Free Printable Regents Review Alg 2

1.

a)

1

b)

2

c)

3

d)

4

2.

a)

1

b)

2

c)

3

d)

4

3.

a)

1

b)

2

c)

3

d)

4

4.

a)

1

b)

2

c)

3

d)

4

5.

a)

1

b)

2

c)

3

d)

4

6.

a)

1

b)

2

c)

3

d)

4

7.

a)

1

b)

2

c)

3

d)

4

8.

a)

Odd

b)

Even

c)

Neither

9.

a)

1

b)

2

c)

3

d)

4

10.

a)

1

b)

2

c)

3

d)

4

11.

What are the zeros of the function f(x) = x² — 13x — 30?

a)

—10 and 3

b)

10 and —3

c)

—15 and 2

d)

15 and —2

12.

f(x) = x². g(x) = f(x - 4) + 2. Name the translation that takes f(x) to g(x).

a)

Four units up, two units right

b)

Two units left, four units down

c)

Four units right, two units up

d)

Four units left, two units up

13.

The function f(x) = √(x - 3) has a domain of:

a)

x ≤ 3

b)

x ≥ -3

c)

x ≥ 3

d)

x ≤ -3

14.

If the area of a rectangle is expressed as x⁴ — 9y², then the product of the length and the width of the rectangle could be expressed as

a)

(x — 3y)(x + 3y)

b)

(x² — 3y)(x² + 3y)

c)

(x²— 3y)(x² — 3y)

d)

(x⁴ + y)(x — 9y)

15.

Note: Recall "average rate of change" means to find the slope between the given points.

a)

4.3

b)

4.5

c)

5.4

d)

6.0

16.

5, 15, 45, 135 is a ...

a)

Geometric sequence with r = 3

b)

Geometric sequence with r = 1/3

c)

Arithmetic sequence with d = 10

d)

Arithmetic sequence with d = 3

17.

Solve the logarithmic function: log₃(x + 5) = 2

a)

x = 14

b)

x = 4

c)

x = 11

d)

x = 6

18.

What are the zeros of the function f(x) = x² — 13x — 30?

a)

—10 and 3

b)

10 and —3

c)

—15 and 2

d)

15 and —2

19.

Which function represents exponential decay?

a)

f(x) = 100(0.9)^x

b)

f(x) = 10(1.09)^x

c)

f(x) = 1.9^x

d)

f(x) = ½(9)^x

20.

f(x) = x². g(x) = f(x - 4) + 2. Name the translation that takes f(x) to g(x).

a)

Four units up, two units right

b)

Two units left, four units down

c)

Four units right, two units up

d)

Four units left, two units up

21.

The function f(x) = √(x - 3) has a domain of:

a)

x ≤ 3

b)

x ≥ -3

c)

x ≥ 3

d)

x ≤ -3

22.

If the area of a rectangle is expressed as x⁴ — 9y², then the product of the length and the width of the rectangle could be expressed as

a)

(x — 3y)(x + 3y)

b)

(x² — 3y)(x² + 3y)

c)

(x²— 3y)(x² — 3y)

d)

(x⁴ + y)(x — 9y)

23.

Note: Recall "average rate of change" means to find the slope between the given points.

a)

4.3

b)

4.5

c)

5.4

d)

6.0

24.

Reese invested $600 in a savings account at a 2.8% annual interest rate. She made no deposits or withdrawals on the account for 2 years. The interest was compounded annually. Find, to the nearest cent, the balance in the account after 2 years.

a)

$634.07

b)

$983.04

c)

$8,864.00

d)

$566.87

25.

2

a)

1

b)

2

c)

3

d)

4

26.

a)

1

b)

2

c)

3

d)

4

27.

a)

1

b)

2

c)

3

d)

4

28.

5, 15, 45, 135 is a ...

a)

Geometric sequence with r = 3

b)

Geometric sequence with r = 1/3

c)

Arithmetic sequence with d = 10

d)

Arithmetic sequence with d = 3

29.

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

a)

20, 100, 500, 2500

b)

5, 20, 80, 320

c)

4, 20, 100, 500

d)

4, 9, 14, 19

30.

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?

a)

14327

b)

4309

c)

839

d)

7680

31.

Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased about 5% per year. How much is the home worth today?

a)

$176,783.29

b)

$424,527.63

c)

$57,357.75

d)

$532,041,076.80

32.

Solve the logarithmic function: log₃(x + 5) = 2

a)

x = 14

b)

x = 4

c)

x = 11

d)

x = 6

33.

Which scenario is best described as an observational study?

a)

For a class project, students in Health class ask every 10^th student entering the school if they eat breakfast in the morning

b)

A social researcher wants to learn whether or not there is a link between attendance and grades. She gathers data from 15 school districts

c)

A researcher wants to learn whether or not there is a link between children’s daily amount of physical activity and their overall energy level. During lunch at the local high school, she distributed a short questionnaire to students in the cafeteria

d)

Sixty seniors taking a course in Advanced Algebra Concepts are randomly divided into two classes. One class uses a graphing calculator all the time, and the other class never uses graphing calculators. A guidance counselor wants to determine whether there is a link between graphing calculator use and students’ final exam grades

34.

a)

b)

c)

d)

35.

Which scenario is best described as an observational study?

a)

For a class project, students in Health class ask every 10^th student entering the school if they eat breakfast in the morning

b)

A social researcher wants to learn whether or not there is a link between attendance and grades. She gathers data from 15 school districts

c)

A researcher wants to learn whether or not there is a link between children’s daily amount of physical activity and their overall energy level. During lunch at the local high school, she distributed a short questionnaire to students in the cafeteria

d)

Sixty seniors taking a course in Advanced Algebra Concepts are randomly divided into two classes. One class uses a graphing calculator all the time, and the other class never uses graphing calculators. A guidance counselor wants to determine whether there is a link between graphing calculator use and students’ final exam grades

36.

a)

b)

c)

d)

37.

a)

The asymptote has equation y=0

b)

The graph has no y-intercept

c)

The domain is the set of positive reals

d)

The range is the set of all real numbers

38.

a)

2 or -4

b)

4 or -2

c)

3, only

d)

2, only

39.

a)

150

b)

70

c)

10

d)

0

40.

Given the parent function p(x)=cos(x), which phrase best describes the transformation used to obtain the graph of g(x)=cos(x+a) - b, if a and b are positive constants?

a)

Right a units, up b units

b)

Right a units, down b units

c)

Left a units, up b units

d)

Left a units, down b units

41.

a)

b)

c)

d)

42.

Which equation is represented by the graph shown below?

a)

y = 1/2 cos(2x)

b)

y = cos(x)

c)

y = 1/2 cos(x)

d)

y = 2 cos(1/2 x)

43.

a)

f(x) = 4/3x - 8/3

b)

f(x) = -4/3x + 8/3

c)

f(x) = 3/4x - 2

d)

f(x) = -3/4x + 2

44.

a)

b)

c)

d)

45.

There was a study done on oxygen consumption of snails as a function of pH, and the result was a degree 4 polynomial function whose graph is shown. Which statement about this function is incorrect?

a)

The degree of the polynomial is even

b)

There is a positive leading coefficient

c)

At two pH values, there is a relative maximum value

d)

There are two intervals where the function is decreasing

46.

Which sinusoid has the greatest amplitude?

a)

b)

c)

d)

47.

A researcher randomly divides 50 bean plants into two groups. He puts one group by a window to receive natural light and the second group under artificial light. He records the growth of the plants weekly. Which data collection method is described in this situation?

a)

Observational study

b)

Controlled experiment

c)

Survey

d)

Systematic sample

48.

a)

p(x) has three real roots and m(x) has two real roots

b)

p(x) has one real root and m(x) has two real roots

c)

p(x) has two real roots and m(x) has three real roots

d)

p(x) has three real roots and m(x) has four real roots

49.

a)

5 - 17i

b)

5 + 27i

c)

-19 - 17i

d)

-19 + 27i

50.

a)

b)

2, only

c)

d)

51.

What are the zeros of the function f(x) = x² — 13x — 30?

a)

—10 and 3

b)

10 and —3

c)

—15 and 2

d)

15 and —2

52.

Which function represents exponential decay?

a)

f(x) = 100(0.9)^x

b)

f(x) = 10(1.09)^x

c)

f(x) = 1.9^x

d)

f(x) = ½(9)^x

53.

f(x) = x². g(x) = f(x - 4) + 2. Name the translation that takes f(x) to g(x).

a)

Four units up, two units right

b)

Two units left, four units down

c)

Four units right, two units up

d)

Four units left, two units up

54.

The function f(x) = √(x - 3) has a domain of:

a)

x ≤ 3

b)

x ≥ -3

c)

x ≥ 3

d)

x ≤ -3

55.

If the area of a rectangle is expressed as x⁴ — 9y², then the product of the length and the width of the rectangle could be expressed as

a)

(x — 3y)(x + 3y)

b)

(x² — 3y)(x² + 3y)

c)

(x²— 3y)(x² — 3y)

d)

(x⁴ + y)(x — 9y)

56.

Reese invested $600 in a savings account at a 2.8% annual interest rate. She made no deposits or withdrawals on the account for 2 years. The interest was compounded annually. Find, to the nearest cent, the balance in the account after 2 years.

a)

$634.07

b)

$983.04

c)

$8,864.00

d)

$566.87

57.

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

a)

20, 100, 500, 2500

b)

5, 20, 80, 320

c)

4, 20, 100, 500

d)

4, 9, 14, 19

58.

Solve the logarithmic function: log₃(x + 5) = 2

a)

x = 14

b)

x = 4

c)

x = 11

d)

x = 6

59.

a)

1

b)

2

c)

3

d)

4

60.

a)

1

b)

2

c)

3

d)

4

61.

a)

1

b)

2

c)

3

d)

4

62.

a)

1

b)

2

c)

3

d)

4

63.

a)

1

b)

2

c)

3

d)

4

64.

a)

1

b)

2

c)

3

d)

4

65.

a)

1

b)

2

c)

3

d)

4

66.

What is the range of the graph?

a)

y≥1

b)

x≥1

c)

All real numbers

d)

none of these

67.

a)

(1)

b)

(2)

c)

(3)

d)

(4)

68.

a)

(1)

b)

(2)

c)

(3)

d)

(4)

69.

a)

(1)

b)

(2)

c)

(3)

d)

(4)

70.

a)

(1)

b)

(2)

c)

(3)

d)

(4)

71.

a)

(1)

b)

(2)

c)

(3)

d)

(4)

72.

a)

(1)

b)

(2)

c)

(3)

d)

(4)

73.

a)

(1)

b)

(2)

c)

(3)

d)

(4)

74.

a)

(1)

b)

(2)

c)

(3)

d)

(4)

75.

a)

(1)

b)

(2)

c)

(3)

d)

(4)

76.

a)

(1)

b)

(2)

c)

(3)

d)

(4)

77.

To find the x-intercept of a function, you should:

a)

Set x = 0

b)

Set y or f(x) = 0

c)

Solve for m

d)

set x =b

78.

To find the y-intercept of a function you should

a)

Set x = 0

b)

Solve for m

c)

Set y or f(x) = 0

d)

Set x =b

79.

The slope of a line is given by which of the following:

a)

$m\ =\ \frac{x_1-x_2}{y_1-y_2}$

b)

$m\ =\ \frac{y_1-y_2}{x_1-x_2}$

c)

$y\ =\ mx\ +\ b$

d)

$y\ -\ y_1=\ m\left(x-x_1\right)$

80.

Which equation below is a quadratic?

a)

y=9x+5

b)

y=3x²-6

c)

y=5x³+6

d)

x=3^x

81.

Find the axis of symmetry for
f(x) = x²- 8x + 15.

a)

x = -4

b)

x = 4

c)

y = 4

d)

y = -4

82.

What is the equation for axis of symmetry?

a)

y=3

b)

x=3

c)

x=5

d)

x=1

83.

The focus is always inside the parabola.

a)

true

b)

false

84.

The vertex is halfway between the focus and directrix.

a)

true

b)

false

85.

If the blue graph is f(x) = x²

then the red must be...

a)

g(x) = x²- 5

b)

g(x) = x²+ 5

c)

g(x) = (x - 5)²

d)

g(x) = (x + 5)²

86.

When b > 0 and d is a positive integer, the expression $\left(3b\right)^{\frac{2}{d}}$ is equivalent to

a)

$\frac{1}{\left(\sqrt[d]{3b}\right)^2}$

b)

$\left(\sqrt[]{3b}\right)^d$

c)

$\frac{1}{\sqrt[]{3b^d}}$

d)

$\left(\sqrt[d]{3b}\right)^2$

87.

Given $i$ is the imaginary unit, $\left(2-yi\right)^2$ in simplest form is

a)

$y^2-4yi+4$

b)

$-y^2-4yi+4$

c)

$-y^2+4$

d)

$y^2+4$

88.

Which graph has the following characteristics:

- three real zeros

- $as\ x\rightarrow-\infty,\ \ f\left(x\right)\rightarrow-\infty$

- $as\ x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$

a)

b)

c)

d)

89.

The zeros for $f\left(x\right)=x^4-4x^3-9x^2+36x$ are

a)

$\left\{0,\ \pm3,\ 4\right\}$

b)

{0, 3, 4}

c)

$\left\{0,\ \pm3,\ -4\right\}$

d)

{0, 3, -4}

90.

When b > 0 and d is a positive integer, the expression $\left(3b\right)^{\frac{2}{d}}$ is equivalent to

a)

$\frac{1}{\left(\sqrt[d]{3b}\right)^2}$

b)

$\left(\sqrt[]{3b}\right)^d$

c)

$\frac{1}{\sqrt[]{3b^d}}$

d)

$\left(\sqrt[d]{3b}\right)^2$

91.

Given $i$ is the imaginary unit, $\left(2-yi\right)^2$ in simplest form is

a)

$y^2-4yi+4$

b)

$-y^2-4yi+4$

c)

$-y^2+4$

d)

$y^2+4$

92.

Which graph has the following characteristics:

- three real zeros

- $as\ x\rightarrow-\infty,\ \ f\left(x\right)\rightarrow-\infty$

- $as\ x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty$

a)

b)

c)

d)

93.

The solution set for the equation $\sqrt[]{56-x}=x$ is

a)

{-8, 7}

b)

{-7, 8}

c)

{7}

d)

{ }

94.

The zeros for $f\left(x\right)=x^4-4x^3-9x^2+36x$ are

a)

$\left\{0,\ \pm3,\ 4\right\}$

b)

{0, 3, 4}

c)

$\left\{0,\ \pm3,\ -4\right\}$

d)

{0, 3, -4}

95.

Anne has a coin. She does not know if it is a fair coin. She flipped the coin 100 times and obtained 73 heads and 27 tails. She ran a computer simulation of 200 samples of 100 fair coin flips.

Given the results of her coin flips and of her computer simulation, which statement is most accurate?

a)

73 of the computer's next 100 coin flips will be heads.

b)

50 of her next 100 coin flips will be heads.

c)

Her coin is not fair.

d)

Her coin is fair.

96.

a)

1

b)

2

c)

3

d)

4

97.

a)

1

b)

2

c)

3

d)

4

98.

a)

1

b)

2

c)

3

d)

4

99.

a)

1

b)

2

c)

3

d)

4

100.

a)

1

b)

2

c)

3

d)

4

101.

Solve the logarithmic function: log₃(x + 5) = 2

a)

x = 14

b)

x = 4

c)

x = 11

d)

x = 6

102.

Which equation is represented by the graph shown below?

a)

y = 1/2 cos(2x)

b)

y = cos(x)

c)

y = 1/2 cos(x)

d)

y = 2 cos(1/2 x)

103.

There was a study done on oxygen consumption of snails as a function of pH, and the result was a degree 4 polynomial function whose graph is shown. Which statement about this function is incorrect?

a)

The degree of the polynomial is even

b)

There is a positive leading coefficient

c)

At two pH values, there is a relative maximum value

d)

There are two intervals where the function is decreasing

104.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

105.

a)

A

b)

B

c)

C

d)

D

106.

a)

1

b)

2

c)

3

d)

4

107.

a)

1

b)

2

c)

3

d)

4

108.

Condense

a)

A

b)

B

c)

C

d)

D

109.

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

a)

19

b)

23

c)

-10

d)

None of these.

110.

a)

b)

c)

d)

111.

a)

10

b)

-10

c)

10i

d)

-10i

112.

To the nearest tenth, the value of x that satisfies $2^x=\ -2x+11$ is

a)

$2.5$

b)

$2.6$

c)

$5.8$

d)

$5.9$

113.

Given the parent function p(x)=cos(x), which phrase best describes the transformation used to obtain the graph of g(x)=cos(x+a) - b, if a and b are positive constants?

a)

Right a units, up b units

b)

Right a units, down b units

c)

Left a units, up b units

d)

Left a units, down b units

114.

If cos A = √5/3 and tan A < 0, what is the value of sin A?

a)

-2/3

b)

2/3

c)

√5/3

115.

Mia has a student loan that is in deferment, meaning that she does " not need to make payments right now. The balance of her loan account during her deferment can be represented by the function f(x) = 35,000(l.0325)x, where x is the number of years since the deferment began. If the bank decides to calculate her balance showing a monthly growth rate, an approximately equivalent function would be

a)

35,000(l.0027)^12x

b)

35,000(l.0027)^12/x

c)

35,000(l.0325)^12x

116.

Algebraically determine the zeros of the function below.

r(x) = 3x³ + 12x² - 3x - 12

a)

{-1, 1, -4}

b)

{-1, 1, 4}

c)

{-1, -1, -4}

117.

The scores on a collegiate mathematics readiness assessment are approximately normally distributed with a mean of 680 and a standard deviation of 120. Determine the percentage of scores between 690 and 900, to the nearest percent.

(a)

118.

$\sqrt{8-x}=x-6$

a)

-7

b)

7

c)

4

d)

-4

119.

For the following pair of complex numbers, what is the quadratic equation that has these roots?

a)

y = x² + 24x +135

b)

y = x² + 24x +153

c)

y = x² + 24x +147

d)

y = x² + 24x +141

120.

What is the Amplitude for the following function?

a)

7

b)

2

c)

d)

-4

e)

121.

The Midline for the following function is y = ?

a)

7

b)

2

c)

d)

-4

e)

122.

Write a polynomial function of least degree with integral coefficients that has the given zeros.

5, -2i

a)

x³-5x²+4x-20

b)

x³-5x²+4x-23

c)

x³-5x²+4x-19

d)

x³-10x²+4x-20

123.

The vertex, (h, k), is halfway between the focus and the directrix.

a)

true

b)

false

124.

If the directrix is y = 4 and the focus is at
(3, 0), the value of p is:

a)

8

b)

-8

c)

2

d)

-2

125.

If a parabola has a focus at (0,3) and a vertex at the origin...what is the equation of the directrix?

a)

y=3

b)

y=-3

c)

x=3

d)

x=-3

126.

What is Mrs. Gordon's rate from 0 to 2 seconds?

a)

2.5 feet per second

b)

.4 feet per second

c)

5 feet per second

d)

.2 feet per second

127.

Expand ln(uw²)

a)

ln u + ln w

b)

2ln uw

c)

ln u + 2ln w

d)

ln (uw) + 2

128.

Solve the following equation. Round to the nearest ten-thousandth.

$e^x=30$

a)

0.2871

b)

3.4012

c)

2.1842

d)

-9.3587

Regents Review Alg 2

Total questions: 128

Worksheet time: 8hrs 4mins

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