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No calculator

$f(x) = 2x^2 + 3$ . Find $f(-3)$ .
No calculator
Describe the end behavior of $f(x) = 7x^{ 3 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 3x^{ 7 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 3x^{ 3 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 8x^{ 3 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 4x^{ 5 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 7x^{ 5 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 5x^{ 7 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 5x^{ 3 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 7x^{ 7 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 2x^{ 3 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 5x^{ 5 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 2x^{ 5 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 9x^{ 3 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 4x^{ 3 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 3x^{ 5 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 6x^{ 7 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 8x^{ 7 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 8x^{ 5 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 9x^{ 7 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 4x^{ 7 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 6x^{ 3 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 6x^{ 5 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 2x^{ 7 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
Describe the end behavior of $f(x) = 9x^{ 5 }$ .
1. As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
2. As $x \to \pm\infty$ , $f(x) \to \infty$
3. As $x \to \infty$ , $f(x) \to -\infty$ ; as $x \to -\infty$ , $f(x) \to \infty$
No calculator

Evaluate $\log_{ 4 } 16$ .
No calculator

Convert $225^\circ$ to radians. Give the exact value.
No calculator

$\sin\theta = \frac{1}{5}$ and $\theta$ is in quadrant II. Find the exact value of $\cos\theta$ .
No calculator

$x(t) = t + 1$ and $y(t) = t^2$ . Tap the point where the curve is at $t = 1$ .
No calculator

$a_1 = 3$ and $a_{n+1} = 2a_n - 7$ . Find $a_3$ .
No calculator

What is the domain of $f(x) = \sqrt{x - 9}$ ? Give it as an interval.
No calculator

$f(x) = 5x^2 - 10x + 20$ . What is the $x$ -coordinate of the vertex?
No calculator

The graph of $y = 3\cdot 4^x + 7$ has a horizontal asymptote $y = c$ . What is $c$ ?
No calculator

Find the exact value of $\cos\left(\frac{\pi}{6}\right)$ .
No calculator

Solve $\sin x = \frac{1}{2}$ for $0 \le x < 2\pi$ .
No calculator

$x = t + 6$ and $y = t^2$ . Write $y$ in terms of $x$ .
No calculator

An arithmetic sequence has $a_1 = 14$ and common difference 2. Find $a_{ 43 }$ .
No calculator

$f(x) = \begin{cases} x + 3 & \text{if } x < 5 \\ 3x & \text{if } x \ge 5 \end{cases}$ . Find $f(5)$ .
No calculator

Find all the zeros of $p(x) = (x - 4)(x + 2)^2$ .
No calculator

A sample of 64 mg of a radioactive substance has a half-life of 2 years. How many mg are left after 6 years?
No calculator

Find the exact value of $\cos\left(\frac{5 \pi}{4}\right)$ .
No calculator

Solve $\sin x\left(\sin x - \frac{\sqrt{3}}{2}\right) = 0$ for $0 \le x < 2\pi$ .
No calculator

The ellipse $x = 3\cos t$ , $y = 4\sin t$ reaches $x$ -values from $-c$ to $c$ . What is $c$ ?
No calculator

A geometric sequence has $a_1 = 3$ and ratio 3. Find $a_{ 4 }$ .
No calculator

Find the average rate of change of $f(x) = 3x^2$ from $x = 0$ to $x = 6$ .
No calculator

What is the remainder when $p(x) = x^3 - 5x + 7$ is divided by $x - 3$ ?
No calculator
Which expression is equal to $\log_{ 8 }(2 \cdot 7)$ ?
1. $\log_{ 8 } 2 + \log_{ 8 } 7$
2. $\log_{ 8 } 2 \cdot \log_{ 8 } 7$
3. $\log_{ 8 }(2 + 7)$
4. $7 \log_{ 8 } 2$
Which expression is equal to $\log_{ 7 }(4 \cdot 9)$ ?
1. $\log_{ 7 } 4 + \log_{ 7 } 9$
2. $\log_{ 7 } 4 \cdot \log_{ 7 } 9$
3. $\log_{ 7 }(4 + 9)$
4. $9 \log_{ 7 } 4$
Which expression is equal to $\log_{ 7 }(5 \cdot 3)$ ?
1. $\log_{ 7 } 5 + \log_{ 7 } 3$
2. $\log_{ 7 } 5 \cdot \log_{ 7 } 3$
3. $\log_{ 7 }(5 + 3)$
4. $3 \log_{ 7 } 5$
Which expression is equal to $\log_{ 7 }(5 \cdot 8)$ ?
1. $\log_{ 7 } 5 + \log_{ 7 } 8$
2. $\log_{ 7 } 5 \cdot \log_{ 7 } 8$
3. $\log_{ 7 }(5 + 8)$
4. $8 \log_{ 7 } 5$
Which expression is equal to $\log_{ 7 }(8 \cdot 9)$ ?
1. $\log_{ 7 } 8 + \log_{ 7 } 9$
2. $\log_{ 7 } 8 \cdot \log_{ 7 } 9$
3. $\log_{ 7 }(8 + 9)$
4. $9 \log_{ 7 } 8$
Which expression is equal to $\log_{ 8 }(3 \cdot 6)$ ?
1. $\log_{ 8 } 3 + \log_{ 8 } 6$
2. $\log_{ 8 } 3 \cdot \log_{ 8 } 6$
3. $\log_{ 8 }(3 + 6)$
4. $6 \log_{ 8 } 3$
Which expression is equal to $\log_{ 5 }(3 \cdot 4)$ ?
1. $\log_{ 5 } 3 + \log_{ 5 } 4$
2. $\log_{ 5 } 3 \cdot \log_{ 5 } 4$
3. $\log_{ 5 }(3 + 4)$
4. $4 \log_{ 5 } 3$
Which expression is equal to $\log_{ 5 }(2 \cdot 9)$ ?
1. $\log_{ 5 } 2 + \log_{ 5 } 9$
2. $\log_{ 5 } 2 \cdot \log_{ 5 } 9$
3. $\log_{ 5 }(2 + 9)$
4. $9 \log_{ 5 } 2$
Which expression is equal to $\log_{ 3 }(7 \cdot 4)$ ?
1. $\log_{ 3 } 7 + \log_{ 3 } 4$
2. $\log_{ 3 } 7 \cdot \log_{ 3 } 4$
3. $\log_{ 3 }(7 + 4)$
4. $4 \log_{ 3 } 7$
Which expression is equal to $\log_{ 6 }(7 \cdot 8)$ ?
1. $\log_{ 6 } 7 + \log_{ 6 } 8$
2. $\log_{ 6 } 7 \cdot \log_{ 6 } 8$
3. $\log_{ 6 }(7 + 8)$
4. $8 \log_{ 6 } 7$
Which expression is equal to $\log_{ 3 }(5 \cdot 6)$ ?
1. $\log_{ 3 } 5 + \log_{ 3 } 6$
2. $\log_{ 3 } 5 \cdot \log_{ 3 } 6$
3. $\log_{ 3 }(5 + 6)$
4. $6 \log_{ 3 } 5$
Which expression is equal to $\log_{ 9 }(7 \cdot 5)$ ?
1. $\log_{ 9 } 7 + \log_{ 9 } 5$
2. $\log_{ 9 } 7 \cdot \log_{ 9 } 5$
3. $\log_{ 9 }(7 + 5)$
4. $5 \log_{ 9 } 7$
Which expression is equal to $\log_{ 7 }(2 \cdot 5)$ ?
1. $\log_{ 7 } 2 + \log_{ 7 } 5$
2. $\log_{ 7 } 2 \cdot \log_{ 7 } 5$
3. $\log_{ 7 }(2 + 5)$
4. $5 \log_{ 7 } 2$
Which expression is equal to $\log_{ 6 }(2 \cdot 7)$ ?
1. $\log_{ 6 } 2 + \log_{ 6 } 7$
2. $\log_{ 6 } 2 \cdot \log_{ 6 } 7$
3. $\log_{ 6 }(2 + 7)$
4. $7 \log_{ 6 } 2$
Which expression is equal to $\log_{ 4 }(5 \cdot 9)$ ?
1. $\log_{ 4 } 5 + \log_{ 4 } 9$
2. $\log_{ 4 } 5 \cdot \log_{ 4 } 9$
3. $\log_{ 4 }(5 + 9)$
4. $9 \log_{ 4 } 5$
Which expression is equal to $\log_{ 3 }(5 \cdot 2)$ ?
1. $\log_{ 3 } 5 + \log_{ 3 } 2$
2. $\log_{ 3 } 5 \cdot \log_{ 3 } 2$
3. $\log_{ 3 }(5 + 2)$
4. $2 \log_{ 3 } 5$
Which expression is equal to $\log_{ 3 }(2 \cdot 6)$ ?
1. $\log_{ 3 } 2 + \log_{ 3 } 6$
2. $\log_{ 3 } 2 \cdot \log_{ 3 } 6$
3. $\log_{ 3 }(2 + 6)$
4. $6 \log_{ 3 } 2$
Which expression is equal to $\log_{ 4 }(9 \cdot 7)$ ?
1. $\log_{ 4 } 9 + \log_{ 4 } 7$
2. $\log_{ 4 } 9 \cdot \log_{ 4 } 7$
3. $\log_{ 4 }(9 + 7)$
4. $7 \log_{ 4 } 9$
Which expression is equal to $\log_{ 7 }(4 \cdot 3)$ ?
1. $\log_{ 7 } 4 + \log_{ 7 } 3$
2. $\log_{ 7 } 4 \cdot \log_{ 7 } 3$
3. $\log_{ 7 }(4 + 3)$
4. $3 \log_{ 7 } 4$
Which expression is equal to $\log_{ 8 }(5 \cdot 6)$ ?
1. $\log_{ 8 } 5 + \log_{ 8 } 6$
2. $\log_{ 8 } 5 \cdot \log_{ 8 } 6$
3. $\log_{ 8 }(5 + 6)$
4. $6 \log_{ 8 } 5$
Which expression is equal to $\log_{ 3 }(2 \cdot 7)$ ?
1. $\log_{ 3 } 2 + \log_{ 3 } 7$
2. $\log_{ 3 } 2 \cdot \log_{ 3 } 7$
3. $\log_{ 3 }(2 + 7)$
4. $7 \log_{ 3 } 2$
Which expression is equal to $\log_{ 2 }(5 \cdot 3)$ ?
1. $\log_{ 2 } 5 + \log_{ 2 } 3$
2. $\log_{ 2 } 5 \cdot \log_{ 2 } 3$
3. $\log_{ 2 }(5 + 3)$
4. $3 \log_{ 2 } 5$
Which expression is equal to $\log_{ 9 }(7 \cdot 8)$ ?
1. $\log_{ 9 } 7 + \log_{ 9 } 8$
2. $\log_{ 9 } 7 \cdot \log_{ 9 } 8$
3. $\log_{ 9 }(7 + 8)$
4. $8 \log_{ 9 } 7$
Which expression is equal to $\log_{ 7 }(4 \cdot 8)$ ?
1. $\log_{ 7 } 4 + \log_{ 7 } 8$
2. $\log_{ 7 } 4 \cdot \log_{ 7 } 8$
3. $\log_{ 7 }(4 + 8)$
4. $8 \log_{ 7 } 4$
Which expression is equal to $\log_{ 2 }(7 \cdot 6)$ ?
1. $\log_{ 2 } 7 + \log_{ 2 } 6$
2. $\log_{ 2 } 7 \cdot \log_{ 2 } 6$
3. $\log_{ 2 }(7 + 6)$
4. $6 \log_{ 2 } 7$
Which expression is equal to $\log_{ 8 }(2 \cdot 4)$ ?
1. $\log_{ 8 } 2 + \log_{ 8 } 4$
2. $\log_{ 8 } 2 \cdot \log_{ 8 } 4$
3. $\log_{ 8 }(2 + 4)$
4. $4 \log_{ 8 } 2$
Which expression is equal to $\log_{ 9 }(4 \cdot 7)$ ?
1. $\log_{ 9 } 4 + \log_{ 9 } 7$
2. $\log_{ 9 } 4 \cdot \log_{ 9 } 7$
3. $\log_{ 9 }(4 + 7)$
4. $7 \log_{ 9 } 4$
Which expression is equal to $\log_{ 7 }(6 \cdot 9)$ ?
1. $\log_{ 7 } 6 + \log_{ 7 } 9$
2. $\log_{ 7 } 6 \cdot \log_{ 7 } 9$
3. $\log_{ 7 }(6 + 9)$
4. $9 \log_{ 7 } 6$
Which expression is equal to $\log_{ 6 }(7 \cdot 9)$ ?
1. $\log_{ 6 } 7 + \log_{ 6 } 9$
2. $\log_{ 6 } 7 \cdot \log_{ 6 } 9$
3. $\log_{ 6 }(7 + 9)$
4. $9 \log_{ 6 } 7$
Which expression is equal to $\log_{ 9 }(6 \cdot 4)$ ?
1. $\log_{ 9 } 6 + \log_{ 9 } 4$
2. $\log_{ 9 } 6 \cdot \log_{ 9 } 4$
3. $\log_{ 9 }(6 + 4)$
4. $4 \log_{ 9 } 6$
Which expression is equal to $\log_{ 9 }(3 \cdot 2)$ ?
1. $\log_{ 9 } 3 + \log_{ 9 } 2$
2. $\log_{ 9 } 3 \cdot \log_{ 9 } 2$
3. $\log_{ 9 }(3 + 2)$
4. $2 \log_{ 9 } 3$
Which expression is equal to $\log_{ 3 }(8 \cdot 6)$ ?
1. $\log_{ 3 } 8 + \log_{ 3 } 6$
2. $\log_{ 3 } 8 \cdot \log_{ 3 } 6$
3. $\log_{ 3 }(8 + 6)$
4. $6 \log_{ 3 } 8$
Which expression is equal to $\log_{ 4 }(8 \cdot 5)$ ?
1. $\log_{ 4 } 8 + \log_{ 4 } 5$
2. $\log_{ 4 } 8 \cdot \log_{ 4 } 5$
3. $\log_{ 4 }(8 + 5)$
4. $5 \log_{ 4 } 8$
Which expression is equal to $\log_{ 2 }(4 \cdot 6)$ ?
1. $\log_{ 2 } 4 + \log_{ 2 } 6$
2. $\log_{ 2 } 4 \cdot \log_{ 2 } 6$
3. $\log_{ 2 }(4 + 6)$
4. $6 \log_{ 2 } 4$
Which expression is equal to $\log_{ 3 }(9 \cdot 5)$ ?
1. $\log_{ 3 } 9 + \log_{ 3 } 5$
2. $\log_{ 3 } 9 \cdot \log_{ 3 } 5$
3. $\log_{ 3 }(9 + 5)$
4. $5 \log_{ 3 } 9$
Which expression is equal to $\log_{ 3 }(8 \cdot 7)$ ?
1. $\log_{ 3 } 8 + \log_{ 3 } 7$
2. $\log_{ 3 } 8 \cdot \log_{ 3 } 7$
3. $\log_{ 3 }(8 + 7)$
4. $7 \log_{ 3 } 8$
Which expression is equal to $\log_{ 2 }(6 \cdot 9)$ ?
1. $\log_{ 2 } 6 + \log_{ 2 } 9$
2. $\log_{ 2 } 6 \cdot \log_{ 2 } 9$
3. $\log_{ 2 }(6 + 9)$
4. $9 \log_{ 2 } 6$
Which expression is equal to $\log_{ 3 }(7 \cdot 5)$ ?
1. $\log_{ 3 } 7 + \log_{ 3 } 5$
2. $\log_{ 3 } 7 \cdot \log_{ 3 } 5$
3. $\log_{ 3 }(7 + 5)$
4. $5 \log_{ 3 } 7$
Which expression is equal to $\log_{ 9 }(8 \cdot 7)$ ?
1. $\log_{ 9 } 8 + \log_{ 9 } 7$
2. $\log_{ 9 } 8 \cdot \log_{ 9 } 7$
3. $\log_{ 9 }(8 + 7)$
4. $7 \log_{ 9 } 8$
Which expression is equal to $\log_{ 8 }(6 \cdot 7)$ ?
1. $\log_{ 8 } 6 + \log_{ 8 } 7$
2. $\log_{ 8 } 6 \cdot \log_{ 8 } 7$
3. $\log_{ 8 }(6 + 7)$
4. $7 \log_{ 8 } 6$
Which expression is equal to $\log_{ 2 }(3 \cdot 5)$ ?
1. $\log_{ 2 } 3 + \log_{ 2 } 5$
2. $\log_{ 2 } 3 \cdot \log_{ 2 } 5$
3. $\log_{ 2 }(3 + 5)$
4. $5 \log_{ 2 } 3$
Which expression is equal to $\log_{ 6 }(3 \cdot 7)$ ?
1. $\log_{ 6 } 3 + \log_{ 6 } 7$
2. $\log_{ 6 } 3 \cdot \log_{ 6 } 7$
3. $\log_{ 6 }(3 + 7)$
4. $7 \log_{ 6 } 3$
Which expression is equal to $\log_{ 6 }(2 \cdot 5)$ ?
1. $\log_{ 6 } 2 + \log_{ 6 } 5$
2. $\log_{ 6 } 2 \cdot \log_{ 6 } 5$
3. $\log_{ 6 }(2 + 5)$
4. $5 \log_{ 6 } 2$
Which expression is equal to $\log_{ 9 }(8 \cdot 4)$ ?
1. $\log_{ 9 } 8 + \log_{ 9 } 4$
2. $\log_{ 9 } 8 \cdot \log_{ 9 } 4$
3. $\log_{ 9 }(8 + 4)$
4. $4 \log_{ 9 } 8$
Which expression is equal to $\log_{ 3 }(2 \cdot 8)$ ?
1. $\log_{ 3 } 2 + \log_{ 3 } 8$
2. $\log_{ 3 } 2 \cdot \log_{ 3 } 8$
3. $\log_{ 3 }(2 + 8)$
4. $8 \log_{ 3 } 2$
Which expression is equal to $\log_{ 7 }(3 \cdot 9)$ ?
1. $\log_{ 7 } 3 + \log_{ 7 } 9$
2. $\log_{ 7 } 3 \cdot \log_{ 7 } 9$
3. $\log_{ 7 }(3 + 9)$
4. $9 \log_{ 7 } 3$
Which expression is equal to $\log_{ 7 }(3 \cdot 2)$ ?
1. $\log_{ 7 } 3 + \log_{ 7 } 2$
2. $\log_{ 7 } 3 \cdot \log_{ 7 } 2$
3. $\log_{ 7 }(3 + 2)$
4. $2 \log_{ 7 } 3$
Which expression is equal to $\log_{ 8 }(9 \cdot 2)$ ?
1. $\log_{ 8 } 9 + \log_{ 8 } 2$
2. $\log_{ 8 } 9 \cdot \log_{ 8 } 2$
3. $\log_{ 8 }(9 + 2)$
4. $2 \log_{ 8 } 9$
Which expression is equal to $\log_{ 5 }(3 \cdot 7)$ ?
1. $\log_{ 5 } 3 + \log_{ 5 } 7$
2. $\log_{ 5 } 3 \cdot \log_{ 5 } 7$
3. $\log_{ 5 }(3 + 7)$
4. $7 \log_{ 5 } 3$
Which expression is equal to $\log_{ 4 }(2 \cdot 8)$ ?
1. $\log_{ 4 } 2 + \log_{ 4 } 8$
2. $\log_{ 4 } 2 \cdot \log_{ 4 } 8$
3. $\log_{ 4 }(2 + 8)$
4. $8 \log_{ 4 } 2$
No calculator

Find the exact value of $\tan\left(\frac{2 \pi}{3}\right)$ .
No calculator

Solve $\sin 2x = \frac{1}{2}$ for $0 \le x < 2\pi$ .
No calculator

Tap the point with polar coordinates $\left(4, \frac{3 \pi}{2}\right)$ .
No calculator

How many terms does $\displaystyle\sum_{k=3}^{ 17 } (2k + 1)$ have?
$f(x) = 2x + 2$ and $g(x) = x^2 - 2$ . Find $f(g(3))$ .
$x = 4$ is a zero of $p(x) = x^3 - 4x^2 - 1x + 4$ . Find all the zeros of $p$ .
Evaluate $\log_{ 10 } 20 + \log_{ 10 } 5$ without a calculator.
A right triangle has hypotenuse 15 and an angle of $30^\circ$ . How long is the side opposite this angle? Give the exact value.
Use a sum identity to find the exact value of $\cos(45^\circ + 30^\circ)$ .
What is the graph of the polar equation $r = 5$ ?
1. A circle of radius 5 centered at the origin
2. A line through the origin
3. The vertical line $x = 5$
What is the graph of the polar equation $r = 7$ ?
1. A circle of radius 7 centered at the origin
2. A line through the origin
3. The vertical line $x = 7$
What is the graph of the polar equation $r = 8$ ?
1. A circle of radius 8 centered at the origin
2. A line through the origin
3. The vertical line $x = 8$
What is the graph of the polar equation $r = 4$ ?
1. A circle of radius 4 centered at the origin
2. A line through the origin
3. The vertical line $x = 4$
What is the graph of the polar equation $r = 2$ ?
1. A circle of radius 2 centered at the origin
2. A line through the origin
3. The vertical line $x = 2$
What is the graph of the polar equation $r = 3$ ?
1. A circle of radius 3 centered at the origin
2. A line through the origin
3. The vertical line $x = 3$
What is the graph of the polar equation $r = 6$ ?
1. A circle of radius 6 centered at the origin
2. A line through the origin
3. The vertical line $x = 6$
What is the graph of the polar equation $r = 9$ ?
1. A circle of radius 9 centered at the origin
2. A line through the origin
3. The vertical line $x = 9$
Find the sum of the first 6 terms of the geometric sequence with $a_1 = 8$ and ratio 3.
Draw the graph of $y = (x - 1)^2 - 3$ : place the vertex and one more point.
A polynomial with real coefficients has the zero $4 + 4i$ . Which other number must be a zero?
1. $4 - 4i$
2. $-4 - 4i$
3. $-4 + 4i$
A polynomial with real coefficients has the zero $8 + 7i$ . Which other number must be a zero?
1. $8 - 7i$
2. $-8 - 7i$
3. $-8 + 7i$
A polynomial with real coefficients has the zero $4 + 5i$ . Which other number must be a zero?
1. $4 - 5i$
2. $-4 - 5i$
3. $-4 + 5i$
A polynomial with real coefficients has the zero $6 + 5i$ . Which other number must be a zero?
1. $6 - 5i$
2. $-6 - 5i$
3. $-6 + 5i$
A polynomial with real coefficients has the zero $6 + 2i$ . Which other number must be a zero?
1. $6 - 2i$
2. $-6 - 2i$
3. $-6 + 2i$
A polynomial with real coefficients has the zero $2 + 1i$ . Which other number must be a zero?
1. $2 - 1i$
2. $-2 - 1i$
3. $-2 + 1i$
A polynomial with real coefficients has the zero $8 + 8i$ . Which other number must be a zero?
1. $8 - 8i$
2. $-8 - 8i$
3. $-8 + 8i$
A polynomial with real coefficients has the zero $5 + 4i$ . Which other number must be a zero?
1. $5 - 4i$
2. $-5 - 4i$
3. $-5 + 4i$
A polynomial with real coefficients has the zero $6 + 1i$ . Which other number must be a zero?
1. $6 - 1i$
2. $-6 - 1i$
3. $-6 + 1i$
A polynomial with real coefficients has the zero $4 + 9i$ . Which other number must be a zero?
1. $4 - 9i$
2. $-4 - 9i$
3. $-4 + 9i$
A polynomial with real coefficients has the zero $5 + 9i$ . Which other number must be a zero?
1. $5 - 9i$
2. $-5 - 9i$
3. $-5 + 9i$
A polynomial with real coefficients has the zero $9 + 8i$ . Which other number must be a zero?
1. $9 - 8i$
2. $-9 - 8i$
3. $-9 + 8i$
A polynomial with real coefficients has the zero $2 + 9i$ . Which other number must be a zero?
1. $2 - 9i$
2. $-2 - 9i$
3. $-2 + 9i$
A polynomial with real coefficients has the zero $3 + 9i$ . Which other number must be a zero?
1. $3 - 9i$
2. $-3 - 9i$
3. $-3 + 9i$
A polynomial with real coefficients has the zero $5 + 6i$ . Which other number must be a zero?
1. $5 - 6i$
2. $-5 - 6i$
3. $-5 + 6i$
A polynomial with real coefficients has the zero $6 + 4i$ . Which other number must be a zero?
1. $6 - 4i$
2. $-6 - 4i$
3. $-6 + 4i$
A polynomial with real coefficients has the zero $4 + 6i$ . Which other number must be a zero?
1. $4 - 6i$
2. $-4 - 6i$
3. $-4 + 6i$
A polynomial with real coefficients has the zero $1 + 5i$ . Which other number must be a zero?
1. $1 - 5i$
2. $-1 - 5i$
3. $-1 + 5i$
A polynomial with real coefficients has the zero $6 + 7i$ . Which other number must be a zero?
1. $6 - 7i$
2. $-6 - 7i$
3. $-6 + 7i$
A polynomial with real coefficients has the zero $1 + 2i$ . Which other number must be a zero?
1. $1 - 2i$
2. $-1 - 2i$
3. $-1 + 2i$
A polynomial with real coefficients has the zero $2 + 3i$ . Which other number must be a zero?
1. $2 - 3i$
2. $-2 - 3i$
3. $-2 + 3i$
A polynomial with real coefficients has the zero $9 + 5i$ . Which other number must be a zero?
1. $9 - 5i$
2. $-9 - 5i$
3. $-9 + 5i$
A polynomial with real coefficients has the zero $2 + 4i$ . Which other number must be a zero?
1. $2 - 4i$
2. $-2 - 4i$
3. $-2 + 4i$
A polynomial with real coefficients has the zero $9 + 6i$ . Which other number must be a zero?
1. $9 - 6i$
2. $-9 - 6i$
3. $-9 + 6i$
A polynomial with real coefficients has the zero $7 + 6i$ . Which other number must be a zero?
1. $7 - 6i$
2. $-7 - 6i$
3. $-7 + 6i$
A polynomial with real coefficients has the zero $5 + 2i$ . Which other number must be a zero?
1. $5 - 2i$
2. $-5 - 2i$
3. $-5 + 2i$
A polynomial with real coefficients has the zero $5 + 8i$ . Which other number must be a zero?
1. $5 - 8i$
2. $-5 - 8i$
3. $-5 + 8i$
A polynomial with real coefficients has the zero $8 + 3i$ . Which other number must be a zero?
1. $8 - 3i$
2. $-8 - 3i$
3. $-8 + 3i$
A polynomial with real coefficients has the zero $4 + 8i$ . Which other number must be a zero?
1. $4 - 8i$
2. $-4 - 8i$
3. $-4 + 8i$
A polynomial with real coefficients has the zero $2 + 5i$ . Which other number must be a zero?
1. $2 - 5i$
2. $-2 - 5i$
3. $-2 + 5i$
A polynomial with real coefficients has the zero $1 + 9i$ . Which other number must be a zero?
1. $1 - 9i$
2. $-1 - 9i$
3. $-1 + 9i$
A polynomial with real coefficients has the zero $9 + 3i$ . Which other number must be a zero?
1. $9 - 3i$
2. $-9 - 3i$
3. $-9 + 3i$
A polynomial with real coefficients has the zero $3 + 1i$ . Which other number must be a zero?
1. $3 - 1i$
2. $-3 - 1i$
3. $-3 + 1i$
A polynomial with real coefficients has the zero $2 + 7i$ . Which other number must be a zero?
1. $2 - 7i$
2. $-2 - 7i$
3. $-2 + 7i$
A polynomial with real coefficients has the zero $6 + 9i$ . Which other number must be a zero?
1. $6 - 9i$
2. $-6 - 9i$
3. $-6 + 9i$
A polynomial with real coefficients has the zero $1 + 1i$ . Which other number must be a zero?
1. $1 - 1i$
2. $-1 - 1i$
3. $-1 + 1i$
A polynomial with real coefficients has the zero $9 + 2i$ . Which other number must be a zero?
1. $9 - 2i$
2. $-9 - 2i$
3. $-9 + 2i$
A polynomial with real coefficients has the zero $2 + 2i$ . Which other number must be a zero?
1. $2 - 2i$
2. $-2 - 2i$
3. $-2 + 2i$
A polynomial with real coefficients has the zero $3 + 7i$ . Which other number must be a zero?
1. $3 - 7i$
2. $-3 - 7i$
3. $-3 + 7i$
A polynomial with real coefficients has the zero $8 + 2i$ . Which other number must be a zero?
1. $8 - 2i$
2. $-8 - 2i$
3. $-8 + 2i$
A polynomial with real coefficients has the zero $7 + 4i$ . Which other number must be a zero?
1. $7 - 4i$
2. $-7 - 4i$
3. $-7 + 4i$
A polynomial with real coefficients has the zero $9 + 1i$ . Which other number must be a zero?
1. $9 - 1i$
2. $-9 - 1i$
3. $-9 + 1i$
A polynomial with real coefficients has the zero $8 + 4i$ . Which other number must be a zero?
1. $8 - 4i$
2. $-8 - 4i$
3. $-8 + 4i$
A polynomial with real coefficients has the zero $6 + 6i$ . Which other number must be a zero?
1. $6 - 6i$
2. $-6 - 6i$
3. $-6 + 6i$
A polynomial with real coefficients has the zero $8 + 9i$ . Which other number must be a zero?
1. $8 - 9i$
2. $-8 - 9i$
3. $-8 + 9i$
A polynomial with real coefficients has the zero $4 + 2i$ . Which other number must be a zero?
1. $4 - 2i$
2. $-4 - 2i$
3. $-4 + 2i$
A polynomial with real coefficients has the zero $9 + 7i$ . Which other number must be a zero?
1. $9 - 7i$
2. $-9 - 7i$
3. $-9 + 7i$
A polynomial with real coefficients has the zero $3 + 2i$ . Which other number must be a zero?
1. $3 - 2i$
2. $-3 - 2i$
3. $-3 + 2i$
A polynomial with real coefficients has the zero $7 + 2i$ . Which other number must be a zero?
1. $7 - 2i$
2. $-7 - 2i$
3. $-7 + 2i$
A polynomial with real coefficients has the zero $3 + 4i$ . Which other number must be a zero?
1. $3 - 4i$
2. $-3 - 4i$
3. $-3 + 4i$
Complete the change of base: $\log_{ 4 } 20 = \dfrac{\ln 20 }{\square}$ . What goes in the box?
A triangle has sides 5 cm and 12 cm with an angle of 30° between them. What is its area, in cm²?
$\theta$ is in quadrant I and $\sin\theta = \frac{15}{17}$ . Find the exact value of $\sin 2\theta$ .

Answers

$21$
As $x \to \infty$ , $f(x) \to \infty$ ; as $x \to -\infty$ , $f(x) \to -\infty$
$2$
$\frac{5 \pi}{4}$
$- \frac{2 \sqrt{6}}{5}$
$(2, 1)$
$-9$
$[9, \infty)$
$1$
$7$
$\frac{\sqrt{3}}{2}$
$\frac{\pi}{6},\ \frac{5 \pi}{6}$
$\left(x - 6\right)^{2}$
$98$
$15$
$4,\ -2$
$8$
$- \frac{\sqrt{2}}{2}$
$0,\ \pi,\ \frac{\pi}{3},\ \frac{2 \pi}{3}$
$3$
$81$
$18$
$19$
$\log_{ 8 } 2 + \log_{ 8 } 7$
$- \sqrt{3}$
$\frac{\pi}{12},\ \frac{5 \pi}{12},\ \frac{13 \pi}{12},\ \frac{17 \pi}{12}$
$(0, -4)$
$15$
$16$
$4,\ 1,\ -1$
$2$
$\frac{15}{2}$
$- \frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}$
A circle of radius 5 centered at the origin
$2912$
$y = \left(x - 1\right)^{2} - 3$
$4 - 4i$
$\ln{\left(4 \right)}$
$15$
$\frac{240}{289}$