Question 1

Which of the following is the correct way to write $$\sqrt{-7} as $$the product of a real number and $$i$$?

Accepted Answer

$$i\sqrt{7}$$

Question 2

Simplify the expression $$\sqrt{-13} \cdot \sqrt{-13}.$$

Accepted Answer

$$-13$$

Question 3

Find the sum $$(6 - 9i) + (3 + 6i)$$ and write the answer in standard form.

Accepted Answer

$$9 - 3i$$

Question 4

Simplify $$i^{66}.$$

Accepted Answer

$$-1$$

Question 5

Multiply $$(4 - 3i)(4 + 5i)$$ and write the answer in standard form.

Accepted Answer

$$31 + 8i$$

Question 6

Solve the quadratic equation $$x^2 + 4x - 45 = 0$.

Accepted Answer

$$x = -9,\ 5$$

Question 7

A ladder is resting against a wall. The top of the ladder touches the wall at a height of 6 ft. The length of the ladder is 2 ft more than its distance from the wall. What is the length of the ladder?

Accepted Answer

$$10\ 	ext{ft}$$

Question 8

Solve the quadratic inequality $$x^2 - 3x - 10$$ \u003c 0$$ and write the solution set in interval notation.

Accepted Answer

$$(-2, 5)$$

Question 9

Find the center and radius of the circle $$x^2$$ + $$y^2 + 10x - 8y - 8 = 0$.

Accepted Answer

Center $$(-5, 4)$$, radius $$7$$

Question 10

Evaluate $$f(3)$$ for $$f(x) = x^2$ - 2x - 5.$$

Accepted Answer

$$-2$$

Question 11

Find $$(f - g)(x)$$ for $$f(x) = 7x - 5$$ and $$g(x) = 5x - 8.$$

Accepted Answer

$$2x + 3$$

Question 12

For $$f(x) = 4x^2$ + 5x + 7$$ and $$g(x) = 5x - 6$$, find $$(g \circ f)(x).$$

Accepted Answer

$$20x^2 + 25x + 29$

Question 13

Use the factor theorem to decide whether $$x + 2 is a $$factor of $$5x^3$$ + $$8x^2 - 3x + 2$.

Accepted Answer

Yes

Question 14

Find all rational zeros of $$f(x) = x^3$ - 5x^2$ - 2x + 24.$$

Accepted Answer

$$x = 3,\ 4,\ -2$$

Question 15

A ball is thrown downward from a window in a tall building. Its position at time $$t in $$seconds is $$s = 16t^2$ + 32t$$, where $$s is in $$feet. How long (to the nearest tenth) will it take the ball to fall 140 feet?

Accepted Answer

$$2.1$$ seconds

Question 16

Which of the following best describes the graph of $$y = |x| - 9$$?

Accepted Answer

A V-shaped graph opening upwards, shifted down 9 units

Question 17

Compute and simplify the difference quotient $$\dfrac{f(x+h) - f(x)}{h}$$ for $$f(x) = 4x - 9.$$

Accepted Answer

$$4$$

Question 18

Given $$y = 3x^2$ + 12x + 17$$, what is the vertex of the parabola?

Accepted Answer

$$(-2, 5)$$

Question 19

Solve the rational inequality $$\dfrac{2x + 7}{x - 2} \leq 0$$ and write the solution set in interval notation.

Accepted Answer

$$\left[ -\dfrac{7}{2},\ 2 \right)$$

Question 20

Which of the following statements is true about the relation defined by the set of points $$\{(1,2), (2,3), (3,4), (4,5)\}$$?

Accepted Answer

It defines a function because each input has exactly one output.

Precalculus Algebra Midterm & Final Exam Study Guide – Step-by-Step Guidance

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