The Texas Success Initiative Assessment 2.0 (TSIA2) is the college readiness exam required for most students entering Texas public colleges and universities. The math section is computer-adaptive and covers four distinct domains, each testing a different type of mathematical reasoning. Knowing what to expect in each domain — and practicing the types of problems that appear in each — is the most effective way to prepare.
This post provides practice questions across all four TSIA2 math domains with complete solutions and explanations for each problem.
ViewMath is not affiliated with or endorsed by the Texas Higher Education Coordinating Board (THECB). Always visit the official TSIA2 page for current test information and registration details.
TSIA2 Math Test Overview
The TSIA2 Math section is untimed and computer-adaptive. Most test takers encounter around 20 questions (the Placement Test section), with some students routed to a Diagnostic Test of 48 additional questions. The test places students into either a college-level math course or a co-requisite/developmental pathway depending on their score.
The four content domains are:
- Quantitative Reasoning
- Algebraic Reasoning
- Geometric and Spatial Reasoning
- Probabilistic and Statistical Reasoning
Domain 1: Quantitative Reasoning
This domain covers arithmetic, number sense, ratio and proportion, percent, and problem-solving with real numbers. Many students feel most comfortable here, but percent and proportional reasoning problems can still trip up unprepared test-takers.
Practice Question 1: A store is offering a 30% discount on all items. A jacket originally costs $120. What is the sale price?
Solution: Discount = 0.30 × 120 = $36. Sale price = 120 − 36 = $84.
Practice Question 2: Maria works 40 hours per week at $16.50 per hour. She also earns a weekly bonus of $75. What is her total weekly earnings?
Solution: Hourly earnings = 40 × $16.50 = $660. Total = $660 + $75 = $735.
Practice Question 3: A car travels 240 miles on 8 gallons of gas. At the same rate, how many gallons would it need to travel 360 miles?
Solution: Miles per gallon = 240/8 = 30 mpg. Gallons for 360 miles = 360/30 = 12 gallons.
Practice Question 4: Which of the following is equivalent to (3/4) × (8/9)?
A) 2/3 B) 1/3 C) 24/36 D) 11/13
Solution: (3/4) × (8/9) = 24/36 = 2/3. Answer: A.
Practice Question 5: A number is increased by 20%, then decreased by 20%. What is the net result compared to the original?
Solution: Start with 100. After 20% increase: 120. After 20% decrease of 120: 120 × 0.80 = 96. Net result: a 4% decrease. The answer is not the original — this is a common trap.
Domain 2: Algebraic Reasoning
This is the largest and most important TSIA2 math domain. It covers linear equations and inequalities, systems of equations, quadratic equations, polynomial operations, and functions. Students who place into developmental math most often struggle here.
Practice Question 6: Solve for x: 3(2x − 4) = 18
Solution: 6x − 12 = 18 → 6x = 30 → x = 5.
Practice Question 7: Find the slope of the line passing through the points (2, 5) and (6, 13).
Solution: Slope = (13 − 5)/(6 − 2) = 8/4 = 2.
Practice Question 8: Solve the system of equations:
x + y = 10
2x − y = 8
Solution: Add the equations: 3x = 18 → x = 6. Substitute: 6 + y = 10 → y = 4.
Practice Question 9: Factor completely: x² − 5x − 14
Solution: Find two numbers that multiply to −14 and add to −5: −7 and 2. Factored form: (x − 7)(x + 2).
Practice Question 10: Solve: x² − 9 = 0
Solution: x² = 9 → x = ±3. Both x = 3 and x = −3 are solutions.
Practice Question 11: What is the y-intercept of the line y = −4x + 7?
Solution: The y-intercept is the constant term: (0, 7).
Practice Question 12: Simplify: (3x² + 2x − 5) − (x² − 4x + 1)
Solution: Distribute the minus: 3x² + 2x − 5 − x² + 4x − 1 = 2x² + 6x − 6.
Domain 3: Geometric and Spatial Reasoning
This domain tests knowledge of lines, angles, triangles, polygons, circles, the Pythagorean theorem, coordinate geometry, and basic transformations. Many test-takers overlook this domain during preparation.
Practice Question 13: A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?
Solution: c² = 6² + 8² = 36 + 64 = 100. c = 10.
Practice Question 14: What is the area of a circle with radius 5 cm? (Use π ≈ 3.14)
Solution: A = πr² = 3.14 × 25 = 78.5 cm².
Practice Question 15: Two parallel lines are cut by a transversal. One interior angle measures 65°. What is the measure of the co-interior (same-side interior) angle?
Solution: Co-interior angles are supplementary: 180° − 65° = 115°.
Practice Question 16: A rectangle has a perimeter of 36 inches. Its length is twice its width. What is the width?
Solution: Let width = w, length = 2w. Perimeter: 2(w + 2w) = 36 → 6w = 36 → w = 6 inches.
Domain 4: Probabilistic and Statistical Reasoning
This domain covers probability concepts, data interpretation (mean, median, mode, range, standard deviation basics), charts and graphs, normal distribution, and statistical inference at a conceptual level.
Practice Question 17: A bag contains 5 red and 3 blue marbles. If one marble is drawn at random, what is the probability it is blue?
Solution: P(blue) = 3/8.
Practice Question 18: The following data set represents quiz scores: 72, 85, 90, 68, 85, 92, 78. What is the median?
Solution: Sort the data: 68, 72, 78, 85, 85, 90, 92. The median (middle value) is 85.
Practice Question 19: A company reports that average employee satisfaction is 7.2 out of 10. The scores range from 4 to 10. Which measure of center would be least affected by the one very low score of 4?
Solution: The median is least affected by outliers. The mean (and average) is pulled down by extreme values.
Practice Question 20: Two dice are rolled. What is the probability that the sum equals 7?
Solution: Favorable outcomes: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6. Total outcomes: 36. P(sum = 7) = 6/36 = 1/6.
TSIA2 Math Preparation Tips
- Spend the most time on Algebraic Reasoning: It is the highest-weight domain and the most common area for placement into developmental courses. Even if you feel confident, practice factoring, solving quadratics, and working with linear systems.
- Don’t skip geometry: Students who prepare for Quantitative and Algebraic Reasoning only sometimes encounter a geometry-heavy adaptive branch and find themselves unprepared.
- Practice untimed, then timed: The TSIA2 is untimed, but many students underestimate how long they actually spend on problems. Practice without time pressure first to build accuracy, then do a timed run to build pacing awareness.
- Use official practice: The Texas Success Initiative website and many Texas colleges publish sample questions. Use these alongside third-party resources to understand the question style.
College Math Placement Resources from ViewMath
ViewMath offers college math placement prep workbooks covering arithmetic through Algebra 2 topics, with practice test sets, worked solutions, and targeted topic review. Explore the collection in the sidebar.
ViewMath is an independent publisher. Our materials are not official TSIA2 or THECB materials.
