Question 1

Which of the following is the correct formula for the distance between two points $$A(x_1$, y_1$)$$ and $$B(x_2$, y_2$) in $$the coordinate plane?

Accepted Answer

$$\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

Question 2

A circle has the equation $$(x - 3)^2 + (y + 2)^2 = 25. $$What are the center and radius of the circle?

Accepted Answer

Center: $$(3, -2)$$, Radius: $$5$$

Question 3

Which of the following is the correct definition of a function?

Accepted Answer

A relation where each input has exactly one output.

Question 4

Given the function $$f(x) = 2x^2$ - 3x + 1$$, what is $$f(-2)$$?

Accepted Answer

$$15$$

Question 5

Which of the following is the correct formula for the sum of the first $$n$$ terms of a geometric sequence with first term $$a$$ and common ratio $$r 
eq 1$$?

Accepted Answer

$$S_n = a \frac{1 - r^n}{1 - r}$$

Question 6

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

Accepted Answer

$$14$$

Question 7

Which of the following is the correct property of logarithms for $$\log_b(MN)$$?

Accepted Answer

$$\log_b(MN) = \log_b(M) + \log_b(N)$$

Question 8

Solve for $$x$$: $$2^{x+1} = 32$.

Accepted Answer

$$4$$

Question 9

A radioactive substance decays according to the formula $$A(t) = A_0$ e$$^{-0.03t}$$, where t$ is in years. If the initial amount is 100$ grams, how much remains after 10$ years? (Round to the nearest gram.)

Accepted Answer

$$74$$ grams

Question 10

Which of the following is the correct expanded form of $$(x + 2)^3$$ using the Binomial Theorem?

Accepted Answer

$$x^3 + 6x^2 + 12x + 8$$

Question 11

Which of the following is the correct solution to the system of equations:

$$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

$$x = 2,\ y = 1$$

Question 12

Which of the following rational expressions is equivalent to $$\frac{x^2$ - 9}{x^2$ - 6x + 9}$$?

Accepted Answer

$$\frac{(x - 3)(x + 3)}{(x - 3)^2$}$$

Question 13

If $$f(x) = x^3$ is a one-to-one function, what is its inverse f$$^{-1}$$(x)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt[3]{x}$$

Question 14

Which of the following is the correct result of dividing $$2x^3$$ - $$3x^2 + 4x - 5$ by x - 2$ using synthetic division?

Accepted Answer

$$2x^2 + x + 6$$ + \frac{7}{x-2}$$

Question 15

Which of the following is the correct partial fraction decomposition of $$\frac{5x + 3}{(x + 1)(x - 2)}$$?

Accepted Answer

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

Question 16

Which of the following is the correct solution to the inequality $$x^2 - 5x + 6$$ \u003c 0$$?

Accepted Answer

$$2 \u003c x \u003c 3$$

Question 17

If $$a_n = 3 \cdot 2$$^{n-1}$$, what is the 5th term of the sequence?

Accepted Answer

$$48$$

Question 18

Which of the following is the correct solution to $$\log_2$(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 19

A bank offers an annual interest rate of $$6\%$$ compounded monthly. If you deposit $$\1000$, what will be the balance after 2$ years? (Round to the nearest dollar.)

Accepted Answer

$$1127$$

Question 20

Which of the following is the correct property of exponents for $$a^{m}$$ \cdot $$a^{n}$$?

Accepted Answer

$$a^{m+n}$$

Precalculus Course Structure and Assignment Guide

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