Free Printable precalc review 1 (all)

1.

a)

-1

b)

1

c)

$2\pi$

d)

does not exist

2.

What is the coterminal angle for -300?

a)

300

b)

-60

c)

-660

d)

60

3.

what is the amplitude of the graph shown

a)

1

b)

2

c)

3

d)

4

4.

What is the equation of the graph?

a)

y = -2cos x - 3

b)

y = 2cos x + 3

c)

y = -3cos x - 2

d)

y = -2sin x - 3

5.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

6.

Find the Area of a triangle if a=9cm, b=4cm, and C=98degrees

a)

16.7cm²

b)

35.6cm²

c)

17.8cm²

d)

not a triangle

7.

What is the measure of angle A?

a)

50 degrees

b)

60 degrees

c)

78 degrees

d)

74 degrees

8.

Find angle T

a)

62.2 degrees

b)

53.1 degrees

c)

59.5 degrees

d)

64.7 degrees

9.

sec 3π/2

a)

0

b)

undefined

c)

1

d)

-1

10.

sin π/4

a)

√2∕2

b)

1/2

c)

√3/2

d)

0

11.

Solve on the interval [0,360)
2cosx-1=0

a)

60,120

b)

60, 240

c)

120, 240

d)

60, 300

12.

a)

5π∕6 + 2πn, 7π/6 + 2πn

b)

π/3 + 2πn, 2π/3 + 2πn

c)

5π/12 +πn, 7π/12 +πn

d)

2π/3 +πn, 4π/3 +πn

13.

a)

cos²x

b)

sin²x

c)

cot²x

d)

tan²x

14.

Convert from radians to degrees: 7π ∕ 4

a)

330°

b)

45°

c)

315°

d)

75°

15.

Convert from degrees to radians: 135°

a)

2π ∕ 3

b)

3π ∕ 4

c)

5π ∕ 4

d)

3π ∕ 5

16.

Find the reference angle for an angle measuring θ = 125⁰

a)

25⁰

b)

35⁰

c)

45⁰

d)

55⁰

17.

Find the reference angle for an angle measuring θ = 7π / 5

a)

π / 5

b)

2π /5

c)

3π / 5

d)

4π / 5

18.

Find the length of the bold arc.Leave pi in your answer.

a)

5688π ft

b)

15.8π ft

c)

150.4π ft

d)

54,150 ft

19.

What is the exact value of sin 210°

a)

-1/2

b)

-√3/2

c)

1/2

d)

√3/2

20.

sec 3π/2

a)

0

b)

undefined

c)

1

d)

-1

21.

Write the equation of a circle with center (2 , -1) and radius 4.

a)

(x + 2)² + (y - 1)²= 4

b)

(x - 2)² + (y + 1)² = 16

c)

(x + 2)² + (y + 1)² = 4

d)

(x - 2)² + (y - 1)² = 16

22.

Give the limit as
x->∞ : (2x - 1) / (4x + 2)

a)

-½

b)

½

c)

0

d)

∞

23.

Write the equation of the ellipse with center (2, -3) , vertex (2 , -8) and focal (2 , -4).

a)

( x +2 )² / 25 (y -3 )² = 1

b)

(x - 2)² + (y + 3)²/ 25 = 1

c)

(x - 2)/24+ (y+3) / 25 = 1

d)

(x -2)²/24+(y +3)²/25 =1

24.

Find angle T

a)

62.2 degrees

b)

53.1 degrees

c)

59.5 degrees

d)

64.7 degrees

25.

#1 Write an equation of a hyperbola with a center at (-4, 6), vertices at (-8, 6) and (0, 6), and foci at (1, 6) and (-9, 6).

a)

A

b)

B

c)

C

d)

D

26.

#4 Convert from rectangular to polar.

a)

A

b)

B

c)

C

d)

D

27.

#13 Graph

a)

A

b)

B

c)

C

d)

D

28.

cos 5π/6

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

29.

Solve on the domain [0, 2π)
4sin²x = 3

a)

π/6, 11π/6

b)

π/3, 2π/3

c)

π/6, 5π/6, 7π/6, 11π/6

d)

π/3, 2π/3, 4π/3, 5π/3

30.

Solve on the domain [0, 2π)
2sin x cos x = √2 cos x

a)

π/2, 3π/2

b)

0, π/4, 3π/4

c)

π/2, 3π/2, π/4, 3π/4

d)

No solution

31.

What is the equation of graph?

a)

y = sin 5x

b)

y = cos 5x

c)

y = 5 sin x

d)

y = 5 cos x

32.

Determine an equation for this graph:

a)

y=csc(x)

b)

y=sec(x)

c)

y=cot(x)

d)

y= tan(x)

33.

Which is an equation of the cosine function with an amplitude of 2, period of Π, phase shift of Π/2?

a)

y= -2cos(x/2 - ∏/4)

b)

y= 2cos (x/2 + ∏)

c)

y= 2cos (2x-∏)

d)

y= -2cos(2x-∏/2)

34.

1+cot²θ=

a)

csc²θ

b)

1

c)

sec²θ

d)

sec²θ - 1

35.

tan²θ=

a)

sec²θ - 1

b)

csc²θ - 1

c)

1 - sin²θ

d)

1 - cos²θ

36.

$\frac{\sin x\cos x}{1-\cos^2x}=$

a)

$\cos x$

b)

$\sin x$

c)

$\cot x$

d)

$\tan x$

37.

$\cos75^o\cos10^o-\sin75^{o\ }\sin10^o$ is equivalent to

a)

$\sin\ 85\degree$

b)

$\sin\ 65\degree$

c)

$\cos\ 85\degree$

d)

$\cos\ 65\degree$

38.

Simplify the trig expression.

a)

tan²x

b)

-tan²x

c)

cot²x

d)

cos²x*sin²x

39.

Solve equation for $0\le\theta<2\pi$ .
$3\sin^2\theta=7\sin^2\theta+4\sin\theta+1$

a)

$\theta=\frac{7\pi}{6}$

b)

$\theta=0,\frac{\pi}{3},\frac{5\pi}{3}$

c)

$\theta=\frac{3\pi}{4},\frac{7\pi}{4}$

d)

$\theta=\frac{7\pi}{6},\frac{11\pi}{6}$

40.

Solve equation for $0\le\theta<2\pi$ .
$\sec^2\theta+3=2\sec\theta+2$

a)

$\theta=0,\frac{\pi}{2},\frac{2\pi}{3},\frac{5\pi}{3}$

b)

$\theta=\frac{\pi}{3},\pi,\frac{5\pi}{3}$

c)

$\theta=\frac{\pi}{4}$

d)

$\theta=0$

41.

Solve for all values of x over the interval [0,2π]

a)

$\frac{3π}{4}and\ \frac{5π}{4}\$

b)

$\frac{π}{4}and\ \frac{3π}{4}$

c)

$\frac{π}{4},\frac{3π}{4},\frac{5π}{4}\ and\ \frac{7π}{4}$

d)

$\frac{\pi}{6}\ and\ \frac{5\pi}{6}$

42.

$2\cos^2x-3\cos\left(x\right)+1=0$ Solve on the interval $\left[0,2\pi\right]$

a)

$x=0,\frac{\pi}{3},\frac{5\pi}{3},2\pi$

b)

$x=\frac{\pi}{6},\frac{\pi}{2},\frac{11}{6}$

c)

$x=0,\pi,2\pi$

d)

$x=\frac{\pi}{6},\frac{\pi}{2},\frac{5\pi}{6}$

43.

Solve for all values of x over the interval [0,2π] : $\tan^{2\ }x\ -2\ \tan x\ =-1$

a)

$\frac{\pi}{4}$

b)

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

c)

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

d)

$\frac{\pi}{4}\ and\ \frac{7\pi}{4}$

44.

What are the asymptotes?

a)

x=1, x= 2, y =1, y= 2

b)

x= 2, x=-2, y = 1

c)

x=2 y =-1

d)

x=1 y =2, y =-2

45.

What is the horizontal asymptote to this function?

a)

y=4

b)

y=0

c)

y=-2

d)

y=1

46.

What (if any) holes exist?

a)

x=2

b)

x=2 and x=3

c)

x=-3

d)

x=3

47.

What is the domain?

a)

All real numbers

b)

All real numbers except 4

c)

All real numbers except 2

d)

All real numbers except 2 and -2

48.

Match the graph to the correct rational equation below.

a)

f(x)=x²/(x²+x-12)

b)

f(x)=4x²/(x²-x-12)

c)

f(x)=(2x²-2)/2x²

d)

f(x)=x/(x²+x-12)

49.

Eliminate the parameter. Convert the parametric equation to rectangular. x= 2+4t and y=-1+6t

a)

y=(3/2)x - 4

b)

t=(x-2)/4

c)

y=x - 4

d)

y= (2/3)x + 4

50.

What curve do the parametric equations make? What is the direction of motion?
x=1+3sint
y=-2+4cost

a)

Circle. Counterclockwise.

b)

Circle. Clockwise.

c)

Ellipse. Counterclockwise.

d)

Ellipse. Clockwise.

51.

What is the center and radius of the curve:
x=1+3cost
y=-2+3sint

a)

(-1,2) , r=3

b)

(-1,2) , r=9

c)

(1,-2) , r=3

d)

(1,-2) , r=9

52.

Eliminate the parameter from x(t) = t² + 5 and y(t) = t² - 4. Which of the following sketches results?

a)

Linear

b)

Quadratic

c)

Quartic

d)

Square Root

53.

Which point represents (3, 3π/4)?

a)

F

b)

E

c)

B

d)

A

54.

The parametric equation x = 3cos(t), y = 3sin(t) is a ..

a)

a circle

b)

an ellipse

c)

a hyperbolas

d)

parabola

55.

Eliminate the parameter. Convert the parametric equation to rectangular. x= t - 1 and y=t² - 2

a)

y=(x+1)² - 2

b)

t=x - 1

c)

x=t - 1

d)

y=t - 2

56.

Given the Rectangular Coordinate
(-7√2, 7√2), write the point as a polar coordinate for 0≤θ≤2π

a)

(14, π/4) , (-14, π/4)

b)

(14, 7π/4) , (14, π/4)

c)

(14, 5π/4) ,
(-14, 3π/4)

d)

(-14, 7π/4),
(14, 3π/4)

57.

Find the polar coordinates of the rectangular point. (0,3)

a)

(3,π)

b)

(3,0)

c)

(3,π/2)

d)

(3,-3π/2)

58.

What is the radius to the following rectangular point:

(5, 2)

a)

5

b)

2

c)

√29

d)

√27

59.

Write the complex number in rectangular form

6 (cos 330 + i sin 330)

a)

$3\sqrt{3}+3i$

b)

$-3\sqrt{3}+3i$

c)

$3\sqrt{3}-3i$

d)

$-3\sqrt{3}-3i$

60.

4i

Write the complex number in trig form
$r\left(\cos\theta+i\sin\theta\right)$

a)

4(cos 270 + i sin 270)

b)

4 (cos 0 + i sin 0)

c)

4 (cos 90 + i sin 90)

d)

4 (cos 180 + i sin 180)

precalc review 1 (all)

Total questions: 60

Worksheet time: 5hrs 0mins

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