Free Printable Honors Pre-Calculus Midterm Exam

1.

Convert 72^o to radians.

a)

$\frac{5\pi}{2}$

b)

$\frac{4\pi}{5}$

c)

$\frac{2\pi}{5}$

d)

$\frac{5\pi}{4}$

2.

$Convert\ \frac{5\pi}{18}\ to\ \deg rees.$

a)

$648\degree$

b)

$100\degree$

c)

$50\degree$

d)

$25\degree$

3.

$Find\ the\ arc\ length\ of\ a\ \sec tor\ with\ a\ radius\ of\ 9\ feet\ and\ a\ central\ angle\ of\ 18\degree.$

a)

$\frac{9\pi}{5}\ feet$

b)

$\frac{9\pi}{10}\ feet$

c)

$\frac{\pi}{2}\ feet$

d)

$162\pi\ feet$

4.

$Evaluate\ \cos\frac{5\pi}{4}\ u\sin g\ the\ Unit\ Circle.$

a)

$0$

b)

$1$

c)

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

d)

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

5.

$Convert\ 24.162\degree\ to\ \deg rees\ \min utes\ \sec onds\ \left(DMS\right).$

a)

$24\degree16'5.7"$

b)

$24\degree9'43.2"$

c)

$24\degree12'18.3"$

d)

$24\degree50'19.2"$

6.

$Simplify\ \sin x\ \csc x.$

a)

$\sin x$

b)

$\cos x$

c)

$\tan x$

d)

$1$

7.

$Simplify\ \sec^2x\left(1-\cos^2x\right).$

a)

$\tan^2x$

b)

$1$

c)

$\cot^2x$

d)

$\sin^2x$

8.

$Simplify\ \csc^2x-\cot^2x.$

a)

$\sin^2x$

b)

$\csc^2x$

c)

$1$

d)

$\cot^2x$

9.

$Simplify\ \frac{1-\sin^2x}{1-\sin x}.$

a)

$\cos^2x$

b)

$1-\sin x$

c)

$1$

d)

$1+\sin x$

10.

$What\ is\ the\ next\ step\ when\ verifying\ \sec x\ \cot x=\csc x?$

a)

$Use\ a\ Pythagorean\ Theorem.$

b)

$Factor.$

c)

$Multiply.$

d)

$Rewrite\ u\sin g\ \sin\ and\ \cos.$

11.

$What\ is\ the\ next\ step\ when\ verifying\ \sin x\left(\sec^2x-\tan^2x\right)=\sin x?$

a)

$Use\ a\ Pythagorean\ Theorem.$

b)

$Multiply.$

c)

$Factor.$

d)

$Rewrite\ u\sin g\ \sin\ and\ \cos.$

12.

$What\ is\ the\ next\ step\ when\ verifying\ \tan x-\tan x\sin^2x=\sin x\ \cos x?$

a)

$Use\ a\ Pythagorean\ Theorem.$

b)

$Multiply.$

c)

$Rewrite\ u\sin g\ \sin\ and\ \cos.$

d)

$Factor.$

13.

$Find\ all\ solutions\ of\ 2\cos x-\sqrt{3}=0\ in\ the\ interval\ \left[0,\ 2\pi\right).$

a)

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

b)

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

c)

$0\ \&\ \pi$

d)

$\frac{\pi}{3}\ \&\ \frac{2\pi}{3}$

14.

$Find\ all\ solutions\ of\ \sin x=\sqrt{3}-\sin x\ in\ the\ interval\ \left[0,\ 2\pi\right).$

a)

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

b)

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

c)

$0\ \&\ \pi$

d)

$\frac{\pi}{3}\ \&\ \frac{2\pi}{3}$

15.

$Find\ all\ solutions\ of\ \sin\left(x+\frac{\pi}{4}\right)+\sin\left(x-\frac{\pi}{4}\right)=1\ in\ the\ interval\ \left[0,\ 2\pi\right).$

a)

$0\ \&\ \pi$

b)

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

c)

$\frac{\pi}{3}\ \&\ \frac{2\pi}{3}$

d)

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

16.

$What\ is\ the\ amplitude\ for\ y=-4\cos\left(2x\ +\frac{\pi}{2}\right)?$

a)

$2$

b)

$\pi$

c)

$-4$

d)

$4$

17.

$What\ is\ the\ period\ for\ y=-4\cos\left(2x+\frac{\pi}{2}\right)?$

a)

$-4$

b)

$4$

c)

$2$

d)

$\pi$

18.

$What\ is\ the\ phase\ shift\ for\ y=5\sin\left(x+\frac{\pi}{2}\right)?$

a)

$\pi\ Left$

b)

$\frac{\pi}{2}\ Right$

c)

$\frac{\pi}{2}\ Left$

d)

$5\ Up$

19.

$Graph\ y=\cos x.$

a)

b)

c)

d)

20.

$Graph\ y=2\sin x.$

a)

b)

c)

d)

21.

a)

$x=16.58$

b)

$x=17.57$

c)

$x=13.24$

d)

$x=29.19$

22.

a)

$\frac{3}{4}$

b)

$\frac{3}{5}$

c)

$\frac{4}{5}$

d)

$1\ \frac{1}{4}$

23.

a)

$\frac{\sqrt{95}}{7}$

b)

$\frac{\sqrt{95}}{12}$

c)

$7\sqrt{95}$

d)

$\frac{12}{7}$

24.

$A\ slide\ 4.1\ m\ long\ makes\ an\ angle\ of\ 27\degree\ with\ the\ ground.\ How\ high\ is\ the\ top\ of\ the\ slide\ above\ the\ ground?$

a)

$1.86\ m$

b)

$3.65\ m$

c)

$1.93\ m$

d)

$2.09\ m$

25.

a)

$\frac{adj.}{hyp.}$

b)

$\frac{opp.}{hyp.}$

c)

$\frac{hyp.}{adj.}$

d)

$\frac{opp.}{adj.}$

Honors Pre-Calculus Midterm Exam

Total questions: 25

Worksheet time: 25mins

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