# Solving Quadratic and Square-Root Equations

> TSI Math Test Study Guide · Hightower High School P-TECH (2023)
>
> Source: [complete Markdown guide](../TSI-Math-Test-Study-Guide.md) · [original PDF](../1062198634-Hightower-TSI-Test-Study-Guide-v2-MATH.pdf)


#### 1. Which of the following is a solution to $x^2 - 5x - 24 = 0$?

**A.** 8

**B.** 3

**C.** 1

**D.** 0


#### 2. Which of the following is a solution to $x^2 + 8x + 7 = 0?$

**A.** 7

**B.** $-1$

**C.** 1

**D.** 0


#### 3. Which of the following is a solution to $x^2 - 12x + 11 = 0?$

**A.** $-8$

**B.** $-11$

**C.** 1

**D.** 0


#### 4. Which of the following is a solution to $x^2 - 3x - 10 = 0?$

**A.** $-8$

**B.** $-6$

**C.** $-5$

**D.** $-2$


#### 5. If $\sqrt{x}$ + 3 = 11 what is the value of x?

**A.** 19

**B.** 8

**C.** 64

**D.** 14


#### 6. If $\sqrt{x} - 3 = 5$, what is the value of x?

**A.** 8

**B.** 25

**C.** 28

**D.** 64


#### 7. If $7w(w - 2) = 0$, what could be the value of w?

**A.** 5

**B.** $-10$

**C.** $-3$

**D.** 2


#### 8. Which of the following equations has solution of x = 5?

**A.** $x^2 = 10$

**B.** $\sqrt{3x + 1} = 4$

**C.** $3x^2 = 225$

**D.** $\sqrt{4x} = 10$


#### 9. If $x = -3$, which of the following is positive?

**A.** $x^3$

**B.** $x^2$

**C.** \$2x$

**D.** $\frac{1}{x}$


#### 10. If $g(x) = \frac{x}{x + 1}$, then which statement is true?

**A.** g(10) < g(20)

**B.** g(20) < g(10)

**C.** g(0) = 1

**D.** g(1) = 0


#### 11. What is a solution to $x^2 + 2x - 15 = 0?$

> Added practice choices; these options were not printed in the original PDF.

**A.** $-5$


**B.** $-4$


**C.** 4


**D.** 5


#### 12. What is a solution to $x^2 - 5x + 6 = 0?$

> Added practice choices; these options were not printed in the original PDF.

**A.** $-3$


**B.** $-2$


**C.** 2


**D.** $-1$


#### 13. What is a solution to $-2x^2 + 7x - 3 = 0?$

> Added practice choices; these options were not printed in the original PDF.

**A.** $-3$


**B.** $\frac{1}{2}$


**C.** 1


**D.** 4


#### 14. If $a + \sqrt{x} = b$, then x = ?

> Added practice choices; these options were not printed in the original PDF.

**A.** $b - a$


**B.** $b^2 - a$


**C.** $a^2 - b^2$


**D.** $(b - a)^2$


#### 15. What is a solution to $6x^2 - 11x - 10 = 0?$

> Added practice choices; these options were not printed in the original PDF.

**A.** $\frac{-2}{3}$


**B.** $\frac{-1}{2}$


**C.** $\frac{5}{2}$


**D.** 2


#### 16. If $\sqrt{x} - 3 = 15$, what is the value of x?

> Added practice choices; these options were not printed in the original PDF.

**A.** 18


**B.** 225


**C.** 228


**D.** 15