The TSI Assessment 2.0 (TSIA2) math section tests four content areas, and nearly every test-taker reports that the hardest part of preparing is not knowing which types of problems to expect. This guide solves that problem by providing original practice questions for all four content areas — with complete answers and brief explanations for each.
ViewMath is not affiliated with or endorsed by the Texas Higher Education Coordinating Board, College Board ACCUPLACER, or any Texas institution. TSI placement policies vary by institution. Always confirm requirements with your specific college or university. For official TSI information, visit highered.texas.gov.
About the TSIA2 Math Section
The TSIA2 math section is a computer-adaptive diagnostic assessment. Students first take a 20-question initial placement test. Depending on their performance, they may continue to a 10-question Diagnostic Test that provides more detailed placement information. The four tested content areas are:
- Quantitative Reasoning (QR): Number sense, operations, ratios, proportions, percents, and basic word problems.
- Algebraic Reasoning (AR): Expressions, equations, inequalities, linear functions, systems of equations, and basic quadratics.
- Geometric and Spatial Reasoning (GR): Geometric figures, measurement, coordinate geometry, area, volume, and the Pythagorean theorem.
- Probabilistic and Statistical Reasoning (SR): Data interpretation, mean, median, range, probability, and basic statistical concepts.
Quantitative Reasoning: 6 Practice Questions
QR-1. A laptop originally costs $840. It goes on sale for 25% off. What is the sale price?
Answer: $630. (0.25 × $840 = $210 off; $840 − $210 = $630)
QR-2. Order from least to greatest: −3/4, 0.6, −1.2, 1/8
Answer: −1.2, −3/4, 1/8, 0.6. (Convert to decimals: −1.2, −0.75, 0.125, 0.6)
QR-3. A car travels 288 miles using 9 gallons of gas. What is the fuel efficiency in miles per gallon?
Answer: 32 mpg. (288 ÷ 9 = 32)
QR-4. A store marks up a product by 40% and sells it for $56. What was the original cost?
Answer: $40. (1.40 × cost = $56 → cost = $56 ÷ 1.40 = $40)
QR-5. Which is larger: 5/8 or 3/5? By how much?
Answer: 5/8 is larger. 5/8 = 25/40; 3/5 = 24/40. Difference = 1/40.
QR-6. A recipe calls for 2¼ cups of flour to make 36 cookies. How much flour is needed for 60 cookies?
Answer: 3¾ cups. (2.25 ÷ 36 × 60 = 3.75 = 3¾)
Algebraic Reasoning: 6 Practice Questions
AR-1. Solve: 4(3x − 2) = 28
Answer: x = 3. (12x − 8 = 28 → 12x = 36 → x = 3)
AR-2. A line passes through (0, −2) and has slope 3/4. Write the equation in slope-intercept form.
Answer: y = (3/4)x − 2
AR-3. Solve the system: y = 2x + 1 and y = −x + 7
Answer: x = 2, y = 5. (2x + 1 = −x + 7 → 3x = 6 → x = 2; y = 2(2) + 1 = 5)
AR-4. Factor: x² − 5x − 14
Answer: (x − 7)(x + 2). (Factors of −14 that add to −5: −7 and +2)
AR-5. Solve: 2x² − 8 = 0
Answer: x = ±2. (2x² = 8 → x² = 4 → x = ±2)
AR-6. Write an inequality and solve: “Three times a number plus 4 is less than 19.”
Answer: 3n + 4 < 19 → 3n < 15 → n < 5
Geometric and Spatial Reasoning: 6 Practice Questions
GR-1. A right triangle has legs of length 9 and 12. Find the hypotenuse.
Answer: 15. (9² + 12² = 81 + 144 = 225; √225 = 15)
GR-2. A cylinder has a radius of 5 cm and height of 10 cm. Find its volume. Use π ≈ 3.14.
Answer: 785 cm³. (V = πr²h = 3.14 × 25 × 10 = 785)
GR-3. Point A is at (−3, 4) and Point B is at (5, −2). What is the distance between them?
Answer: 10 units. (d = √[(5−(−3))² + (−2−4)²] = √[64 + 36] = √100 = 10)
GR-4. The interior angles of a triangle are (2x + 10)°, (3x − 5)°, and (x + 15)°. Find the value of x and the measure of each angle.
Answer: 6x + 20 = 180 → 6x = 160 → x = 26.67°. Angles ≈ 63.3°, 75°, 41.7°.
GR-5. A rectangular prism has dimensions 4 × 6 × 9 cm. Find its volume and surface area.
Volume: 216 cm³. Surface area: 2(4×6 + 6×9 + 4×9) = 2(24 + 54 + 36) = 2(114) = 228 cm².
GR-6. What is the midpoint of the segment with endpoints (−4, 6) and (8, −2)?
Answer: (2, 2). (Midpoint = ((-4+8)/2, (6+(−2))/2) = (4/2, 4/2) = (2, 2))
Probabilistic and Statistical Reasoning: 6 Practice Questions
SR-1. The test scores for 8 students are: 72, 85, 91, 63, 88, 72, 79, 96. Find the mean, median, and mode.
Mean: 743/8 = 74.25 (add all: 72+85+91+63+88+72+79+96 = 646; 646/8 = 80.75 — let me recalculate: 72+85=157, +91=248, +63=311, +88=399, +72=471, +79=550, +96=646; 646/8 = 80.75). Median: sorted = 63, 72, 72, 79, 85, 88, 91, 96; median = (79+85)/2 = 82. Mode: 72.
SR-2. A bag has 5 red and 3 blue marbles. If you draw two marbles without replacement, what is the probability both are red?
Answer: (5/8) × (4/7) = 20/56 = 5/14.
SR-3. A bar chart shows these monthly sales: Jan 120, Feb 95, Mar 140, Apr 110. What is the range?
Answer: 45. (140 − 95 = 45)
SR-4. A die is rolled 60 times. It lands on 3 exactly 14 times. What is the experimental probability of rolling a 3?
Answer: 14/60 = 7/30 ≈ 0.233.
SR-5. A scatter plot shows a strong positive correlation between study hours and test scores. If a student studies 5 hours and the trend line passes through (3, 70) and (6, 88), predict the score for 5 hours.
Slope = (88−70)/(6−3) = 18/3 = 6. Equation: y − 70 = 6(x − 3) → y = 6x + 52. At x = 5: y = 6(5) + 52 = 82.
SR-6. In a class of 30 students, 18 play sports and 12 play an instrument. 6 play both. How many play at least one activity?
Answer: 24. (18 + 12 − 6 = 24, by inclusion-exclusion)
What to Do After This Practice Set
- Score yourself by section. Note which of the four content areas had the most errors.
- Review every missed problem fully. Don’t just check the answer — work through the solution until you understand each step.
- Target the weakest area first. If Algebraic Reasoning had four misses and Quantitative Reasoning had one, spend 60% of your remaining study time on algebra.
- Take a second practice set in one week. Measure whether errors in the target area decreased.
- Simulate test conditions. The TSIA2 is computer-based and untimed, but practicing with focus and without interruptions builds stamina and confidence.
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