Question 1

Which of the following is the result of adding the complex numbers $$ (3 - 4i) $$ and $$ (2 + 7i) $$?

Accepted Answer

$$ 5 + 3i $$

Question 2

Simplify the product $$ (2 + 5i)(3 - 2i) .$$

Accepted Answer

$$ 16 + 11i $$

Question 3

Divide the complex numbers $$ \frac{6 + 8i}{2 - i} $$ and write your answer in the form $$ a + bi .$$

Accepted Answer

$$ 2 + 4i $$

Question 4

What is the value of $$ i$$^{23}$$ $$?

Accepted Answer

$$ i $$

Question 5

Convert $$ \sqrt{-20} $$ into a complex number.

Accepted Answer

$$ 2\sqrt{5}i $$

Question 6

Let $$ f(x) = 2x + 3 $$ and $$ g(x) = x^2$ . $$What is $$ (f \circ g)(2) $$?

Accepted Answer

$$ 11 $$

Question 7

Given $$ f(x) = x^2$ - 4x + 7 $$, use completing the square to rewrite $$ f(x)  in $$vertex form.

Accepted Answer

$$ (x - 2)^2$ + 3 $$

Question 8

Which of the following is a solution to the equation $$ x^2$ + 4x + 13 = 0 $$?

Accepted Answer

$$ -2 + 3i $$

Question 9

Solve $$ 2x^2$ - 8x + 6 = 0 $$ using the quadratic formula.

Accepted Answer

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

Question 10

A ball is thrown upward from the ground with an initial velocity of $$ 32  ft/s. $$Its height after $$ t $$ seconds is given by $$ h(t) = -16t^2$ + 32t . $$After how many seconds does the ball hit the ground again?

Accepted Answer

$$ 2 $$

Question 11

If $$ f(x) = 3x - 5 $$, what is the inverse function $$ f$$^{-1}$$(x) $$?

Accepted Answer

$$ f$$^{-1}$$(x) = \frac{x+5}{3} $$

Question 12

Given $$ f(x) = 2x + 1 $$ and $$ g(x) = \frac{x-1}{2} $$, are $$ f $$ and $$ g $$ inverse functions?

Accepted Answer

Yes, because $$ f(g(x)) = x $$ and $$ g(f(x)) = x $$

Question 13

Evaluate the composite function $$ (g \circ f)(3) $$ where $$ f(x) = x^2$ $$ and $$ g(x) = x + 4 .$$

Accepted Answer

$$ 13 $$

Question 14

Which of the following best describes the translation of the exponential function $$ f(x) = 2^x  to$$ $$ g(x) = 2$$^{x-3}$$ + 5 $$?

Accepted Answer

Right 3 units, up 5 units

Question 15

A population of bacteria triples every 4 hours. If the initial population is 200, which function models the population $$ P $$ after $$ t $$ hours?

Accepted Answer

$$ P(t) = 200 \cdot 3$$^{t/4}$$ $$

Question 16

Which of the following complex numbers is a solution to $$ z^2$ = -9 $$?

Accepted Answer

$$ 3i $$

Question 17

If $$ f(x) = x^2$ + 2x + 5 $$, is $$ 1 + 2i  a $$solution to $$ f(x) = 0 $$?

Accepted Answer

Yes, because $$ (1 + 2i)^2$ + 2(1 + 2i) + 5 = 0 $$

Question 18

Solve the quadratic equation $$ x^2$ - 6x + 10 = 0 $$ using the quadratic formula.

Accepted Answer

$$ x = 3 \pm i $$

Question 19

If $$ f(x) = \sqrt{x+1} $$ and $$ g(x) = x^2$ - 1 $$, what is $$ (f \circ g)(2) $$?

Accepted Answer

$$ 2 $$

Question 20

A certain radioactive substance decays according to the function $$ N(t) = 1000 \cdot (0.5$$)^{t/3}$$ $$, where $$ t  is in $$years. How much of the substance remains after 9 years?

Accepted Answer

$$ 125 $$

Study Guide: Complex Numbers, Quadratic Equations, and Exponential & Logarithmic Functions

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