Read the word "not" twice.

Answer: D ($\tfrac{3}{5}$)

12.Six commute times, in minutes, are 12, 15, 15, 18, 20, and 45. The mean is about 20.8 minutes. What is the median?

A15
B16.5
C18
D20.8

Show solution

The data is already in order. With six values, the median is the mean of the two middle values, the 3rd and the 4th.

\[\tfrac{15 + 18}{2} = 16.5\]

Common trap: Picking one of the two middle numbers, 15 or 18. With an even number of values, average the two in the middle.

Answer: B (16.5)

Count your misses by area. Two or more wrong in the same area tells you exactly where to start studying.

Teacher's note: When a word problem stalls you, stop and write down what the question is asking for before you touch the numbers. Questions 3 and 5 on this page are built to reward that habit: the numbers lead you to an answer, but not to the one the question asks for. I ask my students to underline the last sentence of every problem for exactly this reason.

If you score below 950

A score below 950 is not a failing grade, and it does not stop you from being admitted. It means the diagnostic test decides your placement:

Level 6: you are college ready in math, the same as a 950.
Levels 2 to 5: your college places you in a support course or a course paired with extra help. The diagnostic report shows your level in each of the four areas, which tells you what to practice. Our guide to TSI scores explains every line of the report.

You can retest, and your results count for five years. Each college sets its own fees and retest schedule, so check with its testing center.

Before test day

Do the Pre-Assessment Activity (PAA). It is required before your first TSIA2. You can complete it for free, along with official practice tests, by creating an account on the College Board TSIA2 page.
Take one official practice test and compare your misses with the four areas in the table above.
Practice by hand. Several questions on this page, like question 1, are much faster when you can estimate without a calculator.
Ask your testing center about the fee, what ID to bring, and whether you can test remotely.

$Professor Chacha$

Professor Chacha Math teacher and educational psychologist

Math teacher and educational psychologist with more than 20 years of classroom experience. He writes every practice question on this site from scratch and solves it step by step, the way he explains it to his own students.

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