Free Printable REVIEWER 2 - PRECALCULUS (STEM)

1.

What does the amplitude of a trigonometric function represent?

a)

The vertical shift of the graph

b)

The horizontal shift of the graph

c)

The maximum absolute value of the function's output

d)

The number of cycles completed in one period

2.

In the function $y=3\sin(2x-\frac{\pi}{4})$ , what is the amplitude?

a)

2

b)

3

c)

-3

d)

π/4

3.

Which of the following represents the period of the function $y=4\cos(3x)$ ?

a)

4

b)

3

c)

2π/3

d)

2π/4

4.

For the function $y=-2\cos(x+\frac{\pi}{2})$ , what is the phase shift?

a)

π/2 units to the left

b)

π/2 units to the right

c)

No phase shifts

d)

2π units to the left

5.

What is the range of the function $y=5+3\sin(x)$ ?

a)

[2, 8]

b)

[3, 8]

c)

[-2, 8]

d)

[3, 5]

6.

A Ferris wheel completes a full revolution every 60 seconds. The height of a passenger can be modeled by the function $h(t)=30\sin(\pi/30t)+40$ , where $h(t)$ represents the height in feet above the ground and t represents time in seconds. What is the amplitude of this function?

a)

30 feet

b)

40 feet

c)

10 feet

d)

70 feet

7.

Which of the following statements is true about trigonometric identities?

a)

They are true for specific values of the variables.

b)

They are true for all values of the variables within the domain.

c)

They have limitations in their validity.

d)

They are only true for integers.

8.

Determine if the equation $\sin^2(x)+\cos^2(x)=1$ is an identity or a conditional equation.

a)

Identity

b)

Conditional equation

c)

Neither

d)

Both

9.

Which of the following equations is an identity?

a)

$\tan(x)=\frac{\sin(x)}{\cos(x)}$

b)

$\sin(x)+\cos(x)=\cos(x)$

c)

$\cot(x)=\frac{1}{\tan(x)}$

d)

$\sin(2x)=2\sin(x)\cos(x)$

10.

Determine if the equation $\tan(x)-\frac{\sin(x)}{\cos(x)}=\sec(x)$ is an identity or a conditional equation.

a)

Identity

b)

Conditional equation

c)

Neither

d)

Both

11.

Which of the following equations represents a conditional equation?

a)

$\sin(x)=\frac{1}{\csc(x)}$

b)

$\cos(2x)=1-2\sin x^2(x)$

c)

$\cot(x)=\frac{\cos(x)}{\sin(x)}$

d)

$\tan x^2(x)+1=\sec x^2(x)$

12.

Determine if the equation $\cos(x)∙(\cos(x)+\sin(x))=\cos^2(x)-\sin^2(x)$ is an identity or a conditional equation.

a)

Identity

b)

Conditional equation

c)

Neither

d)

Both

13.

Which identity can be used to simplify $\cos^2(x)-\sin^2(x)$ ?

a)

Pythagorean identity

b)

Double-angle identity for cosine

c)

Double-angle identity for sine

d)

Half-angle identity for cosine

14.

Simplify the expression $\frac{\sin(x)}{\cos(x)}∙\frac{1+\sin(x)}{\cos(x)+1}$ using trigonometric identities. What is the simplified form?

a)

$\tan(x)$

b)

$\cot(x)$

c)

$\sec(x)$

d)

$\csc(x)$

15.

Which identity can be used to simplify $\cos(3x)$ in terms of $\cos(x)$ ?

a)

Double-angle identity for cosine

b)

Triple-angle identity for cosine

c)

Half-angle identity for cosine

d)

Sum-to-product identity for cosine

16.

Simplify the expression $\sin^4(x)-\cos^4(x)$ using trigonometric identities. What is the simplified form?

a)

$\sin(2x)$

b)

$\cos(2x)$

c)

$1-2\sin^2(x)$

d)

$2\cos^2(x)-1$

17.

Which trigonometric identity can be used to rewrite $\tan^2(x)$ in terms of $\sec^2(x)$ ?

a)

Pythagorean identity

b)

Reciprocal identity for tangent

c)

Double-angle identity for tangent

d)

Power-reduction identity for tangent

18.

Simplify the expression $\frac{\sin(x)}{1+\cos(x)}$ using trigonometric identities. What is the simplified form?

a)

$\tan(x)$

b)

$\cot(x)$

c)

$\sec(x)$

d)

$\csc(x)$

19.

A ladder leans against a wall forming an angle of 60° with the ground. If the foot of the ladder is 6 meters away from the wall, what is the length of the ladder?

a)

$3\sqrt{3}meters$

b)

$6\sqrt{3}meters$

c)

12 meters

d)

6 meters

20.

An airplane is flying at an altitude of 5000 meters. If the angle of elevation to the airplane from two radar stations located 10 kilometers apart on the ground is 30° and 45° respectively, what is the difference in their distances to the airplane?

a)

$5\sqrt{3}kilometers$

b)

5 kilometers

c)

5 meters

d)

10 kilometers

21.

A Ferris wheel has a diameter of 50 meters and makes one full revolution every 60 seconds. If a person's seat is located at a distance of 20 meters from the center of the wheel, express the vertical height of the person above the ground in terms of time using trigonometric functions.

a)

$20\sin(\frac{\pi}{30t})meters$

b)

$20\cos(\frac{\pi}{30t})meters$

c)

$20\sin(\frac{\pi}{60t})meters$

d)

$20\cos(\frac{\pi}{60t})meters$

22.

A ship leaves a harbor and travels due east. At a certain point, it changes its course to 45° north of east and continues for 10 kilometers. What is the displacement of the ship from the harbor?

a)

$5\sqrt{2}kilometers$

b)

10 kilometers

c)

$10\sqrt{2}kilometers$

d)

5 kilometers

23.

The length of a shadow cast by a pole is found to be 15 meters when the angle of elevation of the sun is 45°. What is the height of the pole?

a)

10 meters

b)

15 meters

c)

20 meters

d)

25 meters

24.

A wire is attached to the top of a pole that is 20 meters high. When stretched taut, the wire makes an angle of 30° with the ground. What is the length of the wire?

a)

10 meters

b)

20 meters

c)

30 meters

d)

40 meters

25.

A tower casts a shadow that is 20 meters long. If the angle of elevation of the sun is 30° what is the height of the tower?

a)

10 meters

b)

20 meters

c)

30 meters

d)

40 meters

26.

Solve for x in the equation $2\sin(x)+\sqrt{3}=0$ where $x$ is in the interval $[0,2\pi]$ .

a)

$x=\frac{5\pi}{3}$

b)

$x=\frac{2\pi}{3}$

c)

$x=\frac{\pi}{3}$

d)

No solution in the given interval

27.

A ladder is 15 meters long and leans against a wall. If the foot of the ladder is 9 meters away from the base of the wall, what is the measure of the angle between the ladder and the ground?

a)

$30°$

b)

$45°$

c)

$60°$

d)

$75°$

28.

Determine the value of $x$ satisfying the equation $\cos⁡^{-1}(x)=\frac{\pi}{3}$ .

a)

$x=\frac{1}{2}$

b)

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

c)

$x=\frac{\sqrt{2}}{2}$

d)

$x=\frac{1}{\sqrt[]{2}}$

29.

If $2\tan⁡(\theta)=\sqrt[]{3}$ , what is the value of $θ$ in the interval $[0,\pi]$ ?

a)

$θ=\frac{\pi}{6}$

b)

$θ=\frac{\pi}{3}$

c)

$θ=\frac{\pi}{4}$

d)

$θ=\frac{\pi}{2}$

30.

A wheel with a radius of 10 meters rolls 30 meters along the ground. How many complete revolutions does the wheel make?

a)

3

b)

6

c)

9

d)

12

31.

Consider the function $f(x)=3\sin(2x−\frac{\pi}{3})$ . What is the amplitude, period, and phase shift of the function?

a)

Amplitude: 3, Period: π, Phase Shift: π/6

b)

Amplitude: 3, Period: π/2, Phase Shift: π/3

c)

Amplitude: 2, Period: π, Phase Shift: π/3

d)

Amplitude: 3, Period: π, Phase Shift: π/3

32.

A Ferris wheel has a diameter of 50 meters and completes one full rotation in 60 seconds. The height of a rider on the Ferris wheel as a function of time can be modeled by $h(t)=25\sin(\frac{\pi}{30}t−\frac{\pi}{2})+30$ , where $t$ is the time in seconds and $h(t)$ represents the rider's height above the ground. What does the equation represent?

a)

The rider's height on the Ferris wheel at time $t$ seconds

b)

The rider's distance from the center of the Ferris wheel at time $t$ seconds

c)

The rider's velocity on the Ferris wheel at time $t$ seconds

d)

The rider's acceleration on the Ferris wheel at time $t$ seconds

33.

For the function g(x)=4cos(3x+π/4), which of the following statements is correct? $g(x)=4\cos(3x+\frac{\pi}{4})$

a)

The amplitude is 3 and the period is 2π/3

b)

The amplitude is 4 and the period is 2π/3

c)

The amplitude is 4 and the period is π/3

d)

The amplitude is 3 and the period is π/3

34.

Which of the following equations is an identity?

a)

$3x+2=2x+5$

b)

$5x−7=2x−7$

c)

$4x−9=4x+5$

d)

$2x+3=x+4$

35.

Identify the equation that represents a conditional equation:

a)

$2x−7=3x−9$

b)

$5x+2=2x+5$

c)

$4x−9=4x−9$

d)

$3x+2=3x+5$

36.

Determine the identity equation among the following:

a)

$2x−4=2(x−2)$

b)

$3x+5=x+8$

c)

$4x−3=4x−3$

d)

$5x+2=5x-2$

37.

Simplify the expression $\frac{\sin^2x-\cos^2x}{\sin x\cos x}$ and determine its equivalent form:

a)

$\tan x$

b)

$\cot x$

c)

$\sec^2x$

d)

$\csc^2x$

38.

Given the expression $\frac{\cos\ x}{1-\sin x}$ simplify it in terms of secant and tangent:

a)

$\sec x+\tan x$

b)

$\sec x-\tan x$

c)

$\cot x-\csc x$

d)

$\tan x-\sec x$

39.

Determine the value of $\frac{\sin⁡^2θ}{1−\cos^2θ}$ in terms of other trigonometric functions:

a)

$\cot\theta$

b)

$\sec\theta$

c)

$\csc\theta$

d)

$\tan\theta$

40.

A rope is tied from the top of a 15-meter pole to a point on the ground, 9 meters away from the base of the pole. What is the angle formed between the rope and the ground?

a)

30 degrees

b)

45 degrees

c)

60 degrees

d)

75 degrees

41.

The period of the graph shown is (a)

42.

Choose the correct equation for the graph.

a)

$y=\cos\left(x\right)$

b)

$y=\sin\left(x\right)$

c)

$y=\cot\left(x\right)$

d)

$y=\tan\left(x\right)$

e)

$y=\csc\left(x\right)$

43.

Choose the correct equation for the graph.

a)

$y=\sin\left(x\right)$

b)

$y=\sec\left(x\right)$

c)

$y=\csc\left(x\right)$

d)

$y=\tan\left(x\right)$

e)

$y=\cos\left(x\right)$

44.

Choose the correct equation for the graph.

a)

$y=\cot\left(x\right)$

b)

$y=\sec\left(x\right)$

c)

$y=\csc\left(x\right)$

d)

$y=\tan\left(x\right)$

e)

$y=\cos\left(x\right)$

45.

Choose the correct equation for the graph.

a)

$y=\sin\left(x\right)$

b)

$y=\sec\left(x\right)$

c)

$y=\csc\left(x\right)$

d)

$y=\tan\left(x\right)$

e)

$y=\cot\left(x\right)$

46.

Sine or Cosine?

a)

y=sinx

b)

y=cosx

c)

what's the difference?

d)

it's all waves to me

47.

Graph the given trigonometric function. $g(x)=-\sin(x+\frac{\pi}{3})$

48.

Graph the given trigonometric function. $g(x)=-2\cos(x)$

49.

Graph the given trigonometric function. $f(x)=\sin(2x-\pi)$

50.

Graph the given trigonometric function. $h(x)=3\sin(x)$

51.

How has your understanding and perception of Precalculus evolved from the 1st quarter to the 2nd quarter? Additionally, can you use an adjective or a word to describe your experience with me as your teacher? Are there specific teaching methods or experiences that have played a role in shaping your learning journey?

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REVIEWER 2 - PRECALCULUS (STEM)

Total questions: 51

Worksheet time: 38mins

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