Every TSIA2 math problem on this platform is built from one of four official College Board content categories. Browse representative examples below — each shows a worked solution, the common student error, and the underlying skill being measured.
The Texas Higher Education Coordinating Board organizes TSIA2 math into four reasoning strands — twelve diagnostic items each. Our problem bank mirrors that structure exactly. Pick a strand:
Ratios, proportions, and percents. Linear equations and expressions in real-world contexts. The arithmetic backbone of college-readiness math.
A jacket originally priced at $80 is on sale for 35% off. What is the sale price?
The discount is 35% of $80 = 0.35 × 80 = $28. Sale price = 80 − 28 = $52.
Common error: choosing A — students compute the discount amount and stop, forgetting to subtract it from the original price.
A recipe uses 3 cups of flour for every 2 cups of sugar. How many cups of flour are needed with 8 cups of sugar?
Set up the proportion 3⁄2 = x⁄8. Cross-multiply: 2x = 24, so x = 12.
Common error: choosing D — inverting the ratio and solving 2⁄3 = x⁄8 instead.
Solving linear, quadratic, polynomial, exponential, rational, and radical equations. Evaluating functions. Word problems requiring algebraic modeling.
Solve for x: x² − 5x − 24 = 0
Find two numbers that multiply to −24 and add to −5: those are −8 and +3. Factor: (x − 8)(x + 3) = 0, so x = 8 or x = −3.
Common error: choosing A — correct factor pair, but with the signs flipped when reading the roots.
If f(x) = 2x² − 3x + 1, what is f(−2)?
f(−2) = 2(−2)² − 3(−2) + 1 = 2(4) + 6 + 1 = 15.
Common error: choosing A — squaring −2 as −4 (dropping the parentheses), giving −8 + 6 + 1 = −1, or mishandling the −3(−2) sign.
Unit conversion within measurement systems. Perimeter, area, surface area, and volume. Transformations and right-triangle trigonometry.
A rectangular garden measures 14 ft by 9 ft. A walkway 2 ft wide surrounds it. What is the area of the walkway alone?
Outer rectangle: (14 + 4) × (9 + 4) = 18 × 13 = 234 ft². Garden: 14 × 9 = 126 ft². Walkway = 234 − 126 = 108 ft².
Common error: choosing B — computing the outer area and stopping, or adding 2 ft to each dimension instead of 4 ft (2 ft on each side).
A ladder leans against a wall, reaching 12 ft up the wall with its base 5 ft from the wall. How long is the ladder?
Pythagorean theorem: c² = 5² + 12² = 25 + 144 = 169, so c = 13 ft — the classic 5-12-13 triple.
Common error: choosing A — adding the legs (5 + 12) instead of applying the theorem; or D — subtracting instead of adding (144 − 25).
Classifying data and constructing representations. Computing and interpreting probability. Measures of center and spread.
Find the median of: 7, 3, 9, 5, 11, 4, 8
Order the data first: 3, 4, 5, 7, 8, 9, 11. Seven values — the middle (4th) value is 7.
Common error: choosing A — taking the middle value of the unordered list (5) without sorting first.
A bag holds 4 red, 5 blue, and 3 green marbles. One marble is drawn at random. What is the probability it is not blue?
Total marbles = 12. Not-blue marbles = 4 + 3 = 7. P(not blue) = 7⁄12. Equivalently, 1 − 5⁄12.
Common error: choosing A — answering P(blue) and missing the word not; the most-missed word in probability stems.
Students see problems calibrated to their current mastery level within each category. Misses trigger remediation; streaks unlock harder items.
Matches the official TSIA2 format: untimed, computer-adaptive, multiple-choice. Results surface strengths and gaps by category.
Any category — or mix of categories — can be exported to a print-ready worksheet via the Worksheet Generator, branded for your campus.