# TSI Math Test Study Guide — Answers

> Answer key based on the supplied PDF. The sections follow the practice-question documents.
>
> [Complete study guide](TSI-Math-Test-Study-Guide.md) · [Practice questions by type](practice-questions/README.md) · [Original PDF](1062198634-Hightower-TSI-Test-Study-Guide-v2-MATH.pdf)

## Contents

- [A. Factoring](#a-factoring)
- [B. Solving Equations](#b-solving-equations)
- [C. Solving Quadratic and Square-Root Equations](#c-solving-quadratic-and-square-root-equations)
- [D. Rational and Exponents](#d-rational-and-exponents)
- [E. Geometry Concepts](#e-geometry-concepts)
- [F. Algebraic Expressions](#f-algebraic-expressions)
- [G. Ratio and Proportional Relationships](#g-ratio-and-proportional-relationships)
- [H. Percentage](#h-percentage)
- [I. Linear Applications](#i-linear-applications)
- [J. Probability](#j-probability)
- [K. Descriptive Statistics](#k-descriptive-statistics)
- [L. Functions and Systems of Equations](#l-functions-and-systems-of-equations)
- [M. Key Concepts](#m-key-concepts)
- [N. Simplify Expressions](#n-simplify-expressions)
- [O. Self-Check Practice](#o-self-check-practice)

## A. Factoring

### I. Factor by GCF

1. **A** — 4(2x + 7)
2. **A** — 2(12y − 12)
3. **A** — 6(4x − 3)
4. **B** — 3(2x + 3y)
5. **A** — 4(3x + 2)
6. **D** — 3(x − 12)
7. **B** — 3x(4y + 5)
8. **C** — 2(x + 2)
9. **C** — x(x² − 7)
10. **C** — x(x² − 13)
11. **B** — 20x⁴ + 5x² − 35x
12. **A** — x + 1

### II. Factor Trinomials

1. **A** — (x + 3)(x − 6)
2. **C** — (x − 2)(x − 5)
3. **D** — (x + 1)(x − 8)
4. **A** — x − 6
5. **A** — u − v
6. **B** — 3ab
7. **B** — (x − 5)(x + 2)
8. **D** — (x − 11)(x − 1)
9. **D** — 2x + 3
10. **C** — 2x − 5
11. **C** — (x − 5)(x − 2)
12. **A** — (x + 2)(x + 4)
13. **D** — 2(x² − 7x + 8)
14. **B** — (2x − 3)(x + 4)

### III. Factor by Formulas

1. **C** — (x − 3)(x + 3)
2. **D** — x + 6
3. **C** — (a + 5)(a − 5)
4. **A** — 3x + 1
5. **C** — 2(k + 3)(k − 3)
6. **A** — (a − b)(a + b)
7. **B** — 6x − 1
8. **C** — (a + 5b)(a − 5b)
9. **B** — 9x² − 2t
10. **D** — 13² − 2²
11. **B** — (x − 2)(x + 2)
12. **D** — $(12 − \sqrt{5}x)(12 + \sqrt{5}x)$
13. **A** — 4(7c − 6)(7c + 6)
14. **C** — 5(6k − 1)(6k + 1)
15. **D** — (9x² − 2t)(9x² + 2t)
16. **B** — (a − 5b)(a + 5b)

## B. Solving Equations

1. **D** — 3
2. **B** — 1/12
3. **B** — 9/4
4. **A** — 5
5. **C** — 0
6. **D** — 4
7. **C** — 1
8. **B** — 2
9. **C** — 18
10. **D** — 8
11. **A** — 1
12. **C** — 2
13. **C** — 2
14. **D** — 1/12
15. **A** — 1/25
16. **C** — 8
17. **B** — 3
18. **B** — 30

## C. Solving Quadratic and Square-Root Equations

1. **A** — 8
2. **B** — −1
3. **C** — 1
4. **D** — −2
5. **C** — 64
6. **C** — 28
7. **D** — 2
8. **B** — $\sqrt{3x + 1} = 4$
9. **B** — x²
10. **A** — g(10) < g(20)
11. **B** — (x − 2)(x + 2)
12. **D** — $(12 − \sqrt{5}x)(12 + \sqrt{5}x)$
13. **A** — 4(7c − 6)(7c + 6)
14. **C** — 5(6k − 1)(6k + 1)
15. **D** — (9x² − 2t)(9x² + 2t)
16. **B** — (a − 5b)(a + 5b)

## D. Rational and Exponents

1. **B** — 49/x²
2. **C** — 25a²/b²
3. **C** — 4r²/(9s²)
4. **D** — 144/b²
5. **B** — m⁸
6. **C** — 6
7. **B** — 1
8. **A** — 0
9. **A** — b
10. **A** — b

## E. Geometry Concepts

1. **C** — L = 5, W = 7
2. **C** — 28 = 2(5 + 9)
3. **A** — w = 11
4. **D** — 4x − 4
5. **A** — 11,760 ft²
6. **B** — 22
7. **C** — 24 inches
8. **C** — x + 1
9. **D** — 3x − 2
10. **A** — 6
11. **C** — $3\sqrt{7}$
12. **D** — tan(x) = 7,000/5,000
13. **A** — $\sqrt{33}$
14. **D** — 36
15. **A** — a² − b²
16. **A** — 2
17. **B** — 42 inches
18. **A** — 240
19. **D** — 150 cm²
20. **B** — 128 in³
21. **A** — 90
22. **C** — 220 ft²
23. **C** — 10x²
24. **D** — 180° − 2(65°)
25. **B** — ∠X
26. **D** — 5x + 1 = 26
27. **B** — L = 2W − 3

## F. Algebraic Expressions

1. **C** — 45d + 0.25m
2. **A** — x + x + 2x + 2x = 64
3. **A** — 10 + 10 + 30 + 30
4. **B** — Six more than one third of n equals 5
5. **A** — 7
6. **B** — 11
7. **D** — (r + s) × 5
8. **A** — 52x
9. **A** — Maria > Zulma
10. **C** — t + m = 2.10; 2t + 3m = 5.15
11. **C** — p × m = 160
12. **B** — 5(5r + p)

## G. Ratio and Proportional Relationships

1. **D** — 10 tasks in 22.5 minutes
2. **C** — 5⅓ cups
3. **C** — 6,129 feet
4. **C** — 7 yards
5. **B** — 24 feet
6. **B** — 7.5
7. **D** — 150 km
8. **A** — x/20 inches
9. **D** — 60,800 g
10. **A** — \$2.42 per pound
11. **A** — \$120.00
12. **A** — \$189.00
13. **B** — 11 inches
14. **C** — 90°
15. **B** — 21 cups
16. **A** — 20 boxes
17. **C** — 70 minutes
18. **D** — 6:15 pm
19. **C** — \$9.10
20. **C** — 3.5 hours
21. **D** — 7x/15 yards
22. **D** — 100 minutes
23. **C** — 84/5 inches
24. **C** — 6 minutes
25. **C** — 3
26. **B** — 10
27. **B** — 1/2
28. **A** — 1/2
29. **A** — 16
30. **D** — 40

## H. Percentage

1. **A** — 100
2. **A** — 300
3. **A** — 400
4. **B** — 30
5. **B** — 50
6. **C** — \$2,500
7. **B** — 50
8. **C** — 12%
9. **A** — \$720
10. **B** — 0.85x − 5
11. **B** — 7.15k
12. **C** — 0.9P
13. **C** — \$32.50

## I. Linear Applications

1. **C** — \$219.75
2. **3** — 100°C
3. **3** — −263°C
4. **1** — 25°C
5. **B** — 1,650 ft
6. **3** — 0.707 sec
7. **2** — A = πr²
8. **3** — $r = \sqrt{A/π}$
9. **C** — 20
10. **B** — 5.40

## J. Probability

1. **B** — 1/3
2. **D** — (10/24) × (6/23)
3. **C** — 3/4
4. **1** — 108
5. **A** — approximately 3 million
6. **C** — 1/2
7. **B** — 1/4
8. **A** — an even integer
9. **D** — 7/12

## K. Descriptive Statistics

1. **B** — 65
2. **D** — 26
3. **A** — 8
4. **B** — 28
5. **D** — 30
6. **B** — 750 meters
7. **D** — 4.8 miles
8. **A** — \$0.54
9. **D** — 50.2
10. **C** — 18
11. **A** — 7
12. **D** — 181
13. **A** — 37
14. **C** — 44
15. **A** — 21
16. **B** — 120
17. **C** — 13
18. **B** — 11
19. **B** — 28
20. **C** — 13
21. **B** — 3
22. **C** — 13
23. **B** — 3
24. **C** — Mode
25. **B** — 3
26. **B** — 11
27. **C** — Mode

## L. Functions and Systems of Equations

1. **C** — f(x) = |x| + 1
2. **G** — y = (x + 2)² − 9
3. **C** — the graph beginning at the origin and falling to the right
4. **J** — None
5. **A** — $f(x) = −\sqrt{x − 1}$
6. **N** — $f(x) = \sqrt{x}$
7. **B** — (3, 6)
8. **A** — None
9. **A** — \$3.00
10. **D** — Five
11. **C** — 6 children

## N. Simplify Expressions

1. **B** — 8
2. **C** — 25a²/b²
3. **B** — 49/x²
4. **D** — 144/b²
5. **A** — b
6. **B** — (b − a)²

## O. Self-Check Practice

1. **C** — 0.9P
2. **C** — 0.707 sec
3. **A** — 52x
4. **C** — 7.15k
5. **C** — 3
6. **B** — 10
7. **B** — 1/2
8. **A** — 1/2
9. **A** — 16
10. **C** — 7(x² + 3)
11. **A** — w = 11
12. **C** — $r = \sqrt{A/π}$
13. **E** — B and D are the two non-factors
14. **D** — 5 \$3 pens
15. **C** — \$219.75
16. **A** — 8/5
17. **C** — 0
18. **D** — 4
19. **A** — 25°C
20. **C** — t + m = 2.10; 2t + 3m = 5.15
21. **B** — sundaes = 36, banana splits = 28
22. **A** — 5f + 3g = 5.70; 2f + 10g = 3.60
23. **D** — m + n = 54; m = 3n + 8
24. **C** — (x, y) = (6, 9)