Question 1

Which property of logarithms allows you to rewrite $$\log_b(xy) as a $$sum of two logarithms?

Accepted Answer

Product Rule: $$\log_b(xy) = \log_b(x) + \log_b(y)$$

Question 2

Solve the exponential equation $$2^{x+3} = 16$ for x$.

Accepted Answer

$$x = 1$$

Question 3

A population of bacteria doubles every 3 hours. If the initial population is 500, what will the population be after 9 hours?

Accepted Answer

$$4000$$

Question 4

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

Accepted Answer

A function defined by different expressions for different intervals of its domain.

Question 5

Given the function $$f(x) = \begin{cases} x^2$ & x \u003c 0 \ 2x + 1 & x \geq 0 \end{cases}$$, what is $$f(-2)$$?

Accepted Answer

$$4$$

Question 6

Which equation represents the ellipse centered at $$(0,0)$$ with a major axis of length 10 along the x-axis and a minor axis of length 6 along the y-axis?

Accepted Answer

$$\frac{x^2$}{25} + \frac{y^2$}{9} = 1$$

Question 7

If the equation of a circle is $$x^2$$ + $$y^2 = 49$, what is the radius?

Accepted Answer

$$7$$

Question 8

Which of the following is the correct equation for a hyperbola centered at $$(0,0)$$ with vertices at $$(\pm 4, 0)$$ and asymptotes $$y = \pm \frac{1}{2}x$$?

Accepted Answer

$$\frac{x^2$}{16} - \frac{y^2$}{4} = 1$$

Question 9

What is the determinant of the matrix $$\begin{pmatrix} 2 & 3 \ 4 & 5 \end{pmatrix}$$?

Accepted Answer

$$-2$$

Question 10

Which of the following sequences is arithmetic?

Accepted Answer

$$5, 8, 11, 14, 17$$

Question 11

Find the sum of the first 10 terms of the arithmetic sequence $$a_n = 3 + 2(n-1).$$

Accepted Answer

$$95$$

Question 12

Which formula gives the $$nth $$term of a geometric sequence with first term $$a_1$$ and common ratio $$r$$?

Accepted Answer

$$a_n = a_1$ r$$^{n-1}$$

Question 13

If $$a_1 = 2$ and r = 3$, what is the 5th term of the geometric sequence?

Accepted Answer

$$162$$

Question 14

Which of the following is the correct statement of the Binomial Theorem?

Accepted Answer

$$(x+y)^n = \sum_{k=0}^{n} \binom{n}{k} x$$^{n-k}$$ y^k$$

Question 15

Which step is necessary in a proof by mathematical induction?

Accepted Answer

Verify the base case and prove the inductive step.

Question 16

If $$f(x) = e$$^{2x}$$, what is f$$(\ln 3)$$?

Accepted Answer

$$9$$

Question 17

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

Accepted Answer

$$x = 32$$

Question 18

A parabola has the equation $$y = 2x^2$ - 4x + 1. $$What is the vertex of the parabola?

Accepted Answer

$$(1, -1)$$

Question 19

Which of the following is the sum of the infinite geometric series $$\sum_{n=0}^{\infty} 5 \left(\frac{1}{2}\right)^n$$?

Accepted Answer

$$10$$

Precalculus Study Guide: Exponential, Logarithmic, Piecewise, Conic Sections, Matrices, Sequences, Induction, and Binomial Theorem

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