Free Printable A2H Final Exam Practice

1.

Simplify.

a)

$\frac{x+6}{x+4}$

b)

$\frac{1}{x-5}$

c)

$\frac{x+6}{x+5}$

d)

$\frac{x+6}{x-5}$

e)

$\frac{x+6}{\left(x+5\right)\left(x-4\right)}$

2.

Subtract

$\frac{x^2-3}{2x+7}-\frac{2x-5}{2x+7}$

a)

$\frac{x^2-2x-8}{2x+7}\ ,\ x\ne-\frac{7}{2}$

b)

$x^2-2x-8\ ,\ x\ne0$

c)

$x^2-2x+2\ ,\ x\ne0$

d)

$\frac{x^2-2x+2}{2x+7}\ ,\ \ x\ne-\frac{7}{2}$

3.

Add

$\frac{2x}{x^2-36}+\frac{x+4}{x+6}$

a)

$\frac{x^2-24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$

b)

$\frac{x^3+6x^2-24x}{\left(x^2-36\right)\left(x+6\right)}\ x\ne-6,\ 36$

c)

$\frac{x^2+2x-24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$

d)

$\frac{x^2+12x+24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$

4.

Subtract

$\frac{6}{x^2+4x-32}-\frac{x-5}{x-4}$

a)

$\frac{-x^2+3x-34}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-8,\ 4$

b)

$\frac{-x^2+3x-34}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-4,\ 8$

c)

$\frac{-x^2-3x+46}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-8,\ 4$

d)

$\frac{-x^2-3x+46}{\left(x+8\right)\left(x-4\right)}\ ,\ x\ne-4,\ 8$

5.

Simplify: $\frac{\frac{1}{k+2}}{\frac{5}{k^2-4}}$

a)

$\frac{k-2}{5}$

b)

$\frac{k+2}{5}$

c)

$\frac{5}{k-2}$

d)

$k-2$

6.

Simplify: $\frac{\frac{6-y}{6}}{\frac{1}{6}-\frac{1}{y}}$

a)

-y

b)

y

c)

$-\frac{6}{y}$

d)

$-\frac{1}{y}$

7.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 2

d)

y = 4

8.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1

d)

y = 9

9.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1/2

d)

y = 1

10.

What's the vertical asymptote of the function?

a)

x = -9

b)

x = 9

c)

x = 3 , x = -3

d)

x = 3

11.

What's the vertical asymptote of the function?

a)

x = 5

b)

x = 0

c)

x =5 , x = -5

d)

x = 25

12.

What's the vertical asymptote of the function?

a)

x = 4

b)

x = 16

c)

x = 4 , x = -4

d)

No vertical asymptote

13.

What are the x-intercepts?

a)

x= 2/3

b)

x= 4, x = -2

c)

x= -8, x = 1

d)

x= -4, x = 2

14.

What are the coordinates of the hole, if one exists.

a)

(-1, -2)

b)

(-1, ½)

c)

(-1, -½)

d)

there isn't one

15.

Find the x-intercept(s), if one exists.

a)

(1, 0)

b)

(-1, 0)

c)

(1, 0), (-1, 0)

d)

(0, 0), (1, 0)

16.

What is the equation of the slant asymptote?

a)

y = x + 1

b)

y = x + 2

c)

y = x + 3

d)

y = x

17.

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

State the asymptotes as limits

a)

$\lim_{x\rightarrow\pm\infty}\ f\left(x\right)=-1$ , $\lim_{x\rightarrow5^+}f\left(x\right)=\infty$ , $\lim_{x\rightarrow5^-}f\left(x\right)=-\infty$

b)

$\lim_{x\rightarrow5^{-\ }}f\left(x\right)=\infty$ , $\lim_{x\rightarrow5^+}f\left(x\right)=-\infty$ , $\lim_{x\rightarrow\infty^-}f\left(x\right)=-\infty$

c)

$\lim_{x\rightarrow\infty\ }f\left(x\right)=-1$ , $\lim_{x\rightarrow5^{\pm\ }}f\left(x\right)=\infty$ $\lim_{x\rightarrow\infty^-}f\left(x\right)=5$

18.

State the domain and range in words

f\left(x\right)=\frac{5x}{x+2}

a)

Domain: All real numbers excluding y= 5

Range: All real numbers excluding x= -2

b)

Domain: All real numbers excluding x= 2

Range: All real numbers excluding y= 5

c)

Domain: All real numbers excluding x= -2
Range: All real numbers excluding y= 5

19.

State vertical and horizontal asymptotes of the function as limits.

f\left(x\right)=\frac{5x}{x+2}

a)

$\lim_{x\rightarrow5^{\pm}}f\left(x\right)=\infty$ $\lim_{x\rightarrow\infty}f\left(x\right)=-2$ $\lim_{x\rightarrow5^-}f\left(x\right)=-\infty$

b)

$\lim_{x\rightarrow\infty}f\left(x\right)=-2$ $\lim_{x\rightarrow\infty^-}f\left(x\right)=5$

c)

$\lim_{x\rightarrow-2^+}f\left(x\right)=\infty$ $\lim_{x\rightarrow-2^-}f\left(x\right)=-\infty$ $\lim_{x\rightarrow\pm\infty}f\left(x\right)=5$

20.

Evaluate the following logarithm:

log₄16

a)

1

b)

-2

c)

2

d)

¹/₂

21.

Evaluate the following logarithm:

log₅5

a)

1

b)

0

c)

-1

d)

¹/₂

22.

Evaluate.
log₆(¹/₂₁₆)

a)

3

b)

¹/₃

c)

-¹/₃

d)

-3

23.

Rewrite log₂8 = 3 in exponential form

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

24.

Rewrite the equation in logarithmic form.

a)

A

b)

B

c)

C

d)

D

25.

What is the equation for the graph

a)

y=\log_{10}\left(x\right)

b)

$y=\log_5\left(x\right)$

c)

$y=\log_2\left(x\right)$

d)

$y=\log_5\left(-x\right)$

26.

Describe domain of the function shown: y=log₂(x+1)

a)

(-∞,∞)

b)

(-1,∞)

c)

(-1,3)

d)

(∞, -1)

27.

What is the inverse of

c\left(x\right)=\log\left(x\right)

a)

$c^{-1}\left(x\right)=x^e$

b)

$c^{-1}\left(x\right)=\ln x$

c)

$c^{-1}\left(x\right)=x^{10}$

d)

$c^{-1}\left(x\right)=10^x$

28.

What is the inverse of

n\left(x\right)=\ln\left(x\right)

a)

$n^{-1}\left(x\right)=\log e$

b)

$n^{-1}\left(x\right)=x^e$

c)

$n^{-1}\left(x\right)=e^x$

d)

$n^{-1}\left(x\right)=x^{\ln}$

29.

Write as one logarithm. Simplify, if possible.
log₃9 + log₃27

a)

-1

b)

5

c)

4

d)

1

30.

Write as one logarithm. Simplify, if possible.
log₂800 - log₂100

a)

8

b)

3

c)

-3

d)

1

31.

Write as one logarithm. Simplify, if possible.
log₅125 - log₅25

a)

1

b)

0

c)

5

d)

-1

32.

Write as one logarithm. Simplify, if possible.
log₆3 + log₆2

a)

0

b)

log₆5

c)

log₆1

d)

1

33.

Evaluate.
log₃81

a)

4

b)

¹/₄

c)

-4

d)

-¹/₄

34.

Expand

a)

A

b)

B

c)

C

d)

D

35.

Expand

a)

A

b)

B

c)

C

d)

D

36.

Condense

a)

A

b)

B

c)

C

d)

D

37.

Condense

a)

A

b)

B

c)

C

d)

D

38.

Condense

a)

log xyz³

b)

log (xy/z³)

c)

log x + log y + log z³

d)

log x³y³z³

39.

Condense

a)

log₈(x⁶)/log₈ (y³)

b)

log₈ (x⁶/y³)

c)

log₈(x/y³)

d)

log₈(x⁶y³)

40.

Expand log₅(u³v⁵)

a)

1/2(log₅u+log₅v+log₅uw)

b)

5 log₅u - 15 log₅ v

c)

log₅u + log₅v +3 log₅w

d)

3 log₅u + 5 log₅v

41.

Write the expression as a single logarithm. Then simplify if possible.
log 6 - log 3 + 2 log 7

a)

log 98

b)

log 78

c)

log 56

d)

log 45

42.

What is the correct transformed equation for the graph?

a)

y = log(x - 4)

b)

y = log(x) - 4

c)

y = log(x + 4)

d)

y = log(x) + 4

43.

What is the range of the function graphed?

a)

(-∞, ∞)

b)

(-∞, 2] and [2, ∞)

c)

[2, ∞)

d)

(-∞, 2]

44.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

45.

What is the equation of the asymptote on the graph of $y=\log_5\left(x+3\right)+5$ ?

a)

x = -3

b)

x=5

c)

y= -3

d)

y=5

46.

Compared to the graph of $f\left(x\right)=\log_2x$ , the asymptote on $g\left(x\right)=\log_2\left(3x+12\right)$ will be translated...

a)

12 units left to x = -12

b)

12 units right to x = 12

c)

4 units left to x = -4

d)

4 units right to x = 4

e)

not at all and remain x = 0

47.

Which of the following has a vertical asymptote at $x=4$

a)

$y=2^x-4$

b)

$y=\log_2\left(x-4\right)$

c)

$y=2^x+4$

d)

$y=\log_2\left(x+4\right)$

48.

What is the transformation of the logarithmic function
$f\left(x\right)=\log\ \left(x+3\right)-1$

a)

left 3, right 1

b)

right 3, down 1

c)

right 3, up 1

d)

left 3, down 1

49.

Using the change of base identity, which of the following could be typed into the calculator to draw the graph of $y=\log_7x$ ?

a)

$y=\frac{\log\left(7\right)}{x}$

b)

$y=\frac{\log x}{7}$

c)

$y=\frac{\log x}{\log7}$

d)

$y=\frac{\log7}{\log x}$

50.

If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

a)

$1,225,54

b)

$2,225.54

c)

$22,255.40

d)

$225.54

51.

Which of the following is the value of x given;

e^(x+6) = 12

a)

x = ln 6

b)

x = -6 + ln12

c)

x = ln72

d)

x = ln(-2)

52.

Chelsea put $7500 into an account paying 5% compounded continuously. She now has $10,643.01. How long has the money been in the account?

a)

7 years

b)

6 years

c)

5 years

d)

4 years

53.

How long would it take $7,000 to grow to $35,000 at 6% compounded continuously?

a)

27.6 years

b)

27.1 years

c)

26.0 years

d)

26.8 years

54.

log₉(10)-log₉(x-3) =log₉(72)

a)

81/16

b)

113/36

c)

No Solution

d)

92/15

55.

log₉(x)+log₉(x+2)=log₉(35)

a)

5

b)

-7

c)

5, -7

d)

-7, -13

56.

log₅x - log₅(x+4)=log₅38

a)

-152/37, -8

b)

1/2

c)

-152/37

d)

No Solution

57.

log7+log(x²-4)=log35

a)

1, -1

b)

2, -2

c)

3, -3

d)

4, -4

58.

log(-2x)-log(5) =log(30)

a)

-75

b)

8/5

c)

-2/3

d)

2

59.

log₇(x²+8) - log₇8 = log₇33

a)

2, -2

b)

16,-16

c)

1, -1

d)

No Solution

60.

Set up the problem.

a)

sin(47) = x/28

b)

cos(47) = x/28

c)

tan(47) = x/28

d)

cos(47) = 28/x

61.

What is the length of side x?

a)

6.57 cm

b)

7 cm

c)

7.44 cm

d)

26.33 cm

62.

Find the measure of the missing angle.

a)

64^o

b)

26^o

c)

61^o

d)

.008^o

63.

Find the measure of the missing angle.

a)

49^o

b)

50^o

c)

41^o

d)

33^o

64.

What is the value of cosine at 135

a)

0

b)

1/2

c)

√2 /2

d)

-√2 /2

65.

What is the value of sine at 210?

a)

1/2

b)

-1/2

c)

√3 / 2

d)

-√3 / 2

66.

What is the value of cosine at 270

a)

0

b)

1

c)

-1

67.

At what point are sine and cosine the same value?

a)

0

b)

90

c)

45

d)

60

68.

What is the value of sine at 330

a)

1/2

b)

-1/2

c)

√3 / 2

d)

-√3 / 2

69.

What is the value of cosine at 315

a)

0

b)

1

c)

√2 / 2

d)

-√2 /2

70.

What is the value of sine at 150

a)

0

b)

1/2

c)

1

d)

√3 / 2

71.

sinθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

72.

cosθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

73.

tanθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

74.

Given the Cos(x) = -2/3, then the Sec(x) = ?

a)

-2/3

b)

-3/2

c)

3/2

d)

2/3

75.

Find secΘ.

a)

17/15

b)

15/17

c)

8/17

d)

17/8

76.

Find cotΘ.

a)

3/4

b)

4/3

c)

5/4

d)

5/3

77.

Find cscΘ.

a)

15/17

b)

17/15

c)

8/17

d)

17/8

78.

If secx is 4/3, what is the hypotenuse?

a)

3

b)

5

c)

4

d)

$\sqrt{7}$

79.

What is 5π/6 radians in degrees?

a)

180

b)

150

c)

360

d)

120

80.

What is 7π/4 radians in degrees?

a)

300

b)

135

c)

315

d)

45

81.

What is 2π/3 radians in degrees?

a)

150

b)

120

c)

180

d)

30

82.

What is 45 degrees in radians?

a)

π/2

b)

π/6

c)

π/4

d)

3π/4

83.

In what quadrant is 285°

a)

I

b)

II

c)

III

d)

IV

84.

Which quadrant is 2π/3 in?

a)

I

b)

II

c)

III

d)

IV

85.

Convert 150⁰ to Radians

a)

5π/6

b)

3π/4

c)

7π/6

d)

2π/3

86.

Convert -40^o into Radians

a)

-4π / 8

b)

-8π / 9

c)

-2π / 9

d)

-5π / 8

87.

Convert 7π/ 6 radians into degrees

a)

225

b)

210

c)

270

d)

240

88.

What is the reference angle for 125°?

a)

235°

b)

125°

c)

75°

d)

55°

89.

What is the reference angle for -310⁰?

a)

50⁰

b)

-50⁰

c)

20⁰

d)

40⁰

90.

What is the reference angle for 275°?

a)

85°

b)

95°

c)

-85°

d)

-95°

91.

What is the reference angle?

a)

43

b)

-43

c)

47

d)

-47

92.

What is the reference angle?

a)

112

b)

68

c)

158

d)

248

93.

Standard position is when .....

a)

the initial side of the angle is on the positive x-axis.

b)

the initial side of the angle is on the negative x-axis.

c)

the initial side of the angle is on the positive y-axis.

d)

the initial side of the angle is on the negative y-axis.

94.

In which quadrant is -570⁰

a)

I

b)

II

c)

III

d)

IV

95.

Find a coterminal angle to 45°.

a)

360°

b)

405°

c)

315°

d)

295°

96.

Find a coterminal angle to -90°.

a)

-450°

b)

90°

c)

180°

d)

-180°

97.

sin (π/2)

a)

√3/2

b)

√2/2

c)

1/2

d)

1

98.

cos (π/4)

a)

√3/2

b)

√2/2

c)

1/2

d)

1

99.

cos(5π/3)

a)

-√2/2

b)

-1/2

c)

1/2

d)

√3/2

100.

sec(4π/3)

a)

√2/2

b)

-√2/2

c)

√3/2

d)

-2

101.

sec( $\frac{11\pi}{6}$ )

a)

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

b)

$\frac{1}{2}$

c)

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

d)

-√3

102.

cos(30^o)

a)

- ½

b)

√3/2

c)

2√3 /3

d)

½

103.

Based on the unit circle, what is the value of tan?

a)

y/r

b)

x/r

c)

r/y

d)

y/x

104.

csc(11π/6)

a)

-1/2

b)

1/2

c)

-2

d)

-√3/2

105.

tan(3π/4)

a)

√2/2

b)

-√2/2

c)

√3/2

d)

-1

106.

Consider the following table with information about all of the students taking Statistics at Happy High School.

Find P( Full-time | Male)

a)

7/3

b)

3/10

c)

3/7

d)

4/7

107.

The weather forecaster predicted it will be 4/5 chance of rain for Monday and 2/3 chance of rain for Tuesday. What is the probability it will rain both days?

a)

1/2

b)

20/15

c)

8/15

d)

6/8

108.

Event A has a probability of 0.3. What is the probability of the complement of Event A?

a)

30%

b)

3/100

c)

7/100

d)

0.7

109.

An ice cream parlor has 6 different flavors. They have 4 toppings and 2 types of cones. How many possible ice cream combinations are there?

a)

6

b)

48

c)

12

d)

24

110.

A box contains 5 purple marbles, 3 green marbles and 2 orange marbles. Draws are made without replacement.P(both marbles are purple)

a)

2/9

b)

1/3

c)

1/2

d)

1/4

111.

A jar contains 4 white chips, 5 purple chips, and 1 black chip. Chips are selected randomly one at a time, and are not replaced.
P(white, then purple, then black)

a)

1/36

b)

2/39

c)

5/41

d)

6/43

112.

A box contains all the letters of the word U N D E R S T A N D. What is the probability of selecting an 'N' first and a 'D' next, if the first letter is replaced?

a)

3/50

b)

1/25

c)

1/10

d)

2/5

113.

What is the probability of rolling an even number on the first roll of a number cube and rolling an odd number on the second roll?

a)

1/4

b)

1

c)

1/8

d)

1/2

114.

A disc jockey has to choose three songs for the last few minutes of his evening show. If there are nine songs that he feels are appropriate for that time slot, then how many ways can he choose and arrange to play three of those nine songs?

a)

84

b)

504

c)

9!

d)

3!

115.

Eva has eight glasses of water. In how many different orders can the glasses of water be arranged?

a)

8

b)

64

c)

8!

d)

56

116.

An election ballot asks voters to select three city commissioners from a group of six candidates. In how many ways can this be done?

a)

6!

b)

120

c)

20

d)

3!

117.

There are 10 students in a class: 5 boys and 5 girls.

If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a girl?

a)

1/12

b)

1/2

c)

1

d)

1/5

118.

There are 10 men and 6 women working at a company. A hiring committee of 4 staff members is selected by a supervisor.

What is the probability that the committee is made up of 3 women and 1 man?

a)

2/91

b)

1/20

c)

3/16

d)

36/91

119.

In a deck of 52 playing cards, what is the probability of getting a 5 of Hearts or 5 of Diamond?

a)

0

b)

$\frac{2}{13}$

c)

$\frac{1}{4}$

d)

$\frac{1}{26}$

120.

From a well shuffled deck of 52 cards, what is the probability of finding a red and a king card?

a)

$\frac{1}{13}$

b)

$\frac{1}{52}$

c)

$\frac{1}{26}$

d)

$\frac{3}{26}$

121.

From a pack of 52 cards, the black face cards are removed. What is the probability of getting a king?

a)

$\frac{1}{23}$

b)

$\frac{3}{26}$

c)

$\frac{1}{26}$

d)

$\frac{2}{23}$

122.

From a pack of 52 cards, the black face cards are removed. What is the probability of getting a king?

a)

$\frac{1}{23}$

b)

$\frac{3}{26}$

c)

$\frac{1}{26}$

d)

$\frac{2}{23}$

123.

The 40 yards sprint times for a soccer team are found to be normally distributed with a mean of 5.2 seconds and a standard deviation of 0.3 seconds. What is the z-score for a player who runs a time of 5.6 seconds?

a)

-1.33

b)

1.33

c)

0.88

d)

1.02

124.

68% of the marks in a test are between 51 and 64

Assuming this data is normally distributed, what are the mean and standard deviation?

a)

Mean = 57

S.D. = 6.5

b)

Mean = 57

S.D. = 7

c)

Mean = 57.5

S.D. = 6.5

d)

Mean = 57.5

S.D. = 13

125.

95% of students at school weigh between 62 kg and 90 kg.

Assuming this data is normally distributed, what are the mean and standard deviation?

a)

Mean = 66 kg

S.D. = 7 kg

b)

Mean = 76 kg

S.D. = 7 kg

c)

Mean = 86 kg

S.D. = 7 kg

d)

Mean = 76 kg

S.D. = 14 kg

126.

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days.

About what percent of the products last 6 days or less?

a)

68%

b)

34%

c)

16%

d)

2.5%

127.

The mean life of a tire is 30,000 km. The standard deviation is 2000 km.

Then, 68% of all tires will have a life between ___________ km and __________ km.

a)

28,000 km and 32,000 km.

b)

24,000 km and 34,000 km.

c)

26,000 km and 34,000 km.

d)

27,000 km and 31,000 km.

128.

1. Which best describes the shaded part of this normal distribution graph?

a)

All data that is one or higher.

b)

All data that is one or more standard deviations above the mean.

c)

All data that is between 1 and 3.

d)

All data that is above the mean.

A2H Final Exam Practice

Total questions: 128

Worksheet time: 6hrs 24mins

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