Q: Which of the following is a correct application of the quadratic formula to solve $$x^2 + 4x + 3 = 0$?

$$x = \\frac{-4 \\pm \\sqrt{16 - 12}}{2}$$

Question 1

A chemist mixes two solutions, one containing 40% acid and the other containing 25% acid, to obtain 100 mL of a solution that is 30% acid. How many milliliters of the 40% acid solution should be used? (Let $$x be $$the amount of 40% solution.)

Accepted Answer

$$x = 16.67$$

Question 2

Which of the following is the correct solution to the quadratic equation $$2x^2 - 8x + 6 = 0$?

Accepted Answer

$$x = 2 \pm \sqrt{2}$$

Question 3

A car travels at a constant speed. Its position after $$t$$ hours is given by $$s(t) = 60t + 120. $$How long will it take for the car to reach a position of 300 miles?

Accepted Answer

$$t = 3$$

Question 4

Which of the following is a rational equation?

Accepted Answer

$$\frac{2x}{x-1} = 4$$

Question 5

Solve the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

$$x = 2, y = 1$$

Question 6

Which of the following is a radical equation?

Accepted Answer

$$\sqrt{x+3} = 7$$

Question 7

Given the polynomial $$f(x) = x^3$ - 4x^2$ + 5x - 2$$, which of the following is NOT a possible rational root according to the Rational Root Theorem?

Accepted Answer

$$x = 4$$

Question 8

A mixture contains 30% salt. If 200 grams of pure water is added to 100 grams of this mixture, what is the new concentration of salt?

Accepted Answer

$$20\%$$

Question 9

Which substitution would simplify the equation $$x^2 + 4x + 4 = 9$?

Accepted Answer

Let $$u = x + 2$$

Question 10

Solve for $$x$$: $$\sqrt{x+5} = 3$$

Accepted Answer

$$x = 4$$

Question 11

Which of the following is the solution to the equation $$x^2 - 6x + 13 = 0$?

Accepted Answer

$$x = 3 \pm 2i$$

Question 12

A ball is thrown upward with an initial velocity of 20 m/s from a height of 2 m. Its height after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 20t + 2. $$How long does it take for the ball to hit the ground?

Accepted Answer

$$t \approx 4.2$$

Question 13

Which of the following is a solution to the system $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 3, y = 2$$

Question 14

Which of the following is NOT a linear equation?

Accepted Answer

$$x^2 + 2x = 5$

Question 15

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

Accepted Answer

$$x = 2, x = 3$$

Question 16

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

Accepted Answer

$$x^3 - 2x + 1 = 0$

Question 17

A train travels 120 miles in 2 hours. What is its average speed?

Accepted Answer

$$60$$ miles/hour

Question 18

Which of the following is a correct application of the quadratic formula to solve $$x^2 + 4x + 3 = 0$?

Accepted Answer

$$x = \frac{-4 \pm \sqrt{16 - 12}}{2}$$

Question 19

Which of the following is a solution to the equation $$x^2 = 9$?

Accepted Answer

$$x = 3, x = -3$$

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

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