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AP Precalculus Medium practice

15 questions

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Medium practice

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Question 1

What is the unit vector in the direction of $w = ⟨ 6, - 8 ⟩$ ?

⟨ 6, - 8 ⟩

⟨ \frac{3}{5}, - \frac{4}{5} ⟩

⟨ \frac{6}{10}, \frac{- 8}{10} ⟩ \cdot 2

⟨ \frac{1}{6}, - \frac{1}{8} ⟩

Question 2

Solve $2^{x + 1} = 16$ for $x$ .

x = 2

x = 3

x = 4

x = 7

Question 3

A parametric curve is given by $x (t) = 2 cos (t)$ , $y (t) = 2 sin (t)$ for $t \in [0, 2 π)$ . Which curve does it trace?

A.A circle of radius

1

centered at the origin.B.A circle of radius

2

centered at the origin.C.An ellipse with semi-axes

2

and

1

.D.A line of slope

1

through the origin.

Question 4

Simplify $lo g_{5} (25) + lo g_{5} (125)$ using log properties.

3

5

lo g_{5} (150)

lo g_{5} (250)

Question 5

What is the horizontal asymptote of $f (x) = \frac{3 x ^{2} + 7}{2 x ^{2} - x + 5}$ ?

y = 0

y = \frac{2}{3}

y = \frac{3}{2}

D.No horizontal asymptote.

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Question 6

What is the inverse of $f (x) = 3^{x}$ ?

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

f^{- 1} (x) = lo g_{3} (x)

f^{- 1} (x) = x^{1/3}

f^{- 1} (x) = ln (x)

Question 7

The polynomial $f (x) = (x - 2)^{2} (x + 1)$ has a zero at $x = 2$ . Which best describes the graph of $f$ at $x = 2$ ?

A.Crosses the

x

-axis at

x = 2

.B.Touches the

x

-axis and turns around at

x = 2

.C.Has a vertical asymptote at

x = 2

.D.Is undefined at

x = 2

Question 8

If $sin (θ) = \frac{3}{5}$ and $θ$ is in Quadrant II, what is $cos (θ)$ ?

\frac{4}{5}

- \frac{4}{5}

\frac{3}{5}

- \frac{3}{5}

Question 9

Find all solutions to $2 sin (θ) = 1$ on the interval $[0, 2 π)$ .

θ = π /6

onlyB.

θ = π /6

and

θ = 5 π /6

θ = π /3

and

θ = 2 π /3

θ = π /6

and

θ = 7 π /6

Question 10

Compute the dot product of $u = ⟨ 2, 3 ⟩$ and $v = ⟨ 4, - 1 ⟩$ .

5

11

⟨ 8, - 3 ⟩

2

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Question 11

A linear function $g$ has constant rate of change $2$ , and a quadratic function $q (x) = x^{2}$ has rate of change that varies with $x$ . Over the interval $[1, 5]$ , what is the average rate of change of $q$ , and how does it compare to $g$ 's rate?

A.Average rate of

q

4

; faster than

g

's rate.B.Average rate of

q

6

; faster than

g

's rate.C.Average rate of

q

6

; slower than

g

's rate.D.Average rate of

q

24

; faster than

g

's rate.

Question 12

What is the graph of the polar equation $r = 4$ ?

A.A horizontal line

y = 4

.B.A vertical line

x = 4

.C.A circle of radius

4

centered at the origin.D.A spiral.

Question 13

Convert the rectangular point $(x, y) = (1, 3)$ to polar form $(r, θ)$ with $r > 0$ and $θ \in [0, 2 π)$ .

(2, π /6)

(2, π /3)

(4, π /3)

(2, 2 π /3)

Question 14

Find the quotient when $f (x) = x^{3} + 2 x^{2} - 5 x - 6$ is divided by $x - 2$ .

x^{2} + 4 x + 3

x^{2} - 4 x + 3

x^{2} + 2 x - 3

x^{2} + 4 x + 5

Question 15

A bacterial culture grows according to $N (t) = 500 \cdot 2^{t /3}$ where $t$ is in hours. By what factor does the population grow every $3$ hours?

A.Adds

500

.B.Doubles.C.Triples.D.Multiplies by

2^{3} = 8

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