Free Printable CFE Review 2

1.

If

\lim_{x\rightarrow a}\ f\left(x\right)=l

and

\lim_{x\rightarrow a\ }f\left(x\right)=m,

then

a)

l $\ne$ m

b)

l=m

c)

l>m

d)

l<m

2.

a)

Function

b)

Not a Function

3.

What is the domain of the function?

a)

(3, ∞)

b)

[-3, ∞)

c)

(-∞, 4]

d)

(-∞, 4)

4.

What is the RANGE?

a)

{-3, 3]

b)

all real numbers

c)

[-4, 5]

d)

[-4, ∞)

5.

What is the range?

a)

[-∞, +∞]

b)

[-2, 2]

c)

(-∞, ∞)

d)

[0, 2]

6.

For a function,

f\left(x\right)

to be continuous at a point

x=c

, which of the following conditions must be met:

i.

\lim_{x\rightarrow c}f\left(x\right)

must exist

ii.

f\left(c\right)

must be defined

iii.

\lim_{x\rightarrow c}f\left(x\right)=f\left(c\right)

a)

i only

b)

i and ii only

c)

iii only

d)

i, ii, and iii

7.

True or false: The piece-wise function, $f\left(x\right)$ , is continuous at $x=2$ : $f\left(x\right)=\sqrt{x+7},\ x\le2$

$f\left(x\right)=x^2-1,\ x>2$

a)

True

b)

False

8.

True or false: The piece-wise function, $f\left(x\right)$ , is continuous at $x=0$ : $f\left(x\right)=\frac{\sin x}{x},\ x<0$

$f\left(x\right)=\cos x,\ \ x\ge0$

a)

True

b)

False

9.

Which function below has a non-removable, infinite discontinuity at $x=-1$ ?

a)

$y=\frac{1}{x^2+1}$

b)

$y=\frac{x}{x+1}$

c)

$y=\frac{\left|x+1\right|}{x+1}$

d)

$y=\frac{x^2-1}{x+1}$

10.

Which type of discontinuity is shown in the graph?

a)

removable

b)

non-removable, infinite

c)

non-removable, jump

d)

it is continuous everywhere

11.

What is the limit?

a)

Infinity

b)

20

c)

DNE

d)

12

12.

What is the limit?

a)

DNE

b)

Infinity

c)

6

d)

12

13.

a)

0

b)

-1

c)

infinity

d)

-infinity

14.

a)

Does not exist

b)

2

c)

0

d)

1

15.

Simplify

a)

A.4x³/(x+2)

b)

B.4x³/(x+10)

c)

C.2x³/(5x+1)

d)

D. 2x³/(x+5)

16.

Simplify.

a)

(m+6)/(m-3)

b)

7/(m-3)

c)

7(m+6)

d)

(m-3)

17.

Simplify $\frac{8n}{n-3}+\frac{3n}{5n-6}$

a)

$\frac{43n^2-9}{\left(5n-6\right)\left(n-3\right)}$

b)

$\frac{11n}{6n-9}$

c)

$\frac{43n^2-57n}{\left(n-3\right)\left(5n-6\right)}$

d)

$\frac{8n+3n}{n-3+5n-6}$

18.

$2-\frac{7}{x^2+x-30}$ Simplify

a)

$\frac{2x^2-2x-67}{\left(x-6\right)\left(x+5\right)}$

b)

$\frac{-5}{\left(x+6\right)\left(x-5\right)}$

c)

$\frac{-5}{x^2+x-30}$

d)

$\frac{2x^2+2x-67}{\left(x+6\right)\left(x-5\right)}$

19.

Simplify $\frac{1}{n+5}\times\frac{n^2+2n-15}{n-8}$

a)

$\frac{n-3}{n-8}$

b)

$\frac{n-3}{\left(n+5\right)\left(n-8\right)}$

c)

$\frac{n^2+2n-15}{\left(n+5\right)\left(n-8\right)}$

d)

$\frac{n^2+2n-14}{2n-3}$

20.

$\frac{\frac{x+1}{x^2}}{\frac{1}{x}+\frac{x+1}{x}}$ Simplify

a)

$\frac{\frac{x+1}{x^2}}{\frac{x+2}{x}}$

b)

$\frac{x+1}{x\left(x+2\right)}$

c)

$\frac{2x+2}{x\left(x+2\right)}$

d)

$\frac{1}{x}$

21.

(2x³ - 5x² + 3x + 7) ÷ (x - 2)

a)

2x³ - x² + x + 9

b)

2x² - x + 1

c)

2x² - x + 1 + 9/x-2

d)

2x² - 9x - 15 - 23/x-2

22.

(3x³ - 2x² - 7x + 6) ÷ (x + 1)

a)

3x³ - 5x² - 2x + 8

b)

3x² + x - 6

c)

3x² - 5x - 2 + 8/x+1

d)

3x³ + x² - 6x

23.

Let f(x) = 4x^2 -33x -27. Is k = 9 a zero of the function?

a)

yes

b)

no

24.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

25.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

26.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

27.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

28.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

29.

What is the directrix of the parabola
(x - 4)²= 8(y + 3)?

a)

y = - 3

b)

x= 5

c)

y= - 5

d)

y= 2

30.

True or False?
When the x-part is squared, the parabola opens up or down.

a)

True

b)

False

31.

What is the center of the ellipse?

a)

(0, 0)

b)

(1, 5)

c)

(1, 0)

d)

(0, 1)

32.

What direction does the parabola open?
(y-9)²= -40(x+4)

a)

Up

b)

Down

c)

Left

d)

Right

33.

Write an equation for the ellipse with each set of characteristics. Then answer the question.
Vertices ( 4, 3), (4, - 9)
Length of minor axis is 8
what is the center of this ellipse?

a)

(4, 6)

b)

( - 4, 3)

c)

(6, 4)

d)

(4, -3)

34.

sin x =

a)

cos x

b)

1/cosx

c)

1/secx

d)

1/cscx

35.

Rewrite tan(x) in terms of sin(x) and cos(x).

a)

tan(x) = cos(x)/sin(x)

b)

tan(x) = 1/cot(x)

c)

tan(x) = sin(x)/cos(x)

d)

tan(x) = opp/adj

36.

Please select the correct solution

a)

csc² x

b)

cot² x

c)

sin² x

d)

sec² x

37.

Simplify

a)

sin²θ

b)

cosθ

c)

tanθ

d)

1- sin²θ

38.

Simplify

a)

-1

b)

sin θ

c)

csc θ

d)

1

39.

How many radians does a circle have?

a)

360 degrees

b)

2pi radians

c)

pi radians

d)

^{2 radians}

40.

Convert π radians to degrees.

a)

90⁰

b)

180⁰

c)

360⁰

d)

60⁰

41.

Convert 100⁰ to radians

a)

5π/9

b)

π/2

c)

5π/8

d)

5π/6

42.

What is 7π/4 radians in degrees?

a)

300

b)

135

c)

315

d)

45

43.

Find the arc length. Leave your answer in terms of π.

a)

7/4π

b)

7/2π

c)

1/8π

d)

45π

44.

Alison is jogging on a circular track that has a radius of 140 feet. She runs along the track from point R to point N, a distance of 230 feet. Find to the nearest degree, the measure of minor arc RN.

a)

47

b)

74

c)

94

d)

123

45.

Find the length of the arc to 2dp

a)

9.42cm

b)

150.80cm

c)

4.71cm

d)

18.85cm

46.

Use a double-angle or half-angle identity to find the exact value of each expression

cos θ = 4/5 and 270° < θ < 360°Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

47.

Use a double-angle identity to find the exact value of each expression
cos θ = 4/5 and 270° < θ < 360°
Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

48.

Use a double-angle or half-angle identity to find the exact value of each expression
cos θ = 4/5 and 270° < θ < 360°Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

49.

If you are given the opposite side and hypotenuse, which trig function should you use?

a)

sine

b)

cosine

c)

tangent

d)

cotangent

50.

a)

24/32

b)

32/24

c)

32/40

d)

24/40

51.

Choose the correct ratio.

a)

cos(33)=x/14

b)

sin(33)=x/14

c)

cos(33)=14/x

d)

sin(33)=14/x

52.

Choose the correct ratio.

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

53.

A vector is a ray with both ____________ and _____________.

a)

Wings and halos

b)

Space and time

c)

Direction and magnitude

d)

Radicals and exponents

54.

Find the magnitude.

a)

0

b)

5

c)

-5

d)

4

55.

Find the magnitude of the vector <2, -3>.

a)

√11

b)

13

c)

√-4

d)

√13

56.

Find the direction of the vector <-3, -5>.

a)

59.03°

b)

239.03°

c)

210.96°

d)

120.96°

57.

Find the dot product of <1, -2> and <3, 2>.

a)

1

b)

<3, -4>

c)

<4, 0>

d)

-1

58.

Find the angle between vectors <1,3> and <2,-5>.

a)

40.24°

b)

49.76°

c)

139.76°

d)

92.57°

59.

How do you know if two vectors are orthogonal?

a)

Their sum is 0.

b)

The dot product is 1.

c)

The angle between them is 0°.

d)

The dot product is 0.

60.

Given an initial point R ( -12, 4 ) and terminal point S ( 28, -17 ), find the component form of the vector RS.

a)

〈14,-13〉

b)

〈-14,13〉

c)

〈-40,-21〉

d)

〈40,-21〉

61.

Given u = <3, 7> and v =<-5, 4>, find 2v - 3u

a)

<21, 2>

b)

<-19, -13>

c)

<-15, 3>

d)

23

62.

Find the unit vector in the direction of <4, -3>

a)

<⅘, -⅗>

b)

<0.57, -0.43>

c)

<1, -1>

d)

-¾

63.

How many relative maximums does this function have?

a)

1

b)

2

c)

3

d)

4

64.

Find x, if F(x) = 2.

a)

4

b)

-2

c)

-6

d)

8

65.

What is/are the increasing interval(s) for the function shown?

a)

$\left(-3,\ 1\right)$

b)

$\left(4,\ 8\right)$

c)

$\left(-\infty,1\right)\ and\ \left(-3,\ 1\right)$

66.

Choose the best answer to describe boundedness of the graph.

a)

above

b)

bounded

c)

below

d)

not bounded

67.

Use the Law of Sines to solve for BC

a)

33

b)

24

c)

12

d)

29

68.

What is the measure of angle A?

a)

58 degrees

b)

61 degrees

c)

78 degrees

d)

74 degrees

69.

Which one is the easy way to remember trigonometric ratios?

a)

Sah Coh Toa

b)

Soh Cah Toa

c)

Soh Cah Tao

d)

Soh Ceh Toa

70.

What is sin^-1(1/2)?

a)

150

b)

120

c)

60

d)

30

71.

Find QR

a)

34.7 km

b)

2.2 km

c)

13.74

d)

31.1 km

72.

Find XZ

a)

16.004 meters

b)

544.165 meters

c)

34.7 meters

d)

1204.165 meters

73.

Find the inverse
f(x)=2x-2

a)

f^-1(x)=1/2x+1

b)

f^-1(x)=-2-1/2x

c)

f^-1(x)=-7/3x-20/3

d)

2-2/5x

74.

The inverse has been reflected over which line?

a)

y = x

b)

y =1

c)

y = 0

d)

y = x + 1

75.

What's the best description?

a)

They are both functions, but not inverse functions.

b)

They are reflected over y=x, but they are not both functions.

c)

They are not reflected over y=x, and they are not both functions.

d)

They are inverse functions.

76.

If $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then $\left(f+g\right)\left(x\right)=$

a)

$5x^2+1$

b)

$5x^2-3$

c)

$6x+1$

d)

$6x-3$

77.

If $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then $\left(f-g\right)\left(x\right)=$

a)

-4x - 3

b)

-4x +1

c)

6x + 1

d)

6x - 3

78.

If $f\left(x\right)\ =\ x-1$ and $g\left(x\right)=5x-2$ , then $\left(f\cdot g\right)\left(x\right)=$

a)

$5x-3$

b)

$5x^2+2$

c)

$5x^2-7x+2$

d)

$5x-7$

79.

If $f\left(x\right)\ =\ 3x^2-4$ and $g\left(x\right)=x^2-8x+4$ , then $\left(\frac{f}{g}\right)\left(x\right)=$

a)

$\frac{3x^2-4}{x^2-8x+4}$

b)

$\frac{x^2-8x+4}{3x^2-4}$

c)

$\frac{3x^2-1}{x^2-8x}$

d)

$\frac{1}{-4x}$

80.

If $f\left(x\right)\ =\ x+5$ and $g\left(x\right)=3x-7$ , then $\left(f\circ g\right)\left(x\right)=$

a)

$3x-2$

b)

$3x+8$

c)

$3x^2+8x-35$

d)

$3x-12$

81.

Convert from polar coordinates, (6, 5π/4) to rectangular coordinates.

a)

(-3√2, -3√2)

b)

(3√2, 3√2)

c)

(6.0, 0.4)

d)

(-6.0, -0.4)

82.

Convert the rectangular equation to a polar equation.
x=36

a)

r=36cosΘ

b)

r=36cscΘ

c)

r=36secΘ

d)

r=6

83.

Write the polar equation into a rectangular equation?
r=2sinΘ+2cosΘ

a)

x²+y²=2x+2y

b)

r=2x+2y

c)

r=x²+y²

d)

x²-y²=2x-2y

84.

$\left(2-4i\right)\left(-6+4i\right)$

(a)

85.

What does i²= ?

a)

1

b)

-1

c)

√-1

d)

√1

86.

(2i)(3i)

a)

5i

b)

-5

c)

6i²

d)

-6

87.

What is the period of the equation shown?

a)

3π

b)

2π

c)

3π / 2

d)

2π / 3

88.

What is the period of the equation shown?

a)

2π

b)

4π

c)

π / 2

d)

π

89.

Describe the horizontal shift.

a)

left π / 2

b)

left 2π

c)

right 2π

d)

right π / 2

90.

Describe the horizontal and vertical shifts.

a)

right 3π/2 , down 5

b)

left 2π/3 , up 5

c)

right 2π/3 , up 5

d)

left 2π , down 5

91.

What is the equation of the graph shown?

a)

y = 2sin(θ + π/2) + 2

b)

y = 2cos(θ - π/2) + 2

c)

y = 2sin(θ - π/2) + 2

d)

y = 2cos(θ + π/2) + 2

92.

What is the equation of the graph shown?

a)

y = tan θ

b)

y = sin θ

c)

y = cos θ

d)

y = -5tan θ

93.

The __________ represents half the distance between the max and min of a sine or cosine graph.

a)

Period

b)

Frequency

c)

Extreme Values

d)

Amplitude

94.

The period of a sine or cosine graph can be found by ....

a)

It's always 2π

b)

2π/B

c)

B(2π)

d)

2π+B

95.

What is the midline for
y=2cos(1/3x +π/6) +2

a)

1/3

b)

-2

c)

+2

d)

4

96.

What is the value of sine at 30

a)

1/2

b)

√3 / 2

c)

0

d)

√2 ⁄ 2

97.

sin 2π/3

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

98.

a)

√3/3

b)

√3

c)

1

d)

undefined

99.

Simplify

a)

(-10+6i)/17

b)

(-8+15i)/17

c)

(-23+36i)/25

d)

(-21+33i)/34

100.

Simplify

a)

(-8i+1)/10

b)

(8+i)/11

c)

(34-77i)/109

d)

(21-38i)/58

101.

Factor the Trinomial:
x² - 8x + 15

a)

(x + 5) ( x + 3)

b)

(x - 5) (x - 3)

c)

(x + 15) (x - 1)

d)

(x - 7) (x - 8)

102.

Factor:
x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

103.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

104.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

105.

Does Belle marry the Beast?

a)

Yes

b)

NO!!!!!

c)

NO he dies

d)

Yes but he turns into a prince

106.

What color does a reindeer's eyes turn in the winter?

a)

Red

b)

White

c)

Black

d)

Blue

107.

What does a tiger's skin look like?

a)

Orange

b)

Black

c)

White

d)

Striped

108.

A snail can sleep for up to _________ at a time.

a)

10 minutes

b)

3 years

c)

10 years

d)

3 hours

109.

A rhinoceros's horn is made of _________

a)

Ivory

b)

Wood

c)

Hair

d)

The same material as human toenails

110.

What's the capital of Italy?

a)

Rome

b)

Moscow

c)

Helsinki

d)

Boudapest

111.

a)

17

b)

32

c)

27

d)

22

112.

How many "S" do you see ?

a)

6

b)

8

c)

7

d)

5

CFE Review 2

Total questions: 112

Worksheet time: 5hrs 7mins

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