Free Printable Fall final PCKP Hurricane Review

1.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(3\right)\right)$

a)

34

b)

71

c)

35

d)

142

2.

If $f\left(x\right)=2x$ and $g\left(x\right)=2x^2-1$ find $f\left(g\left(x\right)\right)$

a)

$4x^2-1$

b)

$4x^2-2$

c)

$8x^2-1$

d)

$16x^2-1$

3.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $\left(g\circ f\right)\left(x\right)$

a)

$\frac{1}{3x}+2$

b)

$3x+2$

c)

$\frac{3}{x}+2$

d)

$\frac{1}{3x+2}$

4.

If $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=3x+2$ find $f\left(g\left(x\right)\right)$

a)

$\frac{1}{3x}+2$

b)

$3x+2$

c)

$\frac{3}{x}+2$

d)

$\frac{1}{3x+2}$

5.

If $f\left(x\right)=x^2$ and $g\left(x\right)=\sqrt{x}$ find $g\left(f\left(x\right)\right)$

a)

$x^4$

b)

$x$

c)

$\sqrt[]{x}$

d)

$x^2$

6.

Identify the type of symmetry based on the graph:

i. symmetric with respect to the x-axis

ii. symmetric with respect to the y-axis

iii. symmetric with respect to the origin

a)

i only

b)

ii only

c)

iii only

d)

i, ii, and iii

7.

Identify the type of symmetry based on the graph:

i. symmetric with respect to the x-axis

ii. symmetric with respect to the y-axis

iii. symmetric with respect to the origin

a)

i only

b)

ii only

c)

iii only

d)

i, ii, and iii

8.

Which classification is given to a function that exhibits symmetry over the y-axis?

a)

odd

b)

even

9.

Which classification is given to a function that exhibits symmetry over the origin?

a)

odd

b)

even

10.

Use the symmetry tests to determine the type of symmetry for: $y=3x^8-7x^2+2$
i. symmetric with respect to the x-axis
ii. symmetric with respect to the y-axis
iii. symmetric with respect to the origin

a)

i only

b)

ii only

c)

iii only

d)

i, ii, and iii

11.

Use the symmetry tests to determine the type of symmetry for: $x=y^2-4$
i. symmetric with respect to the x-axis
ii. symmetric with respect to the y-axis
iii. symmetric with respect to the origin

a)

i only

b)

ii only

c)

iii only

d)

i, ii, and iii

12.

Use the symmetry tests to determine tif the given function is odd, even, or neither: $f\left(x\right)=x^5+1$

a)

odd

b)

even

c)

neither

13.

Is this an even, odd, or neither function?

f(x) = x⁴ + x²

a)

Even

b)

Odd

c)

Neither

14.

$y=7x^8-9x^2+33$

a)

Even Function

b)

Odd Function

c)

Function - neither even nor odd

d)

Not a function

15.

$y=12x^7+6x^5-8x^3+4x$

a)

Even Function

b)

Odd Function

c)

Function - neither even nor odd

d)

Not a function

16.

Write 1 + 2 + 3 + ... + 10

using sigma notation

a)

$\sum_{d=1}^9d$

b)

$\sum_{d=1}^{10}d+1$

c)

$\sum_{d=1}^{10}d$

17.

Write 1 + 4 + 9 + ... + 49

using sigma notation

a)

$\sum_{k=1}^7k^2$

b)

$\sum_{k=1}^8k^2$

c)

$\sum_{k=1}^{49}k^2$

18.

Find how many terms are in the series below:
7+13+19+25...=1044

a)

16

b)

17

c)

18

d)

19

19.

$a_1=-2,\ \ \ r=-2,\ \ \ S_n=22$ Determine the number of terms n in the series

a)

6

b)

7

c)

8

d)

5

20.

$2,\ 10,\ 50,\ 250,\ ...$ Find the explicit formula

a)

$a_n=10\cdot4^{\left(n-1\right)}$

b)

$a_n=2\cdot5^{\left(n-1\right)}$

c)

$a_n=10\cdot5^{\left(n-1\right)}$

d)

$a_n=5\cdot2^{\left(n-1\right)}$

21.

What is the value of the y-intercept of the graph of the graph of

h\left(x\right)=29\left(5.2\right)^x

?

a)

29

b)

1

c)

5.2

d)

0

22.

What is the horizontal asymptote of the exponential equation

y=10\left(0.85\right)^x

?

a)

$y=0$

b)

$y=10$

c)

$x=0$

d)

$y=0.85$

23.

Which statement about the graph of

y=8\left(0.25\right)^x

is true?

a)

The coordinates of the x-intercept are $\left(0.25,0\right)$ .

b)

The coordinates of the y-intercept are $\left(0,8\right)$ .

c)

The equation of the asymptote is $x=0$ .

d)

The graph includes the point $\left(2,1\right)$ .

24.

The graph of an exponential function is shown on the grid.

Which dashed line is an asymptote for the graph?

a)

Line $q$

b)

Line $r$

c)

Line $s$

d)

Line $t$

25.

Which statement about the graph of

y=\frac{1}{3}\left(\frac{2}{3}\right)^x

is true?

a)

The graph has a vertical asymptote.

b)

The graph crosses the y-axis at $\left(0,\frac{2}{9}\right)$ .

c)

The graph has an asymptote at $y=\frac{1}{3}$

d)

The graph decreases from left to right.

26.

What is it called when the graph of an exponential function increases from left to right?

a)

Growth

b)

Decay

c)

Negative

d)

Positive

27.

What is it called when the graph of an exponential function decreases from left to right?

a)

Growth

b)

Decay

c)

Negative

d)

Positive

28.

What is the horizontal asymptote of a exponential function?

a)

Where the graph crosses the y-axis

b)

Where the graph crosses the x-axis

c)

A line the graph approaches but never crosses

d)

the change in y divided by the change in x

29.

Name the function:

y=e^x

a)

logarithmic parent function

b)

natural logarithm function

c)

natural base exponential function

30.

Name the function:

y=\ln\ x

a)

logarithmic parent function

b)

natural logarithm function

c)

natural base exponential function

31.

Analyze the domain, range, x-intercept, and asymptote of the graph of:

y=\log_ex+1

a)

Domain: All real numbers, Range: y > 0, x-intercept: (0.368, 0), Asymptote: y = 0

b)

Domain: x > 0, Range: All Real numbers, x-intercept: (0.368, 0), Asymptote: y = 0

c)

Domain: x > 0, Range: All Real numbers, x-intercept: (0.368, 0), Asymptote: x = 0

d)

Domain: x > 0, Range: All Real numbers, x-intercept: (0, 0.368), Asymptote: y = 0

32.

What is the asymptote and the x-intercept?
$f\left(x\right)=\ln x+2$

a)

x = 0

b)

x = -2

c)

(0.135, 0)

d)

(0, 0.135)

33.

What is the asymptote and the x-intercept?
$f\left(x\right)=\ln\left(x+2\right)$

a)

x = 2

b)

x = -2

c)

(-1, 0)

d)

(0, 1)

34.

What is g(7) if:

a)

-17

b)

-13

c)

13

d)

17

35.

Using the pictured graph, what is f(-3)?

a)

-3

b)

-1

c)

1

d)

3

36.

What is m(-3) if:

a)

-3

b)

0.5

c)

3

d)

-3.5

37.

a)

A

b)

B

c)

C

d)

D

38.

What is f when x equals 4?

a)

-5

b)

0

c)

3

d)

6

39.

What is f when x equals 0?

a)

-5

b)

0

c)

1/2

d)

1

40.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

41.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

42.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

43.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

44.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

45.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

46.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

47.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

48.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

49.

What is the Vertical Asymptotes?

a)

x= -5

b)

x= 5

c)

x= 6

d)

x= -6

50.

Where are the discontinuities?

a)

holes: x=-1

asymptotes: x=5/3

b)

holes: x=-1

asymptotes: x=2/3

c)

holes: x=1

asymptotes: x=5/3

d)

holes: x=1

asymptotes: x=2/3

51.

Which of the following graphs presents an infinite discontinuity at x = 1?

a)

b)

c)

d)

52.

What is the removable discontinuity?

a)

x= 4

b)

x= -4

c)

x= 5

d)

x= -5

53.

Determine the type(s) and location(s) of all discontinuities.

a)

jump at x = -3, removable at x = 2

b)

removable at x = -3.

c)

infinite at x = 2.

d)

infinite at x = -3.

54.

Determine the type(s) and location(s) of all discontinuitie(s)

a)

jump at x = 1

b)

removable and x = 1

c)

infinite at x = 1

d)

jump at x = -3

55.

Describe the end behavior of
f(x) = -5x⁴ - 2x² + 8

a)

Left side: Rises
Right side: Rises

b)

Left Side: Rises
Right side: Falls

c)

Left side: Falls
Right side: Rises

d)

Left side: Falls
Right side: Falls

56.

a)

y = x(x - 3)(x - 2)

b)

y = x(x - 3)²(x+2)

c)

y = x(x + 3)²(x - 2)

d)

y = -x(x + 3)²(x - 2)

57.

f(x) = (x-4)²(x+1)

a)

Even Degree
- Leading Coeff.

b)

Even Degree
+ Leading Coeff.

c)

Odd Degree
- Leading Coeff.

d)

Odd Degree
+ Leading Coeff.

58.

What is the degree of the function graphed here?

a)

6

b)

4

c)

3

d)

5

59.

What is the y-intercept?
f(x) = -x⁴ + x³ + 5x² + x + 6

a)

-1

b)

1

c)

5

d)

6

60.

Is the leading coefficient positive or negative

a)

positive

b)

negative

61.

For each function, determine the real zeros and state the multiplicity of any repeated zeros.

a)

{0 mult. 3, 5, 2}

b)

{−2 mult. 3, 3, 1}

c)

{0 mult. 3, 3, 2}

d)

{2 mult. 3, 3, 3}

62.

Even or Odd degree?

a)

even

b)

odd

63.

f(x) = (x+2)(x-3)²(x-4)

Which choice best describes the zeros?

a)

-2, 3 (multiplicity 2), 4

b)

-2 (multiplicity 2), 3, 4

c)

2, -3 (multiplicity 2), -4

d)

2 (multiplicity 2), -3, -4

64.

Where do you find relative minimums and relative maximums?

a)

zeros

b)

y-intercepts

c)

turning points

d)

by degree

65.

How many extrema (maxes and mins) are in the picture?

a)

2

b)

3

c)

4

d)

5

66.

What is the relative max of this function?

a)

x = 5

b)

infinity

c)

there is no relative maximum

d)

2.5 and it occurs at x = 5

67.

Which of the following statement are false.

a)

There is a relative min at the point (8,0)

b)

There is another relative min at the point (0,-7.5)

c)

There is a relative max at the point (5,2.5)

d)

There are more relative maximums than there are relative minimums.

68.

How would you describe the point at (0,6)?

a)

Relative Minimum

b)

Absolute Minimum

c)

Relative Maximum

d)

Absolute Maximum

69.

Check all the intervals where this graph is decreasing.

a)

(-∞, -1)

b)

(-1, 0)

c)

(0, 1)

d)

(1, ∞)

70.

Check all the intervals where this graph is increasing.

a)

(-∞, -1)

b)

(-1, 0)

c)

(0, 1)

d)

(1, ∞)

71.

What is the Range of the function being graphed?

a)

(-∞, ∞)

b)

(7, ∞)

c)

(-∞, 7)

d)

(-1, 1)

72.

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

a)

Leading Coefficient Positive
Degree - Even

b)

Leading Coefficient Positive
Degree - Odd

c)

Leading Coefficient Negative
Degree - Even

d)

Leading Coefficient Negative
Degree - Odd

73.

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

a)

Leading Coefficient Positive
Degree - Even

b)

Leading Coefficient Positive
Degree - Odd

c)

Leading Coefficient Negative
Degree - Even

d)

Leading Coefficient Negative
Degree - Odd

74.

In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

75.

Describe the end behavior of the graph.

a)

x → -∞, f(x) → ∞ and x→∞, f(x) →⁻∞

b)

x → -∞, f(x) → ∞ and x→∞, f(x) →∞

c)

x → -∞, f(x) → ∞ and x→∞, f(x) → 0

d)

x → -∞,f(x) → -∞and x→ ∞, f(x) → ∞

76.

What is the degree?

a)

Positive

b)

Negative

c)

Odd

d)

Even

77.

What is the degree?

a)

Positive

b)

Negative

c)

Odd

d)

Even

78.

Which function has this end behavior?

a)

-x²-3x+1

b)

-x³+2x²+3

c)

x⁴+3x³-4x+1

d)

x⁵-4x⁴+2x²-1

79.

Which function has this end behavior?

a)

-1x⁴-3x³+3

b)

-2x⁷+2x⁴+4

c)

3x⁸+3x⁵-4x+7

d)

4x⁵-4x⁴+2x³-9

80.

Which function has this end behavior?

a)

-1x⁴-3x³+3

b)

-2x⁷+2x⁴+4

c)

3x⁸+3x⁵-4x+7

d)

4x⁵-4x⁴+2x³-9

81.

Which function has this end behavior?

a)

-x²-3x+1

b)

-x³+2x²+3

c)

x⁴+3x³-4x+1

d)

x⁵-4x⁴+2x²-1

82.

What is the end behavior of this rational function?

a)

As x goes to the left, y approaches 2 from below the asymptote.

As $x\rightarrow-\infty,\ y\rightarrow2^-$

b)

As x goes to the left, y approaches 2 from above the asymptote.
As

x\rightarrow-\infty,\ y\rightarrow2^+

c)

As x goes to the right, y approaches 2 from below the asymptote.
As $x\rightarrow+\infty,\ y\rightarrow2^-$

d)

As x goes to the right, y approaches 2 from above the asymptote.
As $x\rightarrow+\infty,\ y\rightarrow2^+$

83.

What is the end behavior of this rational function?

a)

As x goes to the left, y approaches 0 from below the asymptote.

As $x\rightarrow-\infty,\ y\rightarrow0^-$

b)

As x goes to the left, y approaches 0 from above the asymptote.
As

x\rightarrow-\infty,\ y\rightarrow0^+

c)

As x goes to the right, y approaches 0 from below the asymptote.
As $x\rightarrow+\infty,\ y\rightarrow0^-$

d)

As x goes to the right, y approaches 0 from above the asymptote.
As $x\rightarrow+\infty,\ y\rightarrow0^+$

84.

What is the end behavior of this rational function?

a)

As x goes to the left, y approaches the asymptote y = x

As $x\rightarrow-\infty,\ y\rightarrow x$

b)

As x goes to the right, y approaches the asymptote y = x.
As

x\rightarrow+\infty,\ y\rightarrow x

c)

As x goes to the left, y goes down.
As $x\rightarrow-\infty,\ y\rightarrow-\infty$

d)

As x goes to the right, y goes up.
As $x\rightarrow+\infty,\ y\rightarrow+\infty$

85.

Define Asymptotic Behavior

a)

It describes the function's direction as it approaches the asymptote it curves towards $\pm$ infinity.

b)

its just crazy

86.

What is the asypmtotic behavior of this rational function?

a)

As x approaches 3 from the left, y goes down

As $x\rightarrow3^-,\ y\rightarrow-\infty$

b)

As x approaches 3 from the left, y goes up
As

x\rightarrow3^-,\ y\rightarrow+\infty

c)

As x approaches 3 from the right, y goes down
As $x\rightarrow3^+,\ y\rightarrow-\infty$

d)

As x approaches 3 from the right, y goes up
As $x\rightarrow3^+,\ y\rightarrow+\infty$

87.

What is the asypmtotic behavior of this rational function?

a)

As x approaches 0 from the left, y goes down

As $x\rightarrow0^-,\ y\rightarrow-\infty$

b)

As x approaches 0 from the left, y goes up
As

x\rightarrow0^-,\ y\rightarrow+\infty

c)

As x approaches 0 from the right, y goes down
As $x\rightarrow0^+,\ y\rightarrow-\infty$

d)

As x approaches 0 from the right, y goes up
As $x\rightarrow0^+,\ y\rightarrow+\infty$

88.

What is the asypmtotic behavior of this rational function as x approaches x = -2?

a)

As x approaches -2 from the left, y goes down

As $x\rightarrow-2^-,\ y\rightarrow-\infty$

b)

As x approaches -2 from the left, y goes up
As

x\rightarrow-2^-,\ y\rightarrow+\infty

c)

As x approaches -2 from the right, y goes down
As $x\rightarrow-2^+,\ y\rightarrow-\infty$

d)

As x approaches -2 from the right, y goes up
As $x\rightarrow-2^+,\ y\rightarrow+\infty$

89.

What is the asypmtotic behavior of this rational function as x approaches x = 1?

a)

As x approaches 1 from the left, y goes down

As $x\rightarrow1^-,\ y\rightarrow-\infty$

b)

As x approaches 1 from the left, y goes up
As

x\rightarrow1^-,\ y\rightarrow+\infty

c)

As x approaches 1 from the right, y goes down
As $x\rightarrow1^+,\ y\rightarrow-\infty$

d)

As x approaches 1 from the right, y goes up
As $x\rightarrow1^+,\ y\rightarrow+\infty$

90.

What is the range of this rational function?

a)

$y\ne2$

b)

$\left(-\infty,+\infty\right)$

c)

$y\ne1$

91.

What is the range of this rational function?

a)

$\left[0,\infty\right)$

b)

$\left(-\infty,+\infty\right)$

c)

$\left(0,\infty\right)$

92.

What is the X-Intercept?

a)

x= 0

b)

x= 4

c)

x= 5

d)

x= -5

93.

What are the x-intercepts?

a)

x= 2/3

b)

x= 4, x = -2

c)

x= -8, x = 1

d)

x= -4, x = 2

94.

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

95.

What is the horizontal asymptote to this function?

a)

y=4

b)

y=0

c)

y=-2

d)

y=1

96.

What (if any) holes exist?

a)

x=2

b)

x=2 and x=3

c)

x=-3

d)

x=3

97.

What is/are the vertical asymptote(s)?

a)

x=-2

b)

x=2 and x=3

c)

x=-3

d)

x=3

98.

What is the horizontal asymptote?

a)

y = -4

b)

y = 1

c)

x = 1

d)

y = -6

99.

Simplify the rational function

a)

1/(x + 5)

b)

1/(x - 5)

c)

(x - 5)(x + 5)

d)

(x - 5)/[(x - 5)(x + 5)]

100.

What are the asymptotes?

a)

x=-1 y = -3

b)

x=1 y = -3

c)

x=-1 y =3

d)

x=1, y=3

101.

Find the coordinates of the hole.

a)

(-3, -3)

b)

(-3, 3)

c)

(3, -3)

d)

(3, 3)

102.

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

103.

Is there a hole or a vertical asymptote?

a)

A hole when x = 2

b)

A vertical asymptote at x = 2

c)

there is no hole or vertical asymptote

104.

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)

105.

What is the end behavior as x approaches negative infinity?

a)

y approaches negative infinity

b)

y approaches positive infinity

c)

y approaches 1

d)

y approaches 2

106.

You want to solve for x. Which of these is the correct "step 1"?

a)

$\log_78=\log_7x$

b)

$\log_742=\log_7x$

c)

$\log_748=\log_7\left(\frac{x}{6}\right)$

d)

$\log_754=\log_7x$

107.

Finish solving for x

a)

x = 6

b)

x = 7

c)

x = 8

d)

x = 56

108.

We want to solve for x. What's the first step?

a)

Rewrite as a logarithm: $\log_{189}3=x$

b)

Rewrite as a logarithm: $\log_3189=x$

c)

Rewrite 189 with a base of 3: $3^x=3^{63}$

d)

Rewrite 189 with a base of 3: $3^x=3^9$

109.

Finish solving for x.

a)

0.210 = x

b)

5 = x

c)

63 = x

d)

4.771 = x

e)

4.462 = x

110.

We want to solve for x. Which of these is the correct "step 1"?

a)

$\log\left(64\right)=\log\left(3x\right)$

b)

$\log\left(16\right)=\log\left(x^3\right)$

c)

$\log\left(16\right)=\log\left(3x\right)$

d)

$\log\left(64\right)=\log\left(x^3\right)$

e)

$\log\left(1\right)=\log\left(x^3\right)$

111.

Continue solving for x. Which is the correct "step 2"?

a)

$64=x^3$

b)

$64^3=x$

c)

$x^{64}=3$

d)

$3^{64}=x$

112.

Which is the correct "step 1" to solve for x?
Hint: look at the schoology discussions if you feel stuck

a)

$\log_2\left(100x^5\right)=7$

b)

$\log_2\left(95x\right)=7$

c)

$\log_2\left(20x\right)=7$

d)

$\log_2\left(500x\right)=7$

113.

Solve for x: $9^x=60$

a)

1.748

b)

x = 6.667

c)

x = 0.537

d)

x = 1.863

114.

Solve for x.
$\log_52+\log_5x=\log_520$
x = (a)

115.

Solve for x.
$2\log_410=\log_4\left(8x\right)+\log_4\left(5\right)$

a)

x = 2.5

b)

x = 0.5

c)

x = 1.538

d)

x = 11.875

116.

log₂32=3x

a)

5/3

b)

3/5

c)

5

d)

3

117.

log₄(3x-1)=log₄(2x+3)

a)

4

b)

3

c)

1

d)

8

118.

log_x1000=3

a)

1

b)

10

c)

30

d)

3

119.

log₈(4x+4)=2

a)

15

b)

12

c)

10

d)

3

120.

log₈₁x = 3/4

a)

2

b)

3

c)

27

d)

81

121.

Solve for x:
(-3)^x = (-3)¹³

a)

13

b)

-3

c)

x + 13

d)

x -13

122.

Solve 3³ = 3^{4x + 2}

a)

x = ¼

b)

x = -¼

c)

x = ½

d)

x = -½

123.

Solve for x:
5^2x = 5^-x

a)

0

b)

-6

c)

8

d)

1

124.

8^3x+3 = 8⁶

a)

x=28

b)

x=3

c)

x=1

d)

x=12

125.

To solve 8 = 2^5x+7, you would need to re-write 8 as what base?

a)

8

b)

4

c)

2

d)

Cannot be determined

126.

Solve: 2^x = 4^x+1

a)

x = -2

b)

x = 2

c)

x = -3

d)

x = 3

127.

Sovle for x:
5^{-3x - 1} = 25

a)

x = -1

b)

x = -4

c)

x = -3

d)

x = 1

128.

Solve for p:
4^p+2 = 64

a)

p = -16/9

b)

p = 1

c)

p = 8

d)

p = 7/6

129.

Solve: 9^8-x = 27^x-3

a)

x = 5

b)

x = -5

c)

x = 1/5

d)

x = -1/5

130.

Solve for a:
5^{a + 2} = 1/125

a)

-1

b)

-6/7

c)

-5

d)

4

131.

Emily’s parents put $1,500 in her bank account for college tuition. At an interest rate of 8.25% compounded semiannually,what will be the balance after 18 years?

a)

$6,273.50 frustrated

b)

$6,314.08 bewildered

c)

$6,385.72 pleased

d)

$6,427.94 tickled pink

132.

Mark took a loan out for $25,690 to purchase a truck. At an interest rate of 5.2% compounded monthly, how much total will he have paid after 5 years?

a)

$33,299.42 playing dodgeball

b)

$33,672.68 climbing trees

c)

$34,157.04 riding unicycles

d)

$34,710.88 flipping pancakes

133.

The Henley's took out a loan for $195,000 to purchase a home. At a 4.3% interest rate compounded annually,how much interest will they have paid after 30 years?

a)

$412,749.79 Labor Day

b)

$429,305.61 the 4th of July

c)

$471,259.24 Groundhog Day

d)

$494,546.99 Valentine’s Day

134.

What does P represent in the equation A=P(1+r)^t

a)

rate

b)

principal

c)

time

d)

amount

135.

What does r represent in the equation A=P(1+r)^t

a)

rate

b)

principal

c)

time

d)

amount

136.

Krystal has $3000 invested at a 2% interest rate. Which expression can be used to determine how much money Krystal had after 16 years?

a)

$A=3000\left(1+.02\right)^{16}$

b)

$A=3000\left(1-.02\right)^{16}$

c)

$A=16\left(1+.2\right)^{3000}$

d)

$A=3000\left(.2\right)^{16}$

137.

Steve deposited $5,000 in a savings account that pays 4% interest compounded annually.

Which equation could be used to find the value of the account after 3 years?

a)

A = 5,000(1 + 4)³

b)

A = 5,000(1 + 0.04)³

c)

A = 5,000(1 + 0.4) x 3

d)

A = 5,000(0.04)³

138.

Emily would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.

a)

$15,415.94

b)

$15,683.28

c)

$15,927.56

d)

$16,109.05

139.

Monthly means how many times a year?

a)

4

b)

12

c)

52

d)

365

140.

Principal: $999
Interest Rate: 5.45%
Time: 19 years
Compounded Quarterly
State the future account balance.

a)

$2794.10

b)

$2738.11

c)

$2774.98

d)

$2807.11

141.

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

142.

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

143.

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

144.

Factor Completely:

2n³ + 7n² - 2n - 7

a)

cannot be factored

b)

(n - 1)²(2n + 7)

c)

(n² - 1)(2n + 7)

d)

(n + 1)(n - 1)(2n + 7)

145.

Factor completely:
2x³+ 5x² - 8x - 20

a)

(x² - 4)(2x + 5)

b)

(2x - 5)(x² + 4)

c)

(2x² - 4)(x + 5)

d)

(x - 2)(x + 2)(2x + 5)

146.

Factor Completely:

k⁴ - 10k² - 39

a)

(k² - 13)(k² + 3)

b)

(k - 13)(k + 3)

c)

(k² + 15)(k² - 3)

d)

(k + 13)(k - 3)

147.

Factor Completely:

4w⁴ + 16w² + 15

a)

(w² + 10)(w² + 6)

b)

(2w²+ 5)(2w² + 3)

c)

(w² + 15)(4w² + 1)

d)

(2w + 5)(2w + 3)

148.

What are the remaining factors for

(x³ +x² -17x +15) if (x -1) is a factor? (use synthetic division)

a)

(x-1) (x+5) (x-3)

b)

(x-1) (x+5) (x + 3)

c)

(x+1) (x+5) (x-3)

d)

(x+1) (x-5) (x-3)

149.

Factor: x³+ 1

a)

(x + 1)³

b)

(x+1)(x²- x + 1)

c)

(x - 1) (x² + x - 1)

d)

(x + 1)(x² - 2x + 1)

150.

Factor Completely:

2n³ + 7n² - 2n - 7

a)

cannot be factored

b)

(n - 1)²(2n + 7)

c)

(n² - 1)(2n + 7)

d)

(n + 1)(n - 1)(2n + 7)

151.

Factor completely:
2x³+ 5x² - 8x - 20

a)

(x² - 4)(2x + 5)

b)

(2x - 5)(x² + 4)

c)

(2x² - 4)(x + 5)

d)

(x - 2)(x + 2)(2x + 5)

152.

What are the remaining factors for

(x³ +x² -17x +15) if (x -1) is a factor?

a)

(x-1) (x+5) (x-3)

b)

(x-1) (x+5) (x + 3)

c)

(x+1) (x+5) (x-3)

d)

(x+1) (x-5) (x-3)

153.

Is (x-1) a factor of f(x)= x³-8x²+14x-4?

a)

Yes, (x-1) is a factor. There is a remainder.

b)

No, (x-1) is not a factor. The remainder is zero.

c)

Yes, (x-1) is a factor. The remainder is zero.

d)

No, (x-1) is not a factor. There is a remainder.

154.

If 𝒙²+𝟑𝒙+𝟕 is divided by 𝒙-𝟐, then what is the remainder?

a)

0

b)

-3

c)

17

d)

5

155.

Divide using long division

$\frac{2x^4-7x^3+14x^2-55x+21}{2x-7}$

a)

$x^3-7x^2-3x$

b)

$x^3+7x-3$

c)

$x^3-7x^2+7x-3$

d)

$x^3-7x+3$

156.

Is this division problem worked correctly? If not, where is the FIRST mistake made?

a)

This is correct!

b)

No, the first mistake is the solver forgot to subtract 2x.

c)

No, the first mistake is the solver forgot to subtract -8.

d)

No, the first mistake is x⋅x is not x².

157.

Find all solutions for the polynomial

0 = x³ -3x²-5x+15

a)

3, √5

b)

3, √5, -√5

c)

-3, √5, -√5

d)

-3, 5i, -5i

158.

What does Descartes' Rule of Signs determine?

a)

How many possible positive real solutions

b)

How many possible negative real solutions

c)

How many possible imaginary or complex solutions

159.

The Fundamental Theorem of Algebra states

a)

Algebra is fundamentally awesome

b)

Any polynomial with $x^n$ has at least n solutions

c)

Imaginary numbers are just complex numbers with a 0 real part

d)

Real numbers are just complex numbers with a 0 imaginary part

160.

$x^5+3x^2-4x+120$ has how many total possible solutions?

(a)

161.

$x^5+3x^2-4x+120$ has how many total possible imaginary solutions?

a)

4

b)

3

c)

2

d)

1

e)

0

162.

$x^5+3x^2-4x+120$ has how many total possible positive real solutions?

a)

4

b)

3

c)

2

d)

1

e)

0

163.

When looking for possible negative roots, we need to look at...

a)

$f\left(x\right)$

b)

$f\left(-x\right)$

c)

$-f\left(x\right)$

d)

$x^n$ (highest power)

164.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = x³ + 2x² - 6x + 8

a)

±1, ±8

b)

±1, ±2, ±4, ±8

c)

±1, ±2, ±4

d)

1, 2, 4, 8

165.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 3x³ + 2x² - 6x + 7

a)

±1, ±7, ±1/3, ±7/3

b)

±1, 7

c)

±1, ±3, ±7, ±7/3

d)

±1, ±3, ±7, ±1/3, ±7/3

166.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 2x³ + 5x² - 9x + 5

a)

±1, ±5, ±1/2, ±5/2

b)

±1, ±2, ±5, ±1/2, ±5/2

c)

±1, ±5

d)

±1, ±2, ±5, ±1/2, ±5/2, ±2/5

167.

Solve by using Rational Root Theorem:
2x³ - 11x² + 12x + 9 = 0

a)

-1, 1, 3

b)

-1, 3/2, 3

c)

-1/2, 3, 3

d)

-1/2, 1, 3

168.

Solve by using Rational Root Theorem:
x³ - 7x - 6 = 0

a)

1, 2, 3

b)

-1, -2, - 3

c)

-1, -2, 3

d)

1,-2,-3

169.

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

a)

0

b)

2

c)

4

d)

6

170.

According to the Rational Root Theorem, what are the all possible rational roots?
2x³ - 11x² + 12x + 9 = 0

a)

±1,±2

b)

±1,±3,±9

c)

±1,±3±9,±1/2,±3/2,±9/2

d)

±1,±2,±1/3,±2/3,±1/9,±2/9

171.

Solve by using Rational Root Theorem:
x³ + 3x² - 6x - 8 = 0

a)

-4, -1, 2

b)

-4, -1, ±√2

c)

1, 2, 4

d)

4,-1,√2

172.

What is this?

a)

This is the speed of light formula.

b)

This is the quadratic formula.

c)

This is the zero product property.

d)

This is scary.

173.

Solve
x² -6x +2 = 0

a)

3+√7 &
3-√7

b)

3/2+√7 &
3/2-√7

c)

-3+√-7
& -3-√-7

d)

-3+√7
& -3-√7

174.

How many zeros will the equation:
5x² - 2x + 3 = 0 have?

a)

1

b)

2

c)

3

d)

none

Fall final PCKP Hurricane Review

Total questions: 174

Worksheet time: 10hrs 53mins

Similar Resources on Wayground