Question 1

Which of the following is the solution to the linear equation $$2x - 5 = 9$$?

Accepted Answer

$$x = 7$$

Question 2

A quadratic equation is given by $$x^2 - 6x + 8 = 0$. What are its solutions?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 3

Which of the following is a rational equation?

Accepted Answer

$$\frac{2x+1}{x-3} = 5$$

Question 4

Solve the system of equations: $$\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

$$x = 2, y = 3$$

Question 5

Which of the following is the correct quadratic formula for solving $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 6

A mixture contains 30 liters of a solution that is 40% acid. How many liters of pure acid must be added to make the solution 50% acid?

Accepted Answer

$$10$$

Question 7

Which of the following equations represents a motion problem where an object travels at a constant speed $$v$$ for time $$t$$?

Accepted Answer

$$d = vt$$

Question 8

Solve for $$x$$: $$\sqrt{x+5} = 4$$

Accepted Answer

$$x = 9$$

Question 9

Which of the following is a polynomial equation of degree 3?

Accepted Answer

$$x^3$$ - $$2x^2 + x - 5 = 0$

Question 10

If $$x^2 + 4x + 4 = 0$, what is the solution set?

Accepted Answer

$$x = -2 ($$double root)

Question 11

Which of the following best describes a system of equations with no solution?

Accepted Answer

The lines are parallel and have different y-intercepts.

Question 12

Given the equation $$\frac{3}{x} + 2 = 5$$, what is the value of $$x$$?

Accepted Answer

Question 13

Which of the following is the correct formula for simple interest?

Accepted Answer

$$I = Prt$$

Question 14

If $$x^2 - 5x + 6 = 0$, what are the solutions?

Accepted Answer

$$x = 2$$ and $$x = 3$$

Question 15

A system of equations is given by $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}. $$What is the value of $$x$$?

Accepted Answer

$$x = 3$$

Question 16

Which of the following is a radical equation?

Accepted Answer

$$\sqrt{x+2} = 5$$

Question 17

If $$x^3 - 8 = 0$, what is the real solution?

Accepted Answer

$$x = 2$$

Question 18

Which of the following best describes the discriminant of a quadratic equation $$ax^2 + bx + c = 0$?

Accepted Answer

$$b^2 - 4ac$

Question 19

A chemist needs to mix a 20% saline solution with a 50% saline solution to obtain 10 liters of a 30% solution. How many liters of the 20% solution should be used?

Accepted Answer

$$6.67$$

Question 20

Which of the following is the correct solution to $$2(x-3) = x + 4$$?

Accepted Answer

$$x = 10$$

Test 1 Review: Linear, Quadratic, and Miscellaneous Equations in Precalculus

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