Question 1

Which of the following is the explicit formula for the geometric sequence where the first term is $$2$$ and the common ratio is $$3$$?

Accepted Answer

$$a_n = 2 \cdot 3$$^{n-1}$$

Question 2

A population of bacteria triples every hour. If the initial population is $$100$$, what is the population after $$5$$ hours?

Accepted Answer

$$100 \cdot 3^5$

Question 3

Which of the following is a polynomial of degree $$4$$?

Accepted Answer

$$x^4$$ + $$2x^2 - 7$

Question 4

Given $$f(x) = x^2$ - 4x + 3$$, what are the zeros of $$f(x)$$?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 5

Which of the following describes the end behavior of $$f(x) = -2x^5$ + 3x^2$ as x$$ 	o \infty$$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 6

Solve the rational equation: $$\frac{2}{x} = 4$$

Accepted Answer

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

Question 7

Which of the following is equivalent to $$x^{-3/2}$$?

Accepted Answer

$$\frac{1}{x$$^{3/2}$$}$$

Question 8

What is the sum of $$2 + 4 + 6 + \ldots + 20$$?

Accepted Answer

$$110$$

Question 9

If $$i is $$the imaginary unit, what is the value of $$i^3$$?

Accepted Answer

$$-i$$

Question 10

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

Accepted Answer

$$x = 2i$$ and $$x = -2i$$

Question 11

A radioactive substance decays according to $$A(t) = 500e$$^{-0.2t}$$. What is the amount left after 10$ hours?

Accepted Answer

$$500e^{-2}$$

Question 12

Which transformation results in the graph of $$f(x) = x^2$ being reflected over the x$-axis?

Accepted Answer

$$f(x) = -x^2$

Question 13

Which of the following is the domain of $$f(x) = \log(x-3)$$?

Accepted Answer

$$x \u003e 3$$

Question 14

If $$\sin(	heta) = \frac{1}{2}$$ and $$0 \leq 	heta \leq \pi$$, what is $$	heta$$?

Accepted Answer

$$\frac{\pi}{6} or$$ $$\frac{5\pi}{6}$$

Question 15

A sample of test scores has a mean of $$80$$ and a standard deviation of $$5. $$What is the $$z-$$score for a test score of $$90$$?

Accepted Answer

$$2$$

Question 16

Which of the following is the correct formula for the sum of the first $$n$$ terms of an arithmetic sequence with first term $$a_1$$ and common difference $$d$$?

Accepted Answer

$$S_n = \frac{n}{2}(2a_1 + (n-1)d)$$

Question 17

Which of the following is a property of even functions?

Accepted Answer

$$f(-x) = f(x)$$

Question 18

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is (f+g)(3$$)$$?

Accepted Answer

$$16$$

Question 19

Which of the following is the correct solution to $$2^{x} = 16$?

Accepted Answer

$$x = 4$$

Question 20

A circle has equation $$x^2$$ + $$y^2 - 6x + 8y + 9 = 0$. What is its center?

Accepted Answer

$$(3, -4)$$

Intermediate Algebra: Key Concepts and Skill Alignment Overview

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