# TSI Math Test Study Guide

> Clean Markdown version of the lessons and corrected practice-question bank.
> The answer key remains in `src/data/quiz.json`; this document presents the questions and choices.

## Section 1 — Lessons and Key Skills

### 1. Calculate a Sale Price

To calculate a sale price, apply percentage discounts and fixed-dollar discounts in order.

- A 10% discount on $10: `$10 × (1 − 0.10) = $9`.
- A $2 discount on $10: `$10 − $2 = $8`.
- A 10% discount followed by a $5 coupon on an original price `x`: `0.90x − 5`.

### 2. Calculate a Unit Rate

When two situations use the same rate, calculate the rate per unit first. For example, mowing time can be found from area and rate:

`time = area ÷ rate`

### 3. Identify a Function’s Graph

Use the function’s domain and range to eliminate graph choices. Substitute convenient values such as `x = 0`, `4`, or `16` to verify points on the graph.

For `y = −√x`, the domain is `x ≥ 0`, the range is `y ≤ 0`, and the graph begins at the origin and falls to the right.

### 4. Descriptive Statistics

- **Range:** largest value minus smallest value.
- **Median:** the middle value after sorting; for an even number of values, average the two middle values.
- **Mean (average):** sum of the values divided by the number of values.
- **Mode:** the value that occurs most frequently.

### 5. Factoring

For a quadratic `ax² + bx + c`, look for factors that multiply to `ac` and add to `b`. Always multiply the factors back together to verify the result.

Important identities:

- `a² − b² = (a − b)(a + b)`
- `(a + b)² = a² + 2ab + b²`
- `(a − b)² = a² − 2ab + b²`

### 6. Geometry

Know the basic angle, perimeter, area, and volume formulas.

- A straight angle measures `180°`.
- A full circle measures `360°`.
- Rectangle area: `A = length × width`.
- Rectangle perimeter: `P = 2(length + width)`.
- Triangle area: `A = ½(base)(height)`.
- Rectangular-prism volume: `V = length × width × height`.

Read carefully to determine whether a question asks for area, perimeter, surface area, or volume.

### 7. Trigonometry

Use **SOH-CAH-TOA**:

- `sin θ = opposite ÷ hypotenuse`
- `cos θ = adjacent ÷ hypotenuse`
- `tan θ = opposite ÷ adjacent`

### 8. Simplifying Equations

Use the order of operations, combine like terms, distribute factors, and perform the same operation on both sides of an equation.

### 9. Pythagorean Theorem

For a right triangle, `a² + b² = c²`, where `c` is the hypotenuse.

### 10. Similar Triangles

Corresponding sides of similar triangles are proportional. Set up a proportion and cross-multiply to find an unknown side.

### 11. Basic Number Calculations

Translate the wording into operations or an equation. For example, if a book is read at `p` pages per minute for `m` minutes and has 160 pages, then `pm = 160`.

### 12. Quadratic Graphs

Know how the equation of a quadratic identifies its vertex, intercepts, direction, and overall shape. Vertex form is `y = a(x − h)² + k`, with vertex `(h, k)`.

### 13. Probability

For independent events:

- `P(A and B) = P(A) × P(B)`
- `P(A or B) = P(A) + P(B) − P(A and B)`

### 14. Ratios

Set up equivalent ratios and use cross multiplication to find the unknown quantity.

### 15. Temperature Conversion

To convert Fahrenheit to Celsius, use:

`C = (F − 32) × 5/9`

### 16. Systems of Equations

Define the variables, translate each condition into an equation, and solve using substitution or elimination. Pay close attention to words such as **more**, **less**, **total**, and **per**.

## Section 2 — Practice Questions

### Chapter 1

#### Question 1

Which expression is equivalent to 4(x + 5) + 4x + 8?

- **A.** 4(2x + 7)
- **B.** 8(x + 4)
- **C.** 5x + 17
- **D.** 8x + 13

#### Question 2

Which expression is not equal to 24y − 12?

- **A.** 2(12y − 12)
- **B.** 2(12y − 6)
- **C.** 4(6y − 3)
- **D.** 12(2y − 1)

#### Question 3

Which expression is equivalent to 24x − 18?

- **A.** 6(4x − 3)
- **B.** 6(3x − 4)
- **C.** 4(6x − 4)
- **D.** 12x − 9

#### Question 4

Which is equivalent to 6x + 9y?

- **A.** 6(x + 3y)
- **B.** 3(2x + 3y)
- **C.** 9x + 6y
- **D.** 6x − 9y

#### Question 5

Which is equivalent to 12x + 8?

- **A.** 4(3x + 2)
- **B.** 4(3x + 8)
- **C.** 4(3x + 2x)
- **D.** 20x

#### Question 6

Which is equivalent to 3x − 36?

- **A.** 3x + 36
- **B.** 3(12 − x)
- **C.** 3(3x − 12)
- **D.** 3(x − 12)

#### Question 7

Which is equivalent to 12xy + 15x?

- **A.** 12xy − 15x
- **B.** 3x(4y + 5)
- **C.** 3x(5y + 4)
- **D.** 12yz + 15x

#### Question 8

Which is equivalent to 2x + 4?

- **A.** 2 + 4x
- **B.** x(2 + 4)
- **C.** 2(x + 2)
- **D.** 4(x + 2)

#### Question 9

Which is equivalent to x³ − 7x?

- **A.** (x − 7)(x² − x)
- **B.** (x − 7)(x² + 1)
- **C.** x(x² − 7)
- **D.** x²(x − 7)

#### Question 10

Which is equivalent to x³ − 13x?

- **A.** (x − 7)(x² − 13)
- **B.** (x − 7)(x² + 13)
- **C.** x(x² − 13)
- **D.** x²(x − 13)

#### Question 11

Which is equivalent to 5x(4x³ + x − 7)?

- **A.** 20x⁴ − 5x² − 35x
- **B.** 20x⁴ + 5x² − 35x
- **C.** 20x⁴ + x − 7
- **D.** 9x⁴ + 6x² − 12x

#### Question 12

Simplify (xy + y) / y.

- **A.** x + 1
- **B.** x(y + 1) / y
- **C.** xy
- **D.** x + y

### Chapter 2

#### Question 1

Which function is equivalent to f(x) = x² − 3x − 18?

- **A.** f(x) = (x + 3)(x − 6)
- **B.** f(x) = (x + 6)(x − 3)
- **C.** f(x) = (x + 6)(x + 3)
- **D.** f(x) = (x − 3)(x + 6)

#### Question 2

Which function is equivalent to f(x) = x² − 7x + 10?

- **A.** (x − 3)(x − 7)
- **B.** (x + 7)(x + 3)
- **C.** (x − 2)(x − 5)
- **D.** (x − 2)(x + 5)

#### Question 3

Which function is equivalent to f(x) = x² − 7x − 8?

- **A.** (x − 1)(x − 8)
- **B.** (x + 1)(x + 8)
- **C.** (x − 1)(x + 8)
- **D.** (x + 1)(x − 8)

#### Question 4

Which expression is a factor of x² − 5x − 6?

- **A.** x − 6
- **B.** x + 6
- **C.** x − 3
- **D.** x − 1

#### Question 5

Which of the following is a factor of u² + uv − 2v²?

- **A.** u − v
- **B.** u − 2v
- **C.** 2u + v
- **D.** u + v

#### Question 6

If a² + n + 2b² = (a + b)(a + 2b), what is n?

- **A.** a²b
- **B.** 3ab
- **C.** ab + ba
- **D.** 3ab²

#### Question 7

Which function is equivalent to f(x) = x² − 3x − 10?

- **A.** (x − 6)(2x + 4)
- **B.** (x − 5)(x + 2)
- **C.** (2x − 3)(x + 4)
- **D.** (x + 5)(x − 2)

#### Question 8

Which function is equal to f(x) = x² − 12x + 11?

- **A.** (x + 11)(x + 1)
- **B.** (x − 11)(x + 1)
- **C.** (x + 11)(x − 1)
- **D.** (x − 11)(x − 1)

#### Question 9

Which expression is a factor of 2x² − x − 6?

- **A.** 3x + 2
- **B.** 2x − 3
- **C.** x + 2
- **D.** 2x + 3

#### Question 10

Which expression is a factor of 2x² − 3x − 5?

- **A.** 2x − 1
- **B.** x − 1
- **C.** 2x − 5
- **D.** 2x + 5

#### Question 11

Factor x² − 7x + 10.

- **A.** (x − 5)(x − 2)
- **B.** (x + 5)(x + 2)
- **C.** (x − 10)(x + 1)
- **D.** (x − 7)(x + 10)

#### Question 12

Factor x² + 6x + 8.

- **A.** (x + 1)(x + 8)
- **B.** (x + 2)(x + 4)
- **C.** (x − 2)(x − 4)
- **D.** (x + 6)(x + 8)

#### Question 13

Factor 2x² − 12x + 16.

- **A.** 2(x − 2)(x − 4)
- **B.** (2x − 2)(x − 8)
- **C.** 2(x + 2)(x + 4)
- **D.** (x − 7)(2x − 16)

#### Question 14

Factor 2x² + 5x − 12.

- **A.** (2x + 3)(x − 4)
- **B.** (2x − 3)(x + 4)
- **C.** (x + 6)(2x − 2)
- **D.** (2x + 4)(x − 3)

### Chapter 3

#### Question 1

Which function is equivalent to f(x) = x² − 9?

- **A.** (x − 9)(x + 9)
- **B.** (9 − x)(9 + x)
- **C.** (x − 3)(x + 3)
- **D.** (3 − x)(3 + x)

#### Question 2

Which expression is a factor of x² − 36?

- **A.** 3x − 6
- **B.** 6 − x
- **C.** 9x − 36
- **D.** x + 6

#### Question 3

Which function is equivalent to a² − 25?

- **A.** (a − 25)(a + 25)
- **B.** (a − 5)(a − 5)
- **C.** (a + 5)(a − 5)
- **D.** (a + 5)(a + 5)

#### Question 4

Which expression is a factor of 9x² − 1?

- **A.** 3x + 1
- **B.** 3x − 2
- **C.** x − 3
- **D.** x + 3

#### Question 5

Which function is equivalent to 2k² − 18?

- **A.** 2(k − 3)(k − 3)
- **B.** 2(k + 3)(k + 3)
- **C.** 2(k + 3)(k − 3)
- **D.** (2k + 3)(k − 3)

#### Question 6

Which function is equivalent to a² − b²?

- **A.** (a − b)(a + b)
- **B.** (a − b)(a − b)
- **C.** (a + b)(b − a)
- **D.** (a + b)(a + b)

#### Question 7

Which expression is a factor of 36x² − 1?

- **A.** 18x − 7
- **B.** 6x − 1
- **C.** 6x − 2
- **D.** 6x − 7

#### Question 8

Which function is equivalent to a² − 25b²?

- **A.** (a − 25b)(a + 25b)
- **B.** (a − 5b)(a − 5b)
- **C.** (a + 5b)(a − 5b)
- **D.** (a + 5b)(a + 5b)

#### Question 9

Which expression is a factor of 81x⁴ − 4t²?

- **A.** 4x − 7
- **B.** 9x² − 2t
- **C.** 2x + 7
- **D.** 7 − 2x

#### Question 10

Which is equivalent to (13 + 2)(13 − 2)?

- **A.** 15² + 11²
- **B.** 15² − 11²
- **C.** 13² + 2²
- **D.** 13² − 2²

#### Question 11

Factor x² − 4.

- **A.** (x − 2)(x + 2)
- **B.** (x − 4)(x + 1)
- **C.** (x − 2)²
- **D.** (x + 4)(x − 1)

#### Question 12

Factor 144 − 5x².

- **A.** (12 − 5x)(12 + 5x)
- **B.** (12 − √5x)(12 + √5x)
- **C.** (144 − x)(1 + 5x)
- **D.** (12 − x)(12 + 5x)

#### Question 13

Factor 196c² − 144.

- **A.** 4(7c − 6)(7c + 6)
- **B.** (14c − 12)(14c + 12)
- **C.** (196c − 144)(c + 1)
- **D.** 4(14c − 6)(14c + 6)

#### Question 14

Factor 180k² − 5.

- **A.** 5(6k − 1)(6k + 1)
- **B.** (18k − 5)(10k + 1)
- **C.** 5(18k − 1)(2k + 1)
- **D.** (180k − 5)(k + 1)

#### Question 15

Factor 81x⁴ − 4t².

- **A.** (9x² − 2t)(9x² + 2t)
- **B.** (81x² − 2t)(x² + 2t)
- **C.** (9x − 2t)(9x + 2t)
- **D.** (81x⁴ − 2t)(x + 2t)

#### Question 16

Factor a² − 25b².

- **A.** (a − 5b)(a + 5b)
- **B.** (a − 25b)(a + 25b)
- **C.** (a − 5b)²
- **D.** (a + 25b)²

### Chapter 4

#### Question 1

If x + 3(2x − 5) = 6, what is the value of x?

- **A.** −2
- **B.** 1 4/7
- **C.** 0
- **D.** 3

#### Question 2

If 3(4x + 2) = 7, what is the value of x?

- **A.** −1
- **B.** 1/12
- **C.** 10
- **D.** −5

#### Question 3

If 4p + 1 = 10, what is the value of p?

- **A.** −2
- **B.** 9/4
- **C.** −1
- **D.** 11/4

#### Question 4

If x = 3 in ax − 10 = x + 2, what is the value of a?

- **A.** 5
- **B.** 10
- **C.** 15
- **D.** 20

#### Question 5

If x − 10 = 5x − 10, what is the value of x?

- **A.** −5
- **B.** −3 2/3
- **C.** 0
- **D.** 5

#### Question 6

If 6(t − 2) − 4 = 2t, then t = ?

- **A.** −2
- **B.** 0
- **C.** 2
- **D.** 4

#### Question 7

If 4 = (7 + y) / 2, then y = ?

- **A.** −1
- **B.** 7/9
- **C.** 1
- **D.** 7

#### Question 8

If x/2 = (x + 1)/3, then x = ?

- **A.** 1
- **B.** 2
- **C.** 3
- **D.** 4

#### Question 9

If 4b − 3 = 2b, then 12b = ?

- **A.** 6
- **B.** 8
- **C.** 18
- **D.** 24

#### Question 10

If 4b − 1 = b, then 24b = ?

- **A.** 1/3
- **B.** 1
- **C.** 25/5
- **D.** 8

#### Question 11

If x/4 = (x + 1)/5, then x = ?

- **A.** 1
- **B.** 2
- **C.** 3
- **D.** 4

#### Question 12

If 3 = (8 − r)/2, then r = ?

- **A.** −1
- **B.** −2
- **C.** 2
- **D.** 4

#### Question 13

If 3 = (8 − r)/r, then r = ?

- **A.** −1
- **B.** −2
- **C.** 2
- **D.** 4

#### Question 14

If 3(4x + 2) = 7, then x = ?

- **A.** 12
- **B.** 1/2
- **C.** 5/12
- **D.** 1/12

#### Question 15

If 2/(5x) + 1/x = 35, then x = ?

- **A.** 1/25
- **B.** 1/5
- **C.** 5
- **D.** 7

#### Question 16

If x + y = 12 and x = 2y, then x = ?

- **A.** 2
- **B.** 6
- **C.** 8
- **D.** 10

#### Question 17

If n + 3n = 12, what is n?

- **A.** 2
- **B.** 3
- **C.** 4
- **D.** 5

#### Question 18

If x = 5 and y = 3, then 3x + 5y = ?

- **A.** 25
- **B.** 30
- **C.** 35
- **D.** 40

### Chapter 5

#### Question 1

Which of the following is a solution to x² − 5x − 24 = 0?

- **A.** 8
- **B.** 3
- **C.** 1
- **D.** 0

#### Question 2

Which of the following is a solution to x² + 8x + 7 = 0?

- **A.** 7
- **B.** −1
- **C.** 1
- **D.** 0

#### Question 3

Which of the following is a solution to x² − 12x + 11 = 0?

- **A.** −8
- **B.** −11
- **C.** 1
- **D.** 0

#### Question 4

Which of the following is a solution to x² − 3x − 10 = 0?

- **A.** −8
- **B.** −6
- **C.** −5
- **D.** −2

#### Question 5

If √x + 3 = 11, what is the value of x?

- **A.** 19
- **B.** 8
- **C.** 64
- **D.** 14

#### Question 6

If √(x − 3) = 5, what is the value of x?

- **A.** 8
- **B.** 25
- **C.** 28
- **D.** 64

#### Question 7

If 7w(w − 2) = 0, what could be the value of w?

- **A.** 5
- **B.** −10
- **C.** −3
- **D.** 2

#### Question 8

Which equation has solution x = 5?

- **A.** x² = 10
- **B.** √(3x + 1) = 4
- **C.** 3x² = 225
- **D.** √(4x) = 10

#### Question 9

If x = −3, which of the following is positive?

- **A.** x³
- **B.** x²
- **C.** 2x
- **D.** 1/x

#### Question 10

If g(x) = x/(x + 1), then which statement is true?

- **A.** g(10) < g(20)
- **B.** g(20) < g(10)
- **C.** g(0) = 1
- **D.** g(1) = 0

#### Question 11

What is a solution to x² + 2x − 15 = 0?

- **A.** −5
- **B.** −4
- **C.** 4
- **D.** 5

#### Question 12

What is a solution to x² − 5x + 6 = 0?

- **A.** −3
- **B.** −2
- **C.** 2
- **D.** −1

#### Question 13

What is a solution to −2x² + 7x − 3 = 0?

- **A.** −3
- **B.** 1/2
- **C.** 1
- **D.** 4

#### Question 14

If a + √x = b, then x = ?

- **A.** b − a
- **B.** (b − a)²
- **C.** b² − a
- **D.** a² − b²

#### Question 15

Which of the following is a negative solution to 6x² − 11x − 10 = 0?

- **A.** −2/3
- **B.** −1/2
- **C.** 5/2
- **D.** 2

#### Question 16

If √(x − 3) = 15, what is the value of x?

- **A.** 18
- **B.** 225
- **C.** 228
- **D.** 15

### Chapter 6

#### Question 1

What is (7/x)²?

- **A.** 14/x²
- **B.** 49/x²
- **C.** 7²/x
- **D.** x²/49

#### Question 2

What is (5a/b)²?

- **A.** 5a²/b²
- **B.** 25a/b²
- **C.** 25a²/b²
- **D.** 10a²/b

#### Question 3

What is (2r/3s)²?

- **A.** 2r²/(3s²)
- **B.** 2r/(3s²)
- **C.** 4r²/(9s²)
- **D.** 9s²/(4r²)

#### Question 4

What is (12/b)²?

- **A.** 24/b²
- **B.** 12/b
- **C.** 144/b
- **D.** 144/b²

#### Question 5

Simplify m¹⁰/m².

- **A.** m⁵
- **B.** m⁸
- **C.** 1/m⁵
- **D.** 1/m⁸

#### Question 6

If h(x) = 10ˣ, for what value of x does h(x) = 1,000,000?

- **A.** 2
- **B.** 4
- **C.** 6
- **D.** 8

#### Question 7

For what value of x is g(x) = x/(1 − x) not defined?

- **A.** 0
- **B.** 1
- **C.** 2
- **D.** 3

#### Question 8

For what value of a would (ax − b)/a not be defined?

- **A.** 0
- **B.** 1
- **C.** 2
- **D.** 3

#### Question 9

If a ≠ 0, a ≠ 1, and (ax − b)/(a − 1) = b, what is x?

- **A.** b
- **B.** 1
- **C.** a
- **D.** b/a

#### Question 10

If a ≠ 0, a ≠ 3, and (ax − 3b)/(a − 3) = b, what is x?

- **A.** b
- **B.** 1
- **C.** a
- **D.** 3

### Chapter 7

#### Question 1

If a rectangle has a perimeter of 24, what could be its length and width?

- **A.** L = 2, W = 12
- **B.** L = 4, W = 20
- **C.** L = 5, W = 7
- **D.** L = 8, W = 3

#### Question 2

If P = 2(L + W) and P = 28, which could be the length and width?

- **A.** 28 = 2(2 + 14)
- **B.** 28 = 2(7 + 21)
- **C.** 28 = 2(5 + 9)
- **D.** 28 = 2(4 + 7)

#### Question 3

If the length of a rectangle is 4 more than its width and the perimeter is 52, find the width.

- **A.** w = 11
- **B.** w = 12
- **C.** w = 15
- **D.** w = 24

#### Question 4

If a rectangle has length x and width x − 2, what is its perimeter?

- **A.** 2x − 2
- **B.** 2x − 4
- **C.** 4x − 2
- **D.** 4x − 4

#### Question 5

A rectangular parking lot is 140 feet long and 84 feet wide. What is its area?

- **A.** 11,760 ft²
- **B.** 10,760 ft²
- **C.** 9,760 ft²
- **D.** 8,760 ft²

#### Question 6

The expressions x − 2 and x + 3 are the length and width of a rectangle. If its area is 24, what is its perimeter?

- **A.** 20
- **B.** 22
- **C.** 24
- **D.** 28

#### Question 7

A rectangular frame is 5 inches wide and 7 inches long. What is its outside perimeter?

- **A.** 20 inches
- **B.** 22 inches
- **C.** 24 inches
- **D.** 26 inches

#### Question 8

Two sides of a triangle are 2x − 5 and x + 3. If the perimeter is 4x − 1, what is the third side?

- **A.** x + 3
- **B.** 2x − 1
- **C.** x + 1
- **D.** x − 1

#### Question 9

If a triangle has side lengths x, x + 2, and x − 4, what is its perimeter?

- **A.** 3x + 3
- **B.** 2x − 1
- **C.** 2x + 1
- **D.** 3x − 2

#### Question 10

What is the area of a right triangle with height √6 and base √24?

- **A.** 6
- **B.** 24
- **C.** 36
- **D.** 73

#### Question 11

In a right triangle, if c = 12 and the other leg is 9, what is a?

- **A.** 3
- **B.** 9
- **C.** 3√7
- **D.** 9√7

#### Question 12

DIAGRAM IN SOURCE PDF: An airplane is 5,000 ft above ground and the beginning of the runway is 7,000 ft horizontally away. Angle x is formed at the airplane between the vertical altitude line and the flight path to the beginning of the runway. Which equation calculates angle x?

- **A.** sin(x) = 5,000/7,000
- **B.** sin(x) = 7,000/5,000
- **C.** tan(x) = 5,000/7,000
- **D.** tan(x) = 7,000/5,000

#### Question 13

In a right triangle, if c = 7 and the other leg is 4, what is a?

- **A.** √33
- **B.** 3
- **C.** 3√7
- **D.** 9

#### Question 14

What is the area of a square with a perimeter of 24 feet?

- **A.** 10
- **B.** 16
- **C.** 26
- **D.** 36

#### Question 15

DIAGRAM IN SOURCE PDF: A large square has side a and contains a smaller square with side b. The region of the large square outside the smaller square is shaded. What is the shaded area?

- **A.** a² − b²
- **B.** (a + b)²
- **C.** (a − b)²
- **D.** ab

#### Question 16

The area of a square is 36 and its side is 3x. What is x?

- **A.** 2
- **B.** 4
- **C.** 9
- **D.** 12

#### Question 17

A rectangle has area 1,176 square inches and width 28 inches. What is its length?

- **A.** 21 inches
- **B.** 42 inches
- **C.** 560 inches
- **D.** 1,148 inches

#### Question 18

How many cubes with side length 2 are needed to fill a box 16 by 12 by 10?

- **A.** 240
- **B.** 120
- **C.** 160
- **D.** 25

#### Question 19

What is the surface area of a rectangular prism with length 4 cm, width 9 cm, and height 3 cm?

- **A.** 75 cm²
- **B.** 108 cm²
- **C.** 120 cm²
- **D.** 150 cm²

#### Question 20

What is the volume of a rectangular solid with dimensions 8, 4, and 4 inches?

- **A.** 160 in³
- **B.** 128 in³
- **C.** 64 in³
- **D.** 32 in³

#### Question 21

Four angles x, y, w, and z form a complete circle. What is their average?

- **A.** 90
- **B.** 100
- **C.** 120
- **D.** It cannot be determined

#### Question 22

An L-shaped room is formed from an 18 ft by 14 ft rectangle with a 4 ft by 8 ft corner removed. What is its area?

- **A.** 112 ft²
- **B.** 196 ft²
- **C.** 220 ft²
- **D.** 252 ft²

#### Question 23

An L-shaped room is formed from a 3x by 3x square and an x by x square. What is its area?

- **A.** 14x + 2
- **B.** 12x + 2
- **C.** 10x²
- **D.** 10x² + 2x

#### Question 24

In an isosceles triangle, the base angles measure 65°. Which expression calculates the third angle?

- **A.** 180° + 65°
- **B.** 180° − 65°
- **C.** 180° + 2(65°)
- **D.** 180° − 2(65°)

#### Question 25

DIAGRAM REQUIRED: Figure 2 is a 90° clockwise rotation of figure 1. Which angle in figure 2 corresponds to angle A in figure 1?

- **A.** ∠W
- **B.** ∠X
- **C.** ∠Y
- **D.** ∠Z

#### Question 26

An isosceles trapezoid has small base x, large base 2x − 3, and two other sides x + 2. If the perimeter is 26, which equation is true?

- **A.** 4x − 3 = 26
- **B.** 4x − 1 = 26
- **C.** 5x − 1 = 26
- **D.** 5x + 1 = 26

#### Question 27

If the length L of a rectangle is 3 less than twice its width W, which equation gives L in terms of W?

- **A.** L = 3 − 2W
- **B.** L = 2W − 3
- **C.** L = 3W − 2
- **D.** L = 2 − 3W

### Chapter 8

#### Question 1

A rental car costs $45 per day plus $0.25 per mile. Which expression is the cost for d days and m miles?

- **A.** 45 + 0.25 + d + m
- **B.** 45(0.25) + dm
- **C.** 45d + 0.25m
- **D.** 45/d + 25/m

#### Question 2

A rectangular pool is x meters wide and twice as long. If its perimeter is 64 meters, which equation represents the information?

- **A.** x + x + 2x + 2x = 64
- **B.** x + 2x = 64
- **C.** x + 2 + x + 2 = 64
- **D.** 2x + 2x + 2x + 2x = 64

#### Question 3

A rectangle is 10 meters wide and three times as long. Which expression is its perimeter?

- **A.** 10 + 10 + 30 + 30
- **B.** 10 + 30
- **C.** 10 × 30
- **D.** 2(10 × 30)

#### Question 4

Which sentence represents n/3 + 6 = 5?

- **A.** Six more than a number n equals 5
- **B.** Six more than one third of a number n equals 5
- **C.** Three more than a number n divided by 6 equals 5
- **D.** A number n plus one third of 6 equals 5

#### Question 5

Which number added to 5 gives a result less than 13?

- **A.** 7
- **B.** 8
- **C.** 9
- **D.** 10

#### Question 6

Twice a number is 4 less than 26. What is the number?

- **A.** 9
- **B.** 11
- **C.** 15
- **D.** 18

#### Question 7

Which expression is 5 times as much as the sum of r and s?

- **A.** 5r + s
- **B.** 5 + r + s
- **C.** r + 5s
- **D.** (r + s) × 5

#### Question 8

Alice earns x dollars per hour for the first 40 hours and 1.5 times as much for each hour over 40. How much does she earn for 48 hours?

- **A.** 52x
- **B.** 48x
- **C.** 40 + 12x
- **D.** 40x + 12

#### Question 9

Maria has three more dollars than Zulma. Which inequality is true?

- **A.** Maria > Zulma
- **B.** Maria < Zulma
- **C.** Maria + 3 < Zulma
- **D.** Maria < Zulma − 3

#### Question 10

A taco and a small milk cost $2.10. Two tacos and three milks cost $5.15. Which system determines taco cost t and milk cost m?

- **A.** t + m = 5.15; 2t + 3m = 2.10
- **B.** t − m = 5.15; 2t − 3m = 2.10
- **C.** t + m = 2.10; 2t + 3m = 5.15
- **D.** t − m = 2.10; 2t − 3m = 5.15

#### Question 11

Jill reads p pages per minute for m minutes, and the book has 160 pages. Which equation represents this?

- **A.** p/m = 160
- **B.** p + m = 160
- **C.** pm = 160
- **D.** 160 + m = p

#### Question 12

A store charges 25 cents per ruler and 5 cents per pencil. What is the charge for r rulers and p pencils?

- **A.** 25r + p
- **B.** 5(5r + p)
- **C.** 30(r + p)
- **D.** 5r + 25p

### Chapter 9

#### Question 1

Khalid completed 40 tasks in 90 minutes. Which is an equivalent rate?

- **A.** 10 tasks in 0.9 minutes
- **B.** 10 tasks in 2.25 minutes
- **C.** 10 tasks in 9 minutes
- **D.** 10 tasks in 22.5 minutes

#### Question 2

A recipe requires 2 cups of water for every 3 cups of flour. If 8 cups of flour are used, how much water is needed?

- **A.** 2 2/3
- **B.** 4
- **C.** 5 1/3
- **D.** 12

#### Question 3

The elevation change from 2,550 m to 4,418 m is approximately how many feet? (1 ft = 0.3048 m)

- **A.** 569 feet
- **B.** 5,604 feet
- **C.** 6,129 feet
- **D.** 14,495 feet

#### Question 4

Jen needs 19.5 feet of ribbon and ribbon is sold by the full yard. How many yards does she need?

- **A.** 6 yards
- **B.** 6.5 yards
- **C.** 7 yards
- **D.** 7.5 yards

#### Question 5

Nancy is 6 feet tall and casts a 9-foot shadow. A flagpole casts a 36-foot shadow. How tall is the flagpole?

- **A.** 12 feet
- **B.** 24 feet
- **C.** 33 feet
- **D.** 54 feet

#### Question 6

One centimeter on a map represents 5 kilometers. What actual distance is represented by 30 centimeters?

- **A.** 6 km
- **B.** 35 km
- **C.** 36 km
- **D.** 150 km

#### Question 7

A map scale says 1/2 inch represents 10 miles. How many inches represent x miles?

- **A.** x/20
- **B.** x/10
- **C.** 5x
- **D.** 20x

#### Question 8

Terry weighs 60.8 kg. What is his weight in grams?

- **A.** 0.608 g
- **B.** 6.08 g
- **C.** 6,080 g
- **D.** 60,800 g

#### Question 9

At $1.25 per square foot, how much does it cost to tile an 8 ft by 12 ft floor?

- **A.** $120.00
- **B.** $97.25
- **C.** $96.00
- **D.** $25.00

#### Question 10

At $1.75 per square foot, how much does it cost to tile a 9 ft by 12 ft floor?

- **A.** $189.00
- **B.** $109.75
- **C.** $108.00
- **D.** $36.75

#### Question 11

John is 6 ft 4 in tall and Beth is 5 ft 5 in tall. How much taller is John?

- **A.** 9 inches
- **B.** 11 inches
- **C.** 13 inches
- **D.** 15 inches

#### Question 12

If 360° measures 6,400 miles, how many degrees are in 1,600 miles?

- **A.** 30°
- **B.** 60°
- **C.** 90°
- **D.** 120°

#### Question 13

Five one-liter containers hold 5 × 33.8 ounces. How many full 8-ounce cups can be poured?

- **A.** 20
- **B.** 21
- **C.** 22
- **D.** 23

#### Question 14

Five bushels of oats are poured into boxes holding 1 peck. How many boxes are needed? (4 pecks = 1 bushel)

- **A.** 20
- **B.** 16
- **C.** 8
- **D.** 4

#### Question 15

Bert takes 30 minutes longer to mow a 30-by-25 lawn than a 20-by-15 lawn at the same rate. How long to mow both?

- **A.** 50 minutes
- **B.** 60 minutes
- **C.** 70 minutes
- **D.** 80 minutes

#### Question 16

A meatloaf bakes for 1 hour 45 minutes and cools for 10 minutes. If it goes in at 4:20 pm, when is it ready?

- **A.** 5:50 pm
- **B.** 5:55 pm
- **C.** 6:05 pm
- **D.** 6:15 pm

#### Question 17

If 3 apples cost $1.95, what is the price of 14 apples?

- **A.** $6.50
- **B.** $7.80
- **C.** $9.10
- **D.** $9.75

#### Question 18

Ron travels 6.8 miles in 1.2 hours. At this rate, which is closest to the time for 20 miles?

- **A.** 3 hours
- **B.** 6 hours
- **C.** 3.5 hours
- **D.** 6.5 hours

#### Question 20

A pump fills 1.5 gallons per minute. How long does it take to fill a 150-gallon tub?

- **A.** 30 minutes
- **B.** 350 minutes
- **C.** 65 minutes
- **D.** 100 minutes

#### Question 21

A 5-inch-wide by 7-inch-long photograph is enlarged to 12 inches wide. What is its new length?

- **A.** 35/12
- **B.** 8
- **C.** 84/5
- **D.** 12

#### Question 22

Ashley runs a lap in 2 minutes and Robin in 3 minutes. After how many minutes will they meet again?

- **A.** 2
- **B.** 3
- **C.** 6
- **D.** 12

#### Question 23

If xy = k and y = 4 when x = 6, what is y when x = 8?

- **A.** 2
- **B.** 4
- **C.** 3
- **D.** 18

#### Question 24

If xy = k and y = 5 when x = 8, what is y when x = 4?

- **A.** 4
- **B.** 10
- **C.** 20
- **D.** 5

#### Question 25

If xy = k and y = 3 when x = 4, what is y when x = 24?

- **A.** 2
- **B.** 1/2
- **C.** 3/2
- **D.** 16

#### Question 26

If y varies directly as x, and y = 8 when x = 2, what is x when y = 2?

- **A.** 1/2
- **B.** 4
- **C.** 1/4
- **D.** 16

#### Question 27

If y varies directly as x, and y = 24 when x = 6, what is y when x = 4?

- **A.** 16
- **B.** 8
- **C.** 12
- **D.** 32

#### Question 28

If y varies directly as x, and y = 24 when x = 6, what is y when x = 10?

- **A.** 16
- **B.** 23
- **C.** 12
- **D.** 40

### Chapter 10

#### Question 1

There are 2,000 jelly beans: 20% green and 25% yellow. How many more are yellow than green?

- **A.** 100
- **B.** 50
- **C.** 5
- **D.** 10

#### Question 2

There are 2,000 jelly beans: 25% yellow and 40% red. How many more are red than yellow?

- **A.** 300
- **B.** 150
- **C.** 15
- **D.** 25

#### Question 3

There are 2,000 jelly beans: 20% green and 40% red. How many more are red than green?

- **A.** 400
- **B.** 300
- **C.** 20
- **D.** 30

#### Question 4

Approximately 200 customers order salad dressing each day. Italian is 45% and vinaigrette is 30%. What is the closest daily difference?

- **A.** 20
- **B.** 30
- **C.** 40
- **D.** 50

#### Question 5

If Wen's 30% share of a carton of baseball cards is 60 cards, what is Gina's 25% share?

- **A.** 25
- **B.** 50
- **C.** 100
- **D.** 200

#### Question 6

In a class of 25 students, 3 have not chosen a writing topic. What is the probability a randomly selected sixth-period student has not chosen one?

- **A.** 3%
- **B.** 5%
- **C.** 12%
- **D.** 14%

#### Question 7

If total utility expenses are $3,600 and water and sewer account for 20%, what are those expenses?

- **A.** 720
- **B.** 750
- **C.** 900
- **D.** 1,080

#### Question 8

A suit is 15% off x dollars, followed by a $5 coupon. Which expression is the price before tax?

- **A.** 0.15x − 5
- **B.** 0.85x − 5
- **C.** 0.85(x − 5)
- **D.** 5 − 0.85x

#### Question 9

Maria bought k pounds at $2.75 per pound, then twice as many pounds at 20% off. What total did she pay?

- **A.** 3k
- **B.** 7.15k
- **C.** 4.95k
- **D.** 8.25k

#### Question 10

A tablet is 10% off an original price P. What is the sale price?

- **A.** P − 10
- **B.** P − 10P
- **C.** 0.9P
- **D.** 0.1P − 1P

#### Question 11

What is 25% of $130?

- **A.** $5.20
- **B.** $25.00
- **C.** $32.50
- **D.** $97.50

### Chapter 11

#### Question 1

It costs 31.95d + 0.10m dollars to rent a car. What does 5 days and 600 miles cost?

- **A.** $159.75
- **B.** $165.75
- **C.** $219.75
- **D.** $759.75

#### Question 2

Using C = (5/9)(F − 32), what is 212°F in Celsius?

- **A.** 125°C
- **B.** 98.6°C
- **C.** 100°C
- **D.** 82.49°C

#### Question 3

K = C + 273. What Celsius temperature corresponds to 10 K?

- **A.** 263°C
- **B.** 283°C
- **C.** −263°C
- **D.** −283°C

#### Question 4

Using C = (5/9)(F − 32), what is 77°F in Celsius?

- **A.** 25°C
- **B.** 45°C
- **C.** 41 2/3°C
- **D.** 60 5/9°C

#### Question 5

In the equation T = 212 − h/550, T represents the boiling point of water in degrees Fahrenheit, and h represents the height above sea level in feet. If T = 209°F, what is the value of h?

- **A.** 1,750 ft
- **B.** 1,650 ft
- **C.** 1,550 ft
- **D.** 1,450 ft

#### Question 6

A ball's fall time is t = √s/4. How much longer is the time from 32 feet than from 8 feet?

- **A.** √2 sec
- **B.** √0.5 sec
- **C.** 0.707 sec
- **D.** 1.414 sec

#### Question 7

If a circle has radius r and area A, which formula gives A?

- **A.** A = rπ²
- **B.** A = πr²
- **C.** A = √(r/π)
- **D.** A = √r/π

#### Question 8

If a circle has radius r and area A, which formula gives r in terms of A?

- **A.** r = Aπ²
- **B.** r = A/π
- **C.** r = √(A/π)
- **D.** r = √A/π

#### Question 9

What number completes 10, 15, __, 25, 30?

- **A.** 16
- **B.** 18
- **C.** 20
- **D.** 23

#### Question 10

What number completes 10.30, 7.85, __, 2.95, 0.50?

- **A.** 6.30
- **B.** 5.40
- **C.** 4.85
- **D.** 3.45

### Chapter 12

#### Question 1

A box contains 3 chocolate-chip, 5 oatmeal-raisin, and 4 peanut-butter cookies. What is the probability of selecting peanut butter?

- **A.** 1/4
- **B.** 1/3
- **C.** 1/2
- **D.** 3/4

#### Question 2

A bowl has 6 green, 10 red, and 8 black grapes. What is the probability of red then green without replacement?

- **A.** 10/24 + 6/24
- **B.** 10/24 + 6/23
- **C.** 10/24 × 6/24
- **D.** 10/24 × 6/23

#### Question 3

A bag has 7 red, 3 yellow, 2 green, and 4 blue cubes. What is the probability of not selecting blue?

- **A.** 1/4
- **B.** 5/8
- **C.** 3/4
- **D.** 7/8

#### Question 4

There are 18 children per classroom in 6 classrooms. What is the total number of children?

- **A.** 108
- **B.** 200
- **C.** 208
- **D.** 300

#### Question 5

A deck has 52 cards, including 26 red cards. What is the probability of selecting a red card?

- **A.** 1/13
- **B.** 1/4
- **C.** 1/2
- **D.** 1

#### Question 6

A deck has 13 diamond cards out of 52. What is the probability of selecting a diamond?

- **A.** 1/13
- **B.** 1/4
- **C.** 1/2
- **D.** 1

#### Question 7

From integers 1 through 50, which event is most likely?

- **A.** The integer is even
- **B.** The integer is a multiple of 5
- **C.** The integer is a multiple of 10
- **D.** The integer is a multiple of 20

#### Question 8

A 12-sided die is rolled. What is the probability of rolling a number less than 8?

- **A.** 1/4
- **B.** 9/8
- **C.** 3/4
- **D.** 7/12

### Chapter 13

#### Question 1

The average of three numbers is 70. Two are 105 and 40. What is the third?

- **A.** 55
- **B.** 65
- **C.** 70
- **D.** 75

#### Question 2

The mean of three numbers is 14. Two are 10 and 6. What is the third?

- **A.** 16
- **B.** 18
- **C.** 24
- **D.** 26

#### Question 3

The average of 8, 14, and x is 10. What is x?

- **A.** 8
- **B.** 10
- **C.** 11
- **D.** 12

#### Question 4

The average of three numbers is 15. Two are 10 and 7. What is the third?

- **A.** 17
- **B.** 28
- **C.** 32
- **D.** 45

#### Question 5

The average of three numbers is 16. If one number is 18, what is the sum of the other two?

- **A.** 12
- **B.** 14
- **C.** 20
- **D.** 30

#### Question 6

Lisa swam 650, 675, 725, 800, and 900 meters over 5 days. What was her average?

- **A.** 700 meters
- **B.** 750 meters
- **C.** 3,650 meters
- **D.** 3,750 meters

#### Question 7

The average of the distances 4, 5, 3, 6, and 6 miles is what?

- **A.** 2.5
- **B.** 2
- **C.** 4
- **D.** 4.8

#### Question 8

A bakery's five cookie costs have mean $0.73: $0.73, $0.82, $0.70, x, and $0.86. Find x.

- **A.** $0.54
- **B.** $0.67
- **C.** $0.79
- **D.** $0.89

#### Question 9

What is the mean stopping distance for 10 cars: 48(1), 49(2), 50(3), 51(2), 52(2)?

- **A.** 25
- **B.** 49.8
- **C.** 50
- **D.** 50.2

#### Question 10

If the mean of 10 and x is 14, what is x?

- **A.** 16
- **B.** 17
- **C.** 18
- **D.** 19

#### Question 11

What is the average of 8, 6.5, 6.5, 7, 6, 7, and 8?

- **A.** 7
- **B.** 8
- **C.** 9
- **D.** 10

#### Question 12

Scores are 451, 500, 600, 422, 603, and 514. What is the range?

- **A.** 109
- **B.** 149
- **C.** 178
- **D.** 181

#### Question 13

James spent $42, $51, $33, $28, and $31. What was the average per trip?

- **A.** 37
- **B.** 38
- **C.** 39
- **D.** 40

#### Question 14

The attendance at three meetings was 44, 28, and 33. If no members left or joined, what is the least possible membership?

- **A.** 28
- **B.** 35
- **C.** 44
- **D.** 105

#### Question 15

A player scores 6 and 9 points on the first two moves. What score gives an average of 12 after three moves?

- **A.** 21
- **B.** 22
- **C.** 25
- **D.** 28

#### Question 16

What is the range of 390, 420, 510, 440, and 490?

- **A.** 100
- **B.** 120
- **C.** 440
- **D.** 2250

#### Question 17

What is the range of 3, 16, 3, 16, 3, 16, 3, 16?

- **A.** 19
- **B.** 9.5
- **C.** 13
- **D.** 16

#### Question 18

The ages are 20, 31, 28, 31, and 25. What is their range?

- **A.** 6
- **B.** 11
- **C.** 13
- **D.** 7

#### Question 19

The average of 3 numbers is 15. Two numbers are 7 and 10. What is the third?

- **A.** 11
- **B.** 28
- **C.** 32
- **D.** 45

#### Question 20

The average of 3 numbers is 15 and the average of 6 other numbers is 12. What is the average of all 9?

- **A.** 11
- **B.** 12
- **C.** 13
- **D.** 15

#### Question 21

The ages are 20, 31, 28, 31, and 25. How many are older than the average age?

- **A.** 2
- **B.** 3
- **C.** 4
- **D.** 5

#### Question 22

If 2 is removed from 2, 3, 4, 6, 6, 7, which measure remains the same?

- **A.** Mean
- **B.** Median
- **C.** Mode
- **D.** Range

### Chapter 14

#### Question 1

Which function could match a V-shaped graph with vertex (0, 1)?

- **A.** f(x) = |x + 1|
- **B.** f(x) = |x − 1|
- **C.** f(x) = |x| + 1
- **D.** f(x) = |x| − 1

#### Question 2

Which equation has a parabola with vertex (−2, −9)?

- **A.** y = (x − 2)² − 9
- **B.** (x + 5)(x − 1) = 0
- **C.** y = (x + 2)² − 9
- **D.** y = x² + 4x + 5

#### Question 3

Which graph could be y = −√x?

- **A.** A graph beginning at the origin and rising right
- **B.** A graph beginning at the origin and rising left
- **C.** A graph beginning at the origin and falling right
- **D.** A graph beginning at the origin and falling left

#### Question 4

How many points does y = x² + 2 intersect the x-axis at?

- **A.** None
- **B.** One
- **C.** Two
- **D.** Three

#### Question 5

Which equation matches a square-root graph beginning at (1, 0) and decreasing to the right?

- **A.** f(x) = −√(x − 1)
- **B.** f(x) = −√(x + 1)
- **C.** f(x) = (x + 1)²
- **D.** f(x) = −(x − 1)²

#### Question 6

Which equation matches a square-root graph beginning at the origin and rising to the right?

- **A.** f(x) = √x
- **B.** f(x) = −√x
- **C.** f(x) = x²
- **D.** f(x) = −x²

#### Question 7

What is the intersection of y = x + 3 and y = 3x − 3?

- **A.** (2, 5)
- **B.** (3, 6)
- **C.** (4, 9)
- **D.** (5, 12)

#### Question 8

How many solutions can x + 4y = 3 and 2x + 8y = 4 have?

- **A.** None
- **B.** One
- **C.** Two
- **D.** Infinite

#### Question 9

Jan and Kim bought 9 notebooks and an $18 schoolbag for $45. How much did each notebook cost?

- **A.** $3.00
- **B.** $3.50
- **C.** $4.50
- **D.** $5.00

#### Question 10

Margo bought 7 pens: some at $3 and the rest at $4, paying $23. How many $3 pens?

- **A.** Two
- **B.** Three
- **C.** Four
- **D.** Five

#### Question 11

Ten children and adults bought tickets: children cost $5, adults $8, total $62. How many children?

- **A.** 4
- **B.** 5
- **C.** 6
- **D.** 7

### Chapter 15

#### Question 1

Five friends are 20, 31, 28, 31, and 25 years old. How many are older than the average?

- **A.** 2
- **B.** 3
- **C.** 4
- **D.** 1

#### Question 2

Five friends are 20, 31, 28, 31, and 25 years old. What is the range?

- **A.** 6
- **B.** 11
- **C.** 13
- **D.** 7

#### Question 3

If 2 is removed from 2, 3, 4, 6, 6, 7, which measure remains the same?

- **A.** Mean
- **B.** Median
- **C.** Mode
- **D.** Range

#### Question 4

If 4b − 1 = b, then 24b = ?

- **A.** 1/3
- **B.** 8
- **C.** 4
- **D.** −3

#### Question 5

What is (5a/b)²?

- **A.** 5a²/b²
- **B.** 25a/b²
- **C.** 25a²/b²
- **D.** 10a²/b

#### Question 6

What is (7/x)²?

- **A.** 14/x²
- **B.** 49/x²
- **C.** 7²/x
- **D.** x²/49

#### Question 7

If a + √x = b, then x = ?

- **A.** b − a
- **B.** (b − a)²
- **C.** b² − a
- **D.** a² − b²

#### Question 8

You receive 10% off the original price P. Which expression is the sale price?

- **A.** P − 10
- **B.** P − 10P
- **C.** 0.9P
- **D.** 0.1P − 1P

#### Question 9

What is the value of x if x − 10 = 5x − 10?

- **A.** −5
- **B.** −3 2/3
- **C.** 0
- **D.** 5

#### Question 10

If 6(t − 2) − 4 = 2t, then t = ?

- **A.** −2
- **B.** 0
- **C.** 2
- **D.** 4

#### Question 11

Using C = (5/9)(F − 32), what is 77°F in Celsius?

- **A.** 25°C
- **B.** 41 2/3°C
- **C.** 45°C
- **D.** 60 5/9°C

#### Question 12

A taco and milk cost $2.10; two tacos and three milks cost $5.15. Which system represents this?

- **A.** t + m = 5.15; 2t + 3m = 2.10
- **B.** t − m = 5.15; 2t − 3m = 2.10
- **C.** t + m = 2.10; 2t + 3m = 5.15
- **D.** t − m = 2.10; 2t − 3m = 5.15

#### Question 13

A shop sells sundaes for $2 and banana splits for $3. It sold 8 more sundaes than splits and made $156. Which system models this?

- **A.** s = b + 8; 2s + 3b = 156
- **B.** s = b − 8; 3s + 2b = 156
- **C.** s + b = 8; 2s + 3b = 156
- **D.** s = 8b; 2s + 3b = 156

#### Question 14

Chase bought 5 pieces of fudge and 3 pieces of gum for $5.70; Sara bought 2 fudge and 10 gum for $3.60. Which system models this?

- **A.** 5f + 3g = 5.70; 2f + 10g = 3.60
- **B.** 5f + 3g = 3.60; 2f + 10g = 5.70
- **C.** 5f − 3g = 5.70; 2f − 10g = 3.60
- **D.** 3f + 5g = 5.70; 10f + 2g = 3.60

#### Question 15

A textbook and novel cost $54 total. The textbook m is $8 more than 3 times the novel n. Which system models this?

- **A.** m + n = 54; m = 3n + 8
- **B.** m − n = 54; m = 3n − 8
- **C.** m + n = 8; m = 54 + 3n
- **D.** m + n = 3; m = 54n + 8

#### Question 16

Marcos has 15 coins, with 3 more quarters than nickels. If x is nickels and y is quarters, which solution is correct?

- **A.** (x, y) = (6, 9)
- **B.** (x, y) = (9, 6)
- **C.** (x, y) = (5, 10)
- **D.** (x, y) = (10, 5)