Free Printable PreCalcA Course Review

1.

Find the common difference of the arithmetic sequence 1, -2, -5, ...

(a)

2.

What is a formula for the nth term in the sequence 12, 20, 28, ...?

a)

$a_n=20+8\left(n-1\right)$

b)

$a_n=-4+8\left(n+1\right)$

c)

$a_n=12+8\left(n+1\right)$

d)

$a_n=12\left(8\right)^n$

3.

Write the explicit formula for the sequence:

5 , 4.5, 4, 3.5, ...

a)

a_n = 5 - n

b)

a_n = 5 - 0.5(n-1)

c)

a_n = 5 - 0.5n

d)

a_n = 5 - 0.5n + 1

4.

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

5.

Principal: $5000
Interest Rate: 3.75%
Time: 25 years
Compounded Monthly
State the future account balance.

a)

$12712.31

b)

$12,749.30

c)

$12,657.59

d)

$12550.84

6.

Bob is 19 and wants to retire when he's 52 years old. He has a savings account with a 5% interest compounded monthly. How much will Bob have to put into the account in order to retire with $500,000?

a)

$92,002.99

b)

$96354.69

c)

$91,662.93

d)

$91,214.79

7.

What are the zeros of the function?

a)

4,1

b)

3,1,-2,-5

c)

-3, -1, 2, 5

d)

-2,4

8.

What are the zeros of the polynomial function?

y = 3x(x - 6)(x + 5)

a)

0, 6, -5

b)

6, -5

c)

0, -6, 5

d)

3, 6, -5

9.

Find the zeros of the function:

f(x) = x⁴-4x³+8x²-16x+16

a)

-3

b)

-2

c)

0

d)

2

10.

Match the graph to the function

a)

f(x) = x⁵-1

b)

f(x) = x⁵-6x³+8x+1

c)

f(x) = x³+8x+1

d)

f(x) = -x⁵-6x³+8x+1

11.

Match the graph to the function

a)

f(x)= -x²+3x+2

b)

f(x) = -x³+2

c)

f(x) = x³+2

d)

f(x) = ⅓x⁴-5x²+2

12.

Match the graph to the function

a)

f(x) = -2x⁶+9x²

b)

f(x) = x⁴+x³-5x²-6

c)

f(x) = -½x⁴+1

d)

f(x) = -x²+3x

13.

Choose the correct expanded common logarithm:

$\log(4x)$

a)

$\log4-\log x$

b)

$\log4+\log x$

c)

$4\log x$

d)

$x\log4$

14.

Choose the correct expanded common logarithm:

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

a)

$\log x+\log y$

b)

$x\log y$

c)

$\log(x-y)$

d)

$\log x-\log y$

15.

Choose the correct expanded common logarithm:

$\log(xy^2)$

a)

$\log x+2\log y$

b)

$\log x+\log y^2$

c)

$\log x-2\log y$

d)

$\log x+\log y+\log2$

16.

Choose the correct expanded common logarithm:

$\log\left(\frac{m^3}{n}\right)$

a)

$\log m-\log3-\log n$

b)

$3\log m+\log n$

c)

$3\log m-\log n$

d)

$3\log(m-n)$

17.

Choose the correct expanded common logarithm:

$\log(3x)^2$

a)

$2\log(3+x)$

b)

$2\log3+\log x$

c)

$\log3+2\log x$

d)

$2(\log3+\log x)$

18.

Choose the correct expanded natural logarithm:

$\ln\left(\frac{2x^2y}{z^4}\right)$

a)

$\ln2+2\ln x+\ln y+4\ln z$

b)

$\ln2+2\ln x+\ln y-4\ln z$

c)

$2\ln(2xy)-4\ln z$

d)

$2\ln2x+\ln y-4\ln z$

19.

True or False

$\ln\left(x+3\right)-\ln\left(2x\right)=\frac{\ln\left(x+3\right)}{\ln\left(2x\right)}$

a)

True, subtraction between two logarithms is division in condensed form.

b)

True, a logarithm is an exponent. When dividing like bases you subtract exponents therefor dividing logarithms as in this example.

c)

False, subtraction between two logarithms is division within a single logarithm in condensed form.

20.

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

21.

a)

p(x) = (x − 1)(x + 2)(x + 5)

b)

p(x) = (x + 1)(x − 2)²(x − 5)

c)

p(x) = (x − 1)²(x + 2)(x + 5)

d)

p(x) = (x − 1)(x + 2)²(x + 5)

22.

a)

A

b)

B

c)

C

d)

D

23.

a)

A

b)

B

c)

C

d)

D

24.

What does C do in the function
A sin B(x – C) + D
?

a)

Changes the amplitude

b)

Changes the period

c)

Changes the vertical position of the 'waves'

d)

Changes the horizontal position of the 'waves'

25.

Which value helps identify a horizontal shift in the following function y=a*sin(bx+c)+d?

a)

a

b)

b

c)

c

d)

d

26.

Which value helps identify a period shift in the following function y=a*sin(bx+c)+d?

a)

a

b)

b

c)

c

d)

d

27.

Which value helps identify a vertical shift in the following function y=a*sin(bx+c)+d?

a)

a

b)

b

c)

c

d)

d

28.

Which value helps identify an amplitude shift in the following function y=a*sin(bx+c)+d?

a)

a

b)

b

c)

c

d)

d

29.

Keon plans to buy a new GMC Sierra for $47,000 at 5.5% APR. Which financing option would have the highest total interest?

a)

60-month term and a $2,000 down payment

b)

60-month term and a $3,500 down payment

c)

36-month term and a $3,500 down payment

d)

36-month term and a $5,000 down payment

30.

Penicillin decays exponentially in the human body. Suppose you receive a 300-milligram dose of penicillin to combat strep throat. About 180 milligrams will remain active in your body after 1 day. Which equation represents the amount of penicillin remaining in your body?

a)

$y=300\left(0.6\right)^x$

b)

$y=300\left(1.6\right)^x$

c)

$y=300\left(1.67\right)^x$

d)

$y=300\left(0.4\right)^x$

31.

Which equation represents the given table?

a)

$y=15\left(1.8\right)^x$

b)

$y=15\left(0.8\right)^x$

c)

$y=15\left(1.2\right)^x$

d)

$y=15\left(0.2\right)^x$

e)

$y=-3x+15$

32.

The population of Bloom Falls, Mass. (population 937) is slowly moving to a bigger city.
Every year the population drops by 4.5%. What is the population after 3 years?

a)

1,069 people

b)

894 people

c)

816 people

d)

854 people

33.

What is the increasing interval on the function shown?

a)

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

b)

$\left(-\infty,\ 2\right)$

c)

$\left(2,\ \infty\right)$

d)

$\left(1,\ \infty\right)$

34.

What are the increasing and decreasing intervals of the graph?

a)

Increasing = (-1.5, 0) & (1.5, ∞)

Decreasing = (-∞, -1.5) & (0, 1.5)

b)

Increasing = (-∞, -1.5) & (0, 1.5)

Decreasing = (-1.5, 0) & (1.5, ∞)

c)

Increasing = (-∞, -1.5) & (1.5, ∞)

Decreasing = (-1.5, 0) & (0, 1.5)

d)

Increasing = (-1.5, 0) & (0, 1.5)

Decreasing = (-∞, -1.5) & (1.5, ∞)

35.

How many increasing/decreasing intervals are there in this graph?

a)

2 max, 2 min

b)

3 max, 2 min

c)

2 man, 3 min

d)

3 increasing intervals, 2 decreasing intervals

e)

2 increasing intervals, 3 decreasing intervals

36.

What is the decreasing interval(s) on the function shown?

a)

$\left(-7,\ -6\right)\ and\ \left(-2,\ 4\right)$

b)

$\left(-7,\ 0\right)\ and\ \left(-2,\ 4\right)$

c)

$\left(-7,\ -6\right)\ and\ \left(-2,\ 0\right)$

d)

$\left(-7,\ 0\right)\ and\ \left(4,\ 5\right)$

37.

Where is the function below decreasing:

f(x) = -x^1/3

a)

The slope is decreasing as x increases for all values of x

b)

The slope is increasing as x decreases for all values of x

c)

the slope is increasing as x increases for all negative values of x and the slope is decreasing for as x increases for all positive values for x

d)

the slope is increasing as x increases for all negative values of x and the slope is decreasing as x increases for all positive values for x

38.

What are the Vertical Asymptotes of...

a)

x = 0, -5

b)

x=0, 5

c)

x = 2, -7

d)

x = -2, 7

39.

What is the Vertical Asymptotes?

a)

x= -5

b)

x= 5

c)

x= 6

d)

x= -6

40.

Find the horizontal asymptote.

a)

None

b)

y = 0

c)

y = -1/3

d)

y = -3

41.

Which asymptote(s) are determined by looking at the denominator?

a)

vertical

b)

horizontal

c)

slant

d)

none

42.

Find the horizontal asymptote.

a)

y = -2

b)

none

c)

y = 0

d)

y = 1/2

43.

When finding the Horizontal asymptotes of a function, you should be thinking...

a)

"Set Denominator = to Zero"

b)

"Numerator = 0"

c)

"f(0)"

d)

"Look at the Degree of the numerator and denominator.."

44.

What are the equations of the asymptotes of the given graph

a)

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

b)

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

c)

x=2 and y= -1

d)

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

45.

Find the vertical asymptote.

g\left(x\right)=\frac{\left(x+3\right)\left(x-2\right)}{\left(x+5\right)\left(2x-1\right)}

a)

x=-5

b)

x=1/2

c)

x=-1/2

d)

x=-3

e)

x=2

46.

Which of the following functions will have a horizontal asymptote at $y=\frac{2}{3}$ ?

a)

$f\left(x\right)=\frac{2x^5}{3x^2-1}$

b)

$f\left(x\right)=\frac{x+2x^2+4}{5+2x\ +3x^2}$

c)

$f\left(x\right)=\frac{-2x^3+1}{3x^3-x^2-1}$

d)

$f\left(x\right)=\frac{2x^5+1}{3x^4+3x^2+2}$

47.

Factor completely.

121x² - 49

a)

( 11x - 7 ) ²

b)

( 11x - 7 ) ( 11x - 7 )

c)

( 11x + 7 ) ( 11x - 7 )

d)

( 12x + 7 ) ( 12x - 7 )

48.

Factor Completely: x⁴-9x²

a)

x²(x+3)(x-3)

b)

(x²+3x)(x²-3x)

c)

(x²+9)(x-3)(x+3)

d)

x²(x²-9)

49.

Factor the polynomial: $x^2 - 25$ .

a)

$(x - 5)(x + 5)$

b)

$(x - 25)(x + 1)$

c)

$(x - 5)^2$

d)

$(x + 5)^2$

50.

Identify the factored form of $4x^2 - 9$ .

a)

$(2x - 3)(2x + 3)$

b)

$(4x - 3)(x + 3)$

c)

$(2x - 9)(2x + 9)$

d)

$(x - 3)(x + 3)$

51.

What is the conjugate you would multiply by?

a)

5+2i

b)

5-2i

c)

-5-2i

d)

-5+2i

52.

Find a polynomial function of degree 3 with zeros 3i and -2.

a)

P(x) = x³+2x²+9x+11

b)

P(x) = x³-2x²+9x+18

c)

P(x) = x³+2x²+9x+18

d)

P(x) = x²-3ix+2x-6i

53.

How many x-intercepts does x⁴+6x²+9= 0 have?

a)

2

b)

1

c)

4

d)

None

54.

Descartes' Rule of Signs is helpful is solving what kind of equation?

a)

rational

b)

exponential

c)

logarithmic

d)

polynomial

55.

State the possible number of positive, negative, and imaginary zeros of each function.

f\left(x\right)=15x^5+25x^4+63x^3+105x^2-60x-100

a)

b)

c)

56.

What information does Descartes' Rule of Signs provide?

a)

How many solutions to expect

b)

What kind of solutions to expect (positive, negative, imaginary)

c)

Possible rational solutions to expect

57.

The degree of the polynomial determines the number of roots.

a)

True

b)

False

58.

How many zeros does the following function have?
f(x)= x⁵- 3x³ + x

a)

8

b)

9

c)

5

d)

3

59.

What are the roots of the polynomial function?
y = (x + 2)(x - 7)³

a)

-2, 7 multiplicity 3

b)

-2, 7, 3

c)

2, -7 multiplicity 3

d)

2, -7, 3

60.

What is the multiplicity of the zero x=1 for the function $f\left(x\right)=x^2\left(x-1\right)^4\left(x+5\right)$ ?

a)

2

b)

1

c)

4

d)

3

61.

Simplify the expression

(4x² - 6x - 8) + (3x² - 2x - 9)

a)

x² - 4x + 1

b)

7x² - 8x - 17

c)

12x² + 12x + 72

d)

7x⁴ - 8x² - 17

62.

Which of these is in Standard Form? (check all that apply)

a)

$4x^2+12x-13x^3$

b)

$5-3x$

c)

$2x^4-12x^2+5x-9$

d)

$5x^5+4x^{\text{4}}+12x^3-23x+15$

63.

3) Degree of

5a^4+7a^2-3a^9+10

is ____

a)

2

b)

4

c)

9

d)

10

64.

2) Degree of

2x^2+50

is _____

a)

50

b)

2

c)

4

d)

1

65.

What is the y-intercept of the polynomial y = (x - 2)(x + 3)?

a)

-6

b)

3

c)

5

d)

2

66.

What is the y-intercept of the polynomial y = (x - 1)(x - 2)(x - 3)?

a)

2

b)

1

c)

0

d)

-6

67.

What is the y-intercept of the polynomial y = 2x^4 - 3x^3 + 4x^2 - 5x + 1?

a)

2

b)

-1

c)

1

d)

0

68.

What is the y-intercept of the polynomial y = (x + 2)(x - 4)(x + 1)?

a)

-2

b)

4

c)

-1

d)

-8

69.

Write log_b(x/y) as two logs

a)

log_bx-log_by

b)

log_bx+log_by

c)

log_bx*log_by

d)

log_bx/log_by

70.

$\log8-\log2+2\log w$

a)

$\log\frac{4}{w^2}$

b)

$\log6w^2$

c)

$\log4w^2$

d)

$\log\frac{6}{w^2}$

71.

$\ln\left(\frac{2x^2y}{z^4}\right)$

a)

ln2+2lnx+lny+4lnz

b)

ln2+2lnx+lny-4lnz

c)

2ln(2xy)-4lnz

d)

2ln2x+lny-4lnz

72.

Condense

a)

A

b)

B

c)

C

d)

D

73.

Students in a group of chess teams submitted data about hours of team practice and the number of matches the team won. The graph shows the results of the data. Based on the linear regression equation y = 3.14x + 3.52, if a team practices 4.5 hours per week next year, which is the best prediction of the number of chess matches a team could expect to win?

a)

about 24

b)

about 12

c)

about 8

d)

about 18

74.

Is the pictured graph exponential growth, decay, or linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

75.

A restaurant sells pizza for the prices in the data table. Calculate the linear regression equation of the data.

a)

y = 1.5x + 12

b)

y = 12x + 1.5

c)

y = 0.67x - 8

d)

y = -8x + 0.67

76.

Find the equation of the line of best fit for the given data

a)

y = 163.41x+1.49

b)

y =- 163.41x+ 4.19

c)

y =- 4.19x+163.41

d)

y = 4.19x -163.41

77.

Find the inverse of $f\left(x\right)=6^x$ .

a)

$f^{-1}\left(x\right)=\log_x6$

b)

$f^{-1}\left(x\right)=\log_6x$

c)

$f^{-1}\left(x\right)=\log_{6x}^{ }$

d)

$f^{-1}\left(x\right)=\log\ \left(6+x\right)$

78.

Find the inverse function of $f\left(x\right)=5^x$

a)

$f^{-1}\left(x\right)\ =\ \log_5x$

b)

$f^{-1}\left(x\right)=\log_{5x}$

c)

$f^{-1}\left(x\right)=5\log x$

d)

$f^{-1}\left(x\right)=\log5x$

79.

Which equation is the inverse of the equation above?

a)

b)

c)

d)

80.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

81.

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

a)

Growth

b)

Decay

PreCalcA Course Review

Total questions: 81

Worksheet time: 5hrs 52mins

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