TSIA2 Math Practice Answer Key
Teacher & Student Review Guide • Form A
TSIA2 Math Practice Worksheet A
Complete Answer Key, Scoring Rubric & Diagnostic Guide
Texas Success Initiative 2.0
CRC Benchmark: 950+
Master Answer Key (Questions 1–40)
10 Questions per TSIA2 Domain
Domain 1: Quant Q1–10
1. Order of OpsC (11)
2. ProportionsB (1¼)
3. Sale & TaxD ($64.80)
4. ExponentsB (16)
5. Unit RateC (4.5 h)
6. Real NumbersD (0.6)
7. Metric UnitsC (15 m/s)
8. Sci. NotationD (6×10⁻²)
9. Percent RaiseC ($20.70)
10. FractionsD (2/3)
Domain 2: Alg Q11–20
11. Linear Eq.B (17)
12. InequalityC (x ≤ -4)
13. Linear SystemB (5, 6)
14. FactoringA ((x-8)(x+3))
15. QuadraticsD (2 & 4)
16. FunctionsB (15)
17. Line Eq.D (y=2x+1)
18. Rational Exp.A ((x-3)/(x-2))
19. Cost ModelC (4 mo)
20. RadicalsC (x = 9)
Domain 3: Geom Q21–30
21. PythagorasC (13 cm)
22. Circle AreaB (36π)
23. Triangle SumD (65°)
24. Cylinder Vol.D (90π)
25. SimilarityA (12)
26. DistanceB (10)
27. MidpointC ((3, 2))
28. Polygon SumB (720°)
29. ReflectionA ((-3, -2))
30. Sine RatioD (3/5)
Domain 4: Stats Q31–40
31. MeanB (14)
32. MedianA (8.5)
33. Dice SumC (1/6)
34. Dependent PD (2/9)
35. PermutationsC (336)
36. CombinationsB (56)
37. Slope Interp.C (+2.5/hr)
38. Spread / SDC (SD B > A)
39. Two-Way TableD (45/60)
40. Expected Val.A (-$0.50)
Score Diagnostic & Placement Guide
34–40 Correct (85%+) Ready (CRC 950–990)
28–33 Correct (70%–82%) Borderline (CRC ~930–949)
20–27 Correct (50%–68%) Dev. Ed Required (Level 4–5)
< 20 Correct (< 50%) Foundational Review (Level 1–3)
Domain Mastery Tracker
Domain 1: Quantitative Reasoning ___ / 10
Domain 2: Algebraic Reasoning ___ / 10
Domain 3: Geometric & Spatial Reasoning ___ / 10
Domain 4: Probabilistic & Statistical Reasoning ___ / 10
Total Score ___ / 40 ( ___ % )
How to Use This Review Document: Pages 2 through 5 provide full, step-by-step mathematical solutions for every problem on Practice Worksheet A, organized by domain. Pay close attention to the "Test Trap" notes to learn how TSIA2 test designers craft tempting wrong answers.
TSIA2 Mathematics Practice Worksheet A • Form A Solutions Page 1 of 5
TSIA2 Math Practice Worksheet A
Domain 1: Quantitative Reasoning (Questions 1–10)
Number Sense & Operations
1. Order of Operations Key: (C) 11
Evaluate: \(3 + 4 \times (10 - 6)^2 \div 8\)
1. Parentheses: \(10 - 6 = 4\)
2. Exponent: \(4^2 = 16\)
3. Multiply/Divide: \(4 \times 16 = 64\); \(64 \div 8 = 8\)
4. Add: \(3 + 8 = \mathbf{11}\)
Trap: Adding \(3+4=7\) first gives 35 (choice B).
2. Proportional Recipe Key: (B) 1 ¼
3/4 cup sugar for 18 cookies. Cups for 30 cookies?
\(\frac{3/4}{18} = \frac{x}{30} \implies 18x = 30 \times \frac{3}{4} = \frac{90}{4} = 22.5\)
\(x = \frac{22.5}{18} = \frac{5}{4} = \mathbf{1\frac{1}{4}\text{ cups}}\) (or \(1.25\)).
3. Sale Price & Sales Tax Key: (D) $64.80
$80 jacket, 25% off, then 8% sales tax.
Sale Price \(= \$80 \times 0.75 = \$60.00\).
Total Cost \(= \$60 \times (1 + 0.08) = \$60 \times 1.08 = \mathbf{\$64.80}\).
(Tax is \(\$60 \times 0.08 = \$4.80\); \(\$60 + \$4.80 = \$64.80\)).
4. Exponent Rules Key: (B) 16
Simplify: \((2^3 \times 2^5) \div 2^4\)
Numerator: \(2^3 \times 2^5 = 2^{3+5} = 2^8\).
Division: \(2^8 \div 2^4 = 2^{8-4} = 2^4 = \mathbf{16}\).
5. Constant Rate & Time Key: (C) 4.5 h
150 mi in 2.5 h. Hours to travel 270 mi?
Speed \(r = \frac{150\text{ mi}}{2.5\text{ h}} = 60\text{ mph}\).
Time \(t = \frac{270\text{ mi}}{60\text{ mph}} = \frac{27}{6} = \mathbf{4.5\text{ hours}}\).
6. Greatest Number Key: (D) 0.6
Compare: 5/9, 0.58, 7/12, 0.6
\(5/9 \approx 0.5555\dots\)
\(0.58 = 0.5800\)
\(7/12 \approx 0.5833\dots\)
\(0.6 = \mathbf{0.6000}\) → Greatest is 0.6.
7. Unit Conversion Key: (C) 15 m/s
Convert 54 km/h to meters per second.
\(54 \times \frac{1000\text{ m}}{3600\text{ s}} = 54 \times \frac{5}{18} = 3 \times 5 = \mathbf{15\text{ m/s}}\).
8. Scientific Notation Key: (D) 6×10⁻²
Calculate: \((3 \times 10^4)(2 \times 10^{-6})\)
Coefficients: \(3 \times 2 = 6\).
Powers of 10: \(10^{4 + (-6)} = 10^{-2}\).
Result: \(\mathbf{6 \times 10^{-2}}\).
9. Percent Wage Increase Key: (C) $20.70
$18.00/hr wage with a 15% raise.
Raise amount \(= \$18.00 \times 0.15 = \$2.70\).
New wage \(= \$18.00 + \$2.70 = \mathbf{\$20.70}\)
(Or directly: \(\$18.00 \times 1.15 = \$20.70\)).
10. Dividing Signed Fractions Key: (D) 2/3
Evaluate: \((-3/4) \div (-9/8)\)
Multiply by reciprocal:
\(\left(-\frac{3}{4}\right) \times \left(-\frac{8}{9}\right) = +\frac{24}{36} = \mathbf{\frac{2}{3}}\).
Negative ÷ Negative = Positive.
TSIA2 Mathematics Practice Worksheet A • Form A Solutions Page 2 of 5
TSIA2 Math Practice Worksheet A
Domain 2: Algebraic Reasoning (Questions 11–20)
Equations, Functions & Models
11. Multi-Step Linear Equation Key: (B) 17
Solve for \(x\): \(3(x - 4) = 2x + 5\)
Distribute: \(3x - 12 = 2x + 5\).
Subtract \(2x\): \(x - 12 = 5\).
Add 12: \(\mathbf{x = 17}\).
12. Solving Inequalities Key: (C) x ≤ -4
Solve: \(5 - 2x \ge 13\)
Subtract 5: \(-2x \ge 8\).
Divide by \(-2\) & flip inequality:
\(x \le \frac{8}{-2} \implies \mathbf{x \le -4}\).
Trap: Forgetting to reverse sign gives \(x \ge -4\) (B).
13. Linear System Key: (B) (5, 6)
Solve: \(x + y = 11\) and \(2x - y = 4\)
Add equations: \(3x = 15 \implies x = 5\).
Substitute: \(5 + y = 11 \implies y = 6\).
Solution: \(\mathbf{(5, 6)}\).
14. Factoring Trinomials Key: (A) (x-8)(x+3)
Factor: \(x^2 - 5x - 24\)
Numbers that multiply to \(-24\) and sum to \(-5\):
\(-8 \times 3 = -24\) and \(-8 + 3 = -5\).
Factors: \(\mathbf{(x - 8)(x + 3)}\).
15. Quadratic Equation Key: (D) 2 & 4
Solve: \(x^2 - 6x + 8 = 0\)
Factor: \((x - 2)(x - 4) = 0\).
Roots: \(x - 2 = 0 \implies x = 2\);
\(x - 4 = 0 \implies x = 4\). Solution: \(\mathbf{x = 2\text{ and }x = 4}\).
16. Function Evaluation Key: (B) 15
\(f(x) = 2x^2 - 3x + 1\); find \(f(-2)\)
\(f(-2) = 2(-2)^2 - 3(-2) + 1\)
\(= 2(4) + 6 + 1 = 8 + 6 + 1 = \mathbf{15}\).
Note: \((-2)^2 = +4\), not \(-4\).
17. Equation of a Line Key: (D) y = 2x + 1
Line passing through \((2, 5)\) and \((6, 13)\).
Slope \(m = \frac{13 - 5}{6 - 2} = \frac{8}{4} = 2\).
\(y - y_1 = m(x - x_1) \implies y - 5 = 2(x - 2)\)
\(y - 5 = 2x - 4 \implies \mathbf{y = 2x + 1}\).
18. Rational Expression Key: (A) (x-3)/(x-2)
Simplify: \((x^2 - 9) \div (x^2 + x - 6)\)
Numerator: \((x - 3)(x + 3)\).
Denominator: \((x + 3)(x - 2)\).
Cancel \((x + 3)\): gives \(\mathbf{\frac{x - 3}{x - 2}}\).
19. Cost Equivalence Model Key: (C) 4
Gym A: $40 + $15/mo. Gym B: $25/mo.
Set costs equal: \(40 + 15m = 25m\).
Subtract \(15m\): \(40 = 10m \implies \mathbf{m = 4\text{ months}}\).
20. Radical Equation Key: (C) x = 9
Solve: \(\sqrt{x + 7} = x - 5\)
Square: \(x + 7 = x^2 - 10x + 25 \implies x^2 - 11x + 18 = 0\)
Factor: \((x - 9)(x - 2) = 0 \implies x = 9, 2\).
Check \(x = 2\): \(\sqrt{9} = 3 \ne 2-5=-3\) (Extraneous).
Check \(x = 9\): \(\sqrt{16} = 4 = 9-5\) (Valid). Only \(\mathbf{x = 9}\).
TSIA2 Mathematics Practice Worksheet A • Form A Solutions Page 3 of 5
TSIA2 Math Practice Worksheet A
Domain 3: Geometric & Spatial Reasoning (Questions 21–30)
Geometry, Trigonometry & Measurement
21. Diagonal of Rectangle Key: (C) 13 cm
Length = 12 cm, Width = 5 cm. Diagonal?
Pythagorean Theorem: \(d^2 = 12^2 + 5^2 = 144 + 25 = 169\).
\(d = \sqrt{169} = \mathbf{13\text{ cm}}\) (5-12-13 right triangle).
22. Area of a Circle Key: (B) 36π
Circle with radius \(r = 6\text{ inches}\).
Formula: \(A = \pi r^2 = \pi (6)^2 = \mathbf{36\pi\text{ sq in}}\).
Trap: \(12\pi\) is circumference (\(2\pi r\)), not area.
23. Triangle Angle Sum Key: (D) 65°
Two angles are \(47^\circ\) and \(68^\circ\). Third angle?
Sum of triangle angles \(= 180^\circ\).
Third angle \(= 180^\circ - (47^\circ + 68^\circ) = 180^\circ - 115^\circ = \mathbf{65^\circ}\).
24. Cylinder Volume Key: (D) 90π
Radius \(r = 3\text{ ft}\), height \(h = 10\text{ ft}\).
Formula: \(V = \pi r^2 h = \pi (3)^2 (10) = \pi (9)(10) = \mathbf{90\pi\text{ cu ft}}\).
25. Similar Triangles Key: (A) 12
\(\Delta ABC \sim \Delta DEF\). \(AB=6, DE=9, BC=8\). \(EF\)?
Proportion: \(\frac{AB}{DE} = \frac{BC}{EF} \implies \frac{6}{9} = \frac{8}{EF}\).
\(\frac{2}{3} = \frac{8}{EF} \implies 2(EF) = 24 \implies \mathbf{EF = 12}\).
26. Distance Formula Key: (B) 10
Distance between \((-2, 3)\) and \((4, 11)\).
\(d = \sqrt{(4 - (-2))^2 + (11 - 3)^2} = \sqrt{6^2 + 8^2}\)
\(d = \sqrt{36 + 64} = \sqrt{100} = \mathbf{10}\).
27. Midpoint Coordinates Key: (C) (3, 2)
Endpoints \((-4, 7)\) and \((10, -3)\).
\(M = \left(\frac{-4 + 10}{2}, \frac{7 + (-3)}{2}\right) = \left(\frac{6}{2}, \frac{4}{2}\right) = \mathbf{(3, 2)}\).
28. Hexagon Angle Sum Key: (B) 720°
Interior angle sum of a hexagon (\(n = 6\)).
Formula: \((n - 2) \times 180^\circ\).
\((6 - 2) \times 180^\circ = 4 \times 180^\circ = \mathbf{720^\circ}\).
29. Reflection across y-axis Key: (A) (-3, -2)
Reflect point \((3, -2)\) across the y-axis.
Rule: \((x, y) \to (-x, y)\).
The x-sign flips, y remains unchanged: \(\mathbf{(-3, -2)}\).
30. Right Triangle Sine Key: (D) 3/5
\(\angle C = 90^\circ\), \(AC = 12, BC = 9, AB = 15\). \(\sin A\)?
\(\sin A = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{BC}{AB} = \frac{9}{15} = \mathbf{\frac{3}{5}}\).
(\(\cos A = 12/15 = 4/5\); \(\tan A = 9/12 = 3/4\)).
TSIA2 Mathematics Practice Worksheet A • Form A Solutions Page 4 of 5
TSIA2 Math Practice Worksheet A
Domain 4: Probability & Statistics (Questions 31–40)
Data, Counting & Inference
31. Arithmetic Mean Key: (B) 14
Mean of \(12, 15, 9, 20, 14\):
\(\text{Sum} = 12 + 15 + 9 + 20 + 14 = 70\).
\(\text{Mean} = \frac{70}{5} = \mathbf{14}\).
32. Median of Even Set Key: (A) 8.5
Data: \(4, 9, 6, 15, 11, 8\)
Order: \(4, 6, \mathbf{8, 9}, 11, 15\).
Average middle two: \(\frac{8 + 9}{2} = \mathbf{8.5}\).
33. Rolling Sum of 7 Key: (C) 1/6
Probability two dice sum to 7:
6 favorable pairs: \((1,6),(2,5),(3,4),(4,3),(5,2),(6,1)\).
\(P(\text{sum}=7) = \frac{6}{36} = \mathbf{\frac{1}{6}}\).
34. Without Replacement Key: (D) 2/9
5 red, 3 blue, 2 green. Draw 2 red?
Total = 10. \(P(\text{1st Red}) = \frac{5}{10} = \frac{1}{2}\).
\(P(\text{2nd Red}) = \frac{4}{9}\). \(P = \frac{1}{2} \times \frac{4}{9} = \mathbf{\frac{2}{9}}\).
35. Permutation (Offices) Key: (C) 336
Elect Pres, VP, Sec from 8 students:
Titles differ (order matters):
\(P(8, 3) = 8 \times 7 \times 6 = \mathbf{336\text{ ways}}\).
36. Combination (Committee) Key: (B) 56
Choose committee of 3 from 8 students:
Unordered group (combination):
\(C(8, 3) = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = \frac{336}{6} = \mathbf{56\text{ ways}}\).
37. Slope Interpretation Key: (C)
Line of best fit: \(y = 2.5x + 40\)
Slope \(m = 2.5 = \frac{\Delta \text{score}}{\Delta \text{hours}}\):
Each extra hour of studying adds 2.5 points to predicted score.
38. Standard Deviation Key: (C) SD B > A
Set A: 10,10,10,10. Set B: 6,8,12,14.
Set A has zero deviation (\(s_A = 0\)).
Set B values deviate from mean 10 (\(s_B > 0\)).
Therefore, Set B has greater SD than Set A.
39. Conditional Probability Key: (D) 45/60
Sophomore chosen; probability passed?
Total Sophomores \(= 45 + 15 = 60\).
Sophomores who passed \(= 45\).
\(P(\text{Passed} \mid \text{Sophomore}) = \mathbf{\frac{45}{60}}\).
40. Expected Net Gain Key: (A) -$0.50
Cost $2. 1 section wins $6, 3 win $0.
Expected Payout \(= \frac{1}{4}(\$6) + \frac{3}{4}(\$0) = \$1.50\).
Expected Net Gain \(= \$1.50 - \$2.00 = \mathbf{-\$0.50}\).
TSIA2 Quick Formula Reference & Retention Checklist
Slope & Lines \(m = \frac{y_2 - y_1}{x_2 - x_1}\)
\(y = mx + b\)
Distance & Midpoint \(d = \sqrt{(\Delta x)^2 + (\Delta y)^2}\)
\(M = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\)
Permutations / Combs \(P(n, r) = \frac{n!}{(n-r)!}\)
\(C(n, r) = \frac{n!}{r!(n-r)!}\)
TSIA2 Mathematics Practice Worksheet A • Form A Solutions Page 5 of 5
