Free Printable Pre-Calculus 2

1.

Determine the quadrant in which the terminal side of θ lies: $\sin\theta<0\ and\ \cot\ \theta<0$

a)

Quadrant IV

b)

Quadrant I

c)

Quadrant II

d)

Quadrant III

2.

Solve for w.

w² - 8w + 16

a)

w = 16

b)

w = - 4

c)

w = 4

d)

w = - 8

3.

If θ = 120°, find the exact value of $\sin\ \frac{\theta}{2}$

a)

$\frac{2}{\sqrt[]{2}}$

b)

$\frac{\sqrt[]{3}}{3}$

c)

$\infty$

d)

$\frac{\sqrt[]{3}}{2}$

4.

Suppose that $\left(\frac{3}{5},\ y\right)$ is a point in Quadrant IV lying on the Unit Circle? Find y.

a)

$y\ =\ \frac{4}{5}$

b)

$y\ =\ \pi$

c)

$y\ =\ \frac{16}{25}$

d)

$y\ =\ -\frac{4}{5}$

5.

Determine the quadrant in which the terminal side of θ lies: $\csc\ \theta<0\ and\ \cos\theta>0$

a)

Quadrant III

b)

Quadrant II

c)

Quadrant IV

d)

Qaudrant I

6.

a)

4.4 in

b)

8.7 ft

c)

4.4 ft

d)

7.9 ft

7.

a)

Undefined

b)

96.5 ft

c)

1158 ft

d)

143 ft

8.

a)

$\sec\ \theta\ =\ -\frac{13}{12};\ \cot\ \theta\ =\ -\frac{12}{5}$

b)

$\sec⁡\theta=\frac{−12}{13};\cot⁡\theta=\frac{−5}{12}$

c)

$\cos\theta⁡=\frac{−13}{12};\cot⁡\theta=\frac{−12}{5}$

d)

$\sec\ \theta\ =\ undefined;\ \tan\ \theta\ =\ \frac{\sqrt[]{3}}{2}$

9.

Find the exact value of $\cos\left(-270\degree\right)$

a)

undefined

b)

0.5

c)

2

d)

0

10.

Let (5, -√11) be the terminal side of θ, and find sec θ.

a)

$\frac{6}{5}$

b)

$\frac{5}{6}$

c)

9

d)

0.8660

11.

$What\ is\ the\ exact\ value\ of\cos\ \frac{5\pi}{4}$ ?

a)

1

b)

$\frac{\sqrt[]{2}}{2}$

c)

$\frac{2}{\sqrt[]{2}}$

d)

$-\frac{\sqrt[]{2}}{2}$

12.

a)

$38.659\degree$

b)

$\pi$

c)

$0.6747$

d)

$38.7\degree$

13.

If θ = 45°, find the exact value of $\sin\left(2\theta\right)$

a)

0.7071

b)

1

c)

0.5

d)

Undefined

14.

Find the exact value of $\sin\ \frac{4\pi}{3}$

a)

$Undefined$

b)

$-\frac{\sqrt[]{3}}{2}$

c)

$\frac{2\ \sqrt[]{3}}{3}$

d)

$\frac{\sqrt[]{3}}{2}$

15.

Determine the quadrant in which the terminal side of θ lies for

sin θ > 0 and cot θ > 0

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

16.

Use your calculator to evaluate $\sin^{-1}\left(0.63\right)\ in\ radians$

a)

0.56

b)

$90\pi$

c)

0.68

d)

39.05

17.

Find cot θ, where θ is the angle shown. Give an exact value, not a decimal approximation.

a)

$\frac{3}{4}$

b)

$\frac{4}{3}$

c)

$\frac{5}{4}$

d)

$\frac{5}{3}$

18.

A slice of bread is roughly 14 cm by 10 cm. If the slice is cut diagonally in half, what acute angles are formed?

Leave your answer to the nearest tenth of a degree.

a)

$30\degree\ and\ 60\degree$

b)

$35.5\degree\ and\ 54.5\degree$

c)

$54.5\degree\ and\ 30.0\degree$

d)

$35.54\degree\ and\ 53.45\degree$

19.

Simplify $\frac{24x^4y^2}{8x^5y^4}$

a)

$\frac{3\left(x+y\right)}{xy^2}$

b)

$\frac{3}{xy^2}$

c)

$\frac{x^2y^4}{8}$

d)

Inconclusive...

20.

Simplify $\frac{a^{-3}b^4c^{-5}}{a^{-1}c}$

a)

$-\frac{b^{12}}{a^6c^{18}}$

b)

$\frac{b}{a^6c}$

c)

$\frac{b^{12}}{a^6c^{18}}$

d)

21.

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Pre-Calculus 2

Total questions: 21

Worksheet time: 45mins

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