Free Printable EPISM Interactive Quiz Bee (Algebra)

1.

Which of the following equations represent a unit circle?

a)

$x^2+y^2=1$

b)

$\left(x-h\right)^2+\left(y-k\right)^2=r^2$

c)

$x^2-y^2=1$

d)

$\left(x+h\right)^2-\left(y+k\right)^2=r^2$

2.

If $P\left(\theta\right)$ is a point on the unit circle and $\theta=-\frac{5\pi}{6}$ , find $\csc\ \theta.$

a)

$-\frac{1}{2}$

b)

$\sqrt{3}$

c)

$\frac{\sqrt{3}}{3}$

d)

2

3.

Find the exact value of $\sin\ 300\degree.$

a)

$\frac{1}{2}$

b)

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

c)

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

d)

0

4.

The point $P\left(\frac{\sqrt{3}}{2},y\right)$ is on the unit circle in Quadrant IV. Find its y-coordinate.

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

$-\frac{1}{4}$

d)

$\frac{1}{4}$

5.

Express $\frac{3\pi}{2}$ in degrees.

a)

$270\degree$

b)

$180\degree$

c)

$360\degree$

d)

$260\degree$

6.

Convert $570\degree$ into radians.

a)

$\frac{11\pi}{6}$

b)

$\frac{15\pi}{6}$

c)

$\frac{17\pi}{6}$

d)

$\frac{19\pi}{6}$

7.

Which of the following is an example of an angle in standard position?

a)

b)

c)

d)

8.

Find the largest negative angle coterminal with $\frac{137\pi}{5}$ .

a)

$-2\pi\ rad$

b)

$-\frac{3\pi}{5}\ rad$

c)

$-\frac{7\pi}{4}\ rad$

d)

$-\frac{4\pi}{7}\ rad$

9.

Find an angle between $0\ and\ 2\pi$ that is co-terminal with $\frac{22\pi}{3}$ .

a)

$\frac{\pi}{3}$

b)

$\frac{\pi}{4}$

c)

$\frac{3\pi}{4}$

d)

$\frac{4\pi}{3}$

10.

Find the length of an arc of a circle with radius 15 m that subtends a central angle of 60◦.

a)

$2\pi$

b)

$3\pi$

c)

$4\pi$

d)

$5\pi$

11.

Find the area of a sector of a circle with central angle 60◦ if the radius of the circle is 3 m.

a)

4\pi\ m^2

b)

$\frac{7\pi}{3}\ m^2$

c)

$\frac{3\pi}{2}\ m^2$

d)

$2\pi\ m^2$

12.

A sprinkler on a golf course fairway is set to spray water over a distance of 70 feet and rotates through an angle of 120◦. Find the area of the fairway watered by the sprinkler.

a)

$3197\ ft.^2$

b)

$5131\ ft.^2$

c)

$5221\ ft.^2$

d)

$6002\ ft.\ ^2$

13.

As shown below, find the radius of the pulley if a rotation of 51.6 degrees raises the weight by 11.4 cm.

a)

12.7 cm

b)

13.7 cm

c)

11.7 cm

d)

10.7 cm

14.

A frequent problem in surveying city lots and rural lands adjacent to curves of highways and railways is that of finding the area when one or more of the boundary lines is the arc of a circle. Approximate the total area of the lot shown in the figure.

a)

$1837.3\ m^2$

b)

$2054.1\ m^2$

c)

$1909.0\ m^2$

d)

$1953.2\ m^2$

15.

A jeepney has a windshield wiper on the driver’s side that has total arm and blade 10 inches long and rotates back and forth through an angle of 95◦. The shaded region in the figure is the portion of the windshield cleaned by the 7-inch wiper blade. What is the area of the region cleaned?

a)

65.4\ in^2

b)

$85.4\ in^2$

c)

$75.4\ in^2$

d)

$95.4\ in^2$

16.

Determine the exact value of $\tan\ \frac{15\pi}{4}$ .

a)

$undefined$

b)

$-1$

c)

$0$

d)

$1$

17.

Given $\cos\ \theta=\frac{3}{5}$ , θ in Q IV, find the value of csc θ.

a)

$\frac{4}{5}$

b)

$\frac{5}{4}$

c)

$\frac{3}{5}$

d)

$\frac{5}{3}$

18.

If $P\left(\theta\right)$ is a point on the unit circle and $\theta=\frac{19\pi}{6}$ , find the value of $\sin\ \theta$ .

a)

$\frac{\sqrt{3}}{3}$

b)

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

c)

$-\frac{1}{2}$

d)

$\sqrt{3}$

19.

If $P\left(\theta\right)$ is a point on the unit circle and $\theta=\frac{19\pi}{6}$ , find the value of $\cos\ \theta$ .

a)

$-\frac{1}{2}$

b)

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

c)

$\sqrt{3}$

d)

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

20.

If $P\left(\theta\right)$ is a point on the unit circle and $\theta=\frac{19\pi}{6}$ , find the value of $\tan\ \theta$ .

a)

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

b)

$-2$

c)

$\frac{\sqrt{3}}{3}$

d)

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

21.

If $P\left(\theta\right)$ is a point on the unit circle and $\theta=\frac{19\pi}{6}$ , find the value of $\csc\ \theta$ .

a)

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

b)

$\sqrt{3}$

c)

$\frac{\sqrt{3}}{3}$

d)

$-2$

22.

If $P\left(\theta\right)$ is a point on the unit circle and $\theta=\frac{19\pi}{6}$ , find the value of $\sec\ \theta$ .

a)

$-2$

b)

$\sqrt{3}$

c)

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

d)

$-\frac{1}{2}$

23.

If $P\left(\theta\right)$ is a point on the unit circle and $\theta=\frac{19\pi}{6}$ , find the value of $\cot\ \theta$ .

a)

$\sqrt{3}$

b)

$\frac{\sqrt{3}}{3}$

c)

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

d)

$-2$

24.

If you are able to solve for the sine and cosine of an angle given a point on its terminal side, you have enough information to also solve for its tangent. Which of the following best describes the validity of the above statement?

a)

The statement is true in all cases.

b)

The statement is true in some cases, but not all.

c)

The statement is false in all cases.

d)

None of the statements above is correct.

25.

What is the sine of an angle if a point on the terminal side of the angle is (1,5)?

a)

\frac{\sqrt{26}}{26}

b)

$\frac{1}{6}$

c)

$\frac{5}{6}$

d)

$\frac{5\sqrt{26}}{26}$

26.

Find the sine value of (1,√3) if it is a point on the terminal side of an angle in standard position.

a)

$\frac{1}{2}$

b)

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

c)

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

d)

$-\frac{1}{2}$

27.

Find the sine and cosine of the following angle. (2 pts)

a)

$\sin\ \theta=\frac{6\sqrt{61}}{61},\ \cos\ \theta=\frac{5\sqrt{61}}{61}$

b)

$\sin\ \theta=\frac{6}{5},\ \cos\ \theta=\frac{5}{6}$

c)

$\sin\ \theta=\frac{\sqrt{61}}{61},\ \cos\ \theta=\frac{\sqrt{61}}{61}$

d)

$\sin\ \theta=6\sqrt{61},\ \cos\ \theta=5\sqrt{61}$

28.

Find the exact value of each expression.

\tan^2\ \frac{\pi}{4}+\ 2\cos\ \frac{8\pi}{3}-\ \sin\ \frac{13\pi}{6}

a)

$-\frac{1}{2}$

b)

$0$

c)

$1$

d)

$undefined$

29.

Find the exact value of each expression

\frac{\left(\sin\ \frac{11\pi}{6}-\cos\ \frac{\pi}{6}\right)}{\sin\ -\frac{\pi}{6}+\cos\ \frac{5\pi}{6}}

a)

$-\frac{1}{2}$

b)

$1$

c)

$undefined$

d)

$0$

EPISM Interactive Quiz Bee (Algebra)

Total questions: 29

Worksheet time: 17mins

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