Free Printable LAM2--Final Exam Review

1.

Graph

a)

b)

c)

d)

2.

Evaluate f(-5)

a)

0

b)

2

c)

5

d)

-4

3.

Graph

a)

b)

c)

d)

4.

Is the relation a function? Why.

a)

Yes, because the x-value 11 has two y-values pair with it.

b)

Yes, because each x-value has only one y-value paired with it.

c)

No, because the x-value 11 has two y-values pair with it.

d)

No, because each x-value has only one y-value paired with it.

5.

Which of the following lines is PARALLEL to the graph of y = -6x + 3 and goes through the point (-1,4)?

a)

y=1/6x +25/6

b)

y = 1/6x + 4

c)

y = -6x - 2

d)

y = -6x + 4

6.

Level 3

Which two equations below are parallel?

a)

y = 2x + 1 and y = -1/2x + 1

b)

y = 2x + 3 and y = -2x + 3

c)

y = 2x - 1 and y = 1/2x - 1

d)

y = -x + 4 and y = -x + 2

7.

$j\left(j-9\right)=0$

a)

$j=0,\ j=9$

b)

$j=0,\ j=-9$

c)

$j=9$

d)

$j=-9$

8.

Solve

x² + 2x - 20 = 4

a)

x = -6, x = 4

b)

x = 6, x = -4

c)

x = 12, x = -2

d)

x = 8, x = -3

9.

Solve by taking square roots:
5b² - 4 = 41

a)

b = 9, b = -9

b)

b = 3, b = -3

c)

b = 8, b = -8

d)

no solution

10.

-5x² = -50

a)

± 5

b)

± 10

c)

± √10

d)

-10

11.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3
*remember right side should =0

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

12.

Convert x²- 9x + 20 to factored form and solve.

a)

(x-10)(x+2); x = -2, 10

b)

(x+4)(x+5); x = -5, -4

c)

(x-4)(x-5); x = 4, 5

d)

Not factorable

13.

Which of the following equations matches standard form of a quadratic?

a)

ax + by = c

b)

y = a(x - h)² + k

c)

y = ax² + bx + c

d)

y = mx + b

14.

What is another word for zeros?

a)

y-intercepts

b)

roots

c)

vertex

d)

axis of symmetry

15.

Solve the equation by finding the square roots. a²=64

a)

8

b)

-8

c)

±8

d)

{0,8}

16.

Determine the number of solutions to the given linear-quadratic system.

a)

0 solutions

b)

1 solution

c)

2 solutions

d)

3 solutions

17.

a)

A

b)

B

c)

C

d)

D

18.

$y-3=\left(x-1\right)^2$

$2x+y=5$

Solve the system graphically.

a)

(-1,7) and (1,3)

b)

(7,-1) and (3,1)

c)

(1,-7) and (-1,3)

d)

(-1,7) and (1,-3)

19.

Select all the Statements that are TRUE. $y\ =\ -3\left(x\ +\ 2\right)^2\ +\ 5$

a)

The Vertex is (-2, 5)

b)

There is a Minimum Value of 5

c)

There is a Maximum Value of 5

d)

The Axis of Symmetry is x = -2

20.

Complete the square of the following quadratic equation determine the Vertex.

$x^2\ +\ 14x\ -\ 15\ =\ 0$

a)

Vertex = (7, 64)

b)

Vertex = (-7 , 64)

c)

Vertex = (-7, -64)

d)

Vertex = (7 - 64)

21.

What do you do to the b value to correctly complete the square?

a)

square it

b)

divide it by 2 and square the result

c)

divide it by 2 and take the square root of the result

d)

divide it by 2 only

22.

Convert the quadratic equation $y\ =\ x^2\ -\ 2x\ +\ 5$ into vertex form.

a)

$y\ =\ \left(x\ -\ 1\right)^2\ +4$

b)

$y\ =\ \left(x\ -\ 1\right)^2\ -\ 6$

c)

$y\ =\ \left(x\ +\ 1\right)^2\ +4$

d)

$y\ =\ \left(x\ +\ 4\right)^2\ -\ 1$

23.

What is the equation of the circle given in the picture?

a)

$\left(x-4\right)^2+\left(y+2\right)^2=9$

b)

$\left(x+4\right)^2+\left(y-2\right)^2=9$

c)

$\left(x-4\right)^2+\left(y-2\right)^2=9$

d)

$\left(x+4\right)^2+\left(y+2\right)^2=9$

24.

$x^2+\left(y-4\right)^2=1$ Choose the graph that matches the equation of a circle.

a)

b)

c)

d)

25.

Simplify

a)

5i

b)

-5i

c)

±5i

d)

±

26.

Simplify

a)

± 2 √5

b)

± 4 √5

c)

± 5 √2

d)

± 5 √4

27.

Simplify:
(3 + 2i) + (4i + 6)

a)

9 + 6i

b)

7i + 8

c)

9 + 6i²

d)

9 - 6i

28.

Simplify:
(4 + 7i) - (3 + 2i)

a)

1 + 5i

b)

7 + 9i

c)

1 + 9i

d)

-1 + 5i

29.

Simplify:
2i(4 - 3i)

a)

6 + 8i

b)

6 - 8i

c)

8i - 6i²

d)

8i + 6i²

30.

Simplify:
(2 - 3i)(5 + 4i)

a)

22 - 7i

b)

22 + 7i

c)

22 - 7i²

d)

22 + 7i²

31.

Multiply:
(4 – 3i)(-7 – 2i)

a)

A. -23 + 13i

b)

B. -23 - 29i

c)

C. -34 + 13i

d)

D. -34 - 29i

32.

Multiply:
(2-5i)(2+5i)

a)

29

b)

4 - 25i

c)

25 - 10i

d)

-21

33.

Use the quadratic formula to find the solutions for
$y=-x^2-5x+12$

a)

No Real Solution

b)

$\frac{5\pm\sqrt{73}}{-2}$

c)

$\frac{-5\pm\sqrt{73}}{-2}$

d)

$\frac{5\pm\sqrt{73}}{2}$

34.

Solve using the quadratic formula. $f\left(x\right)=2x^2-4x+7$

a)

$\frac{2\pm2i\sqrt{10}}{2}$

b)

$\frac{4\pm\sqrt{40}}{4}$

c)

$\frac{2\pm i\sqrt{10}}{2}$

d)

$\frac{2\pm2i\sqrt{40}}{4}$

35.

Solve using the Quadratic Formula: $-x^2+4x=13$

a)

$2\pm3i$

b)

$-2\pm3i$

c)

$2\pm i\sqrt{17}$

d)

$-2\pm i\sqrt{17}$

36.

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

a)

-1

b)

1

c)

5

d)

6

37.

How many real zeros does the function have?

a)

None

b)

2

c)

3

d)

4

38.

Which root has a multiplicity of 2?

a)

-1

b)

2

c)

4

d)

-4

39.

Identify the zeros

a)

x=2, x=6, x=-4

b)

(x+2)(x+6)(x-4)

c)

(x-2)(x-6)(x+4)

d)

x=-2, x=-6, x=4

40.

Find the decreasing interval

a)

(-1, infinity)

b)

(-infinity, -1)

c)

(-infinity, 4)

d)

(4, infinity)

41.

What is the end behavior of this graph?

a)

x → ⁻∞, y→ ⁻∞ and

x→ ∞, y→ ⁻∞

b)

x → ⁻∞, y→ ∞ and

x→ ∞, y→ ∞

c)

x → ⁻∞, y→ ⁻∞ and

x→ ∞, y→ ∞

d)

x → ⁻∞, y→ ∞ and

x→ ∞, y→ ⁻∞

42.

What is the end behavior for the graph?

a)

x → ⁻∞, y→ ⁻∞ and

x→ ∞, y→ ⁻∞

b)

x → ⁻∞, y→ ∞ and

x→ ∞, y→ ∞

c)

x → ⁻∞, y→ ⁻∞ and

x→ ∞, y→ ∞

d)

x → ⁻∞, y→ ∞ and

x→ ∞, y→ ⁻∞

43.

What is the degree of x² + 3x³ - x⁴?

a)

2

b)

3

c)

4

d)

5

44.

Which of the following is a zero of (x + 2)(x - 1)?

a)

2

b)

1

c)

-1

d)

0

45.

State the point that you identify the relative maximum on the graph?

a)

(–2, 0)

b)

(–1, 4)

c)

(1, 0)

d)

(3, 20)

46.

State the point where you identify the relative minimum on the graph?

a)

(–2, 0)

b)

(–1, 4)

c)

(1, 0)

d)

(3, 20)

47.

Which points show the relative minimum on the graph?

a)

(0, 0)

b)

(–2, 16)

c)

(2, 16)

d)

(–2.5, 12)

48.

Which of the following polynomials in standard form?

a)

f(x)= 4x² - 2x + 7x⁴ + 5

b)

f(x)= -2x + 7x⁴ + 5 + 4x²

c)

f(x) = 5 - 2x + 7x⁴ + 4x²

d)

f(x)= 7x⁴ + 4x² - 2x + 5

49.

What is the leading coefficient for a non standard polynomial function? f(x) = -6x⁴ + x⁸ + 5x² - 2

a)

1

b)

5

c)

-2

d)

-6

50.

Determine the average rate of change over the interval [0, 1].

a)

-3

b)

3

c)

0

d)

2

51.

What are the zeros with multiplicities?

$g(x)=(x+4)^2(x+8)^3(x-5)$

a)

-4 multiplicity 1, -8 multiplicity 1, 5 multiplicity 3

b)

4 multiplicity 2, 8 multiplicity 3, -5 multiplicity 1

c)

4 multiplicity 3, 8 multiplicity 2, -5 multiplicity 1

d)

-4 multiplicity 2, -8 multiplicity 3, 5 multiplicity 1

52.

In the above graph, which root has a multiplicity of 2?

a)

-1

b)

-3

c)

-120

d)

4

53.

For synthetic division, what would be the number in the left hand box?

a)

0

b)

1

c)

2

d)

3

54.

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

55.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x+12

b)

2x⁴-x³-25x²-12x+0

c)

2x³-x²-25x-12

d)

2x⁴-x³-25x²-12x-0

56.

Which of the following are words that mean SOLUTIONS? Choose ALL of the possible answers.

a)

Zeroes

b)

Roots

c)

X-intercepts

d)

Y-intercepts

57.

(8p³-38p²-17p+43)÷(p-5)

a)

8p²+2p-7, R 8

b)

8p²+p-9, R 9

c)

8p²+p-5, R 13

d)

8p²+p-10, R 4

58.

What should you add to this problem?

(2x³ + 5x² + 9) ÷ (x + 3)

a)

0x⁴

b)

0x³

c)

0x²

d)

0x

59.

What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x³- 5x²+ 2x - 10

a)

0

b)

2x-10

c)

-2x-10

d)

2x+10

60.

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?

a)

Cam wrote the remainder incorrectly.

b)

Cam did not use a zero place holder for the x³ term.

c)

Cam added instead of subtracting the rows.

d)

Cam should have used -2 as his division since the factor was x-2.

61.

The following expression $x^{\frac{5}{2}}$ is equivalent to:

a)

$\frac{5x}{2}$

b)

$\frac{2x}{5}$

c)

$\sqrt{x^5}$

d)

$\ ^5\sqrt{x^2}$

62.

Rewrite the following

∛x⁵

a)

x^3/5

b)

x^5/3

c)

x²

d)

x³⋅x⁵

63.

Simplify:

a)

2

b)

8

c)

16

d)

32

64.

Simplify:

a)

2

b)

4

c)

16

d)

64

65.

Simplify:

a)

∛121

b)

121

c)

√11

d)

1331

66.

Which exponential expression is equivalent to

a)

b)

c)

d)

67.

Which radical expression is equivalent to $x^{\frac{1}{8}}$

a)

b)

c)

d)

68.

What is the value of the index?

a)

$\frac{1}{8}$

b)

$8$

c)

$5$

d)

$\frac{5}{8}$

69.

What is the value of the power?

a)

$\frac{1}{9}$

b)

$9$

c)

$-1$

d)

$1$

e)

$-\frac{1}{9}$

70.

Which expression results in a rational number?

a)

$\sqrt{2}\cdot\sqrt{18}$

b)

$5\cdot5\sqrt{5}$

c)

$\sqrt{2}+\sqrt{2}$

d)

$3\sqrt{2}+2\sqrt{3}$

71.

Simplify: 2√40 - 3√10

a)

5√10

b)

√10

c)

-√30

d)

$\sqrt[]{30}$

72.

The common logarithm has what base?

a)

10

b)

0

c)

e

d)

-e

73.

Solve for x:

log_x1000=3

a)

1

b)

10

c)

30

d)

3

74.

Solve for x:
log₄ x = 3

a)

4

b)

12

c)

32

d)

64

75.

Solve

a)

8

b)

-8

c)

1/8

d)

-1/8

76.

Solve

a)

1

b)

-1

c)

6

d)

-6

77.

Solve

a)

1/2

b)

-1/2

c)

2

d)

-2

78.

Solve

a)

1/81

b)

-1/81

c)

-81

d)

81

79.

Solve

a)

1/3

b)

-1/3

c)

3

d)

-3

80.

Solve

a)

9

b)

-9

c)

1/9

d)

-1/9

81.

What is the equation that represents the exponential function in the image below?

a)

y=3(½)^x

b)

y=3(2)^x

c)

y=(2)^x

d)

y=2(3)^x

82.

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

83.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

84.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

85.

Which of the following is an example of exponential decay?

a)

y = 3(5)^x

b)

y = .5(5)^x

c)

y = 2(.5)^x

d)

y = 8(1)^x

86.

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

87.

Suppose you deposit $3000 in a savings account that pays interest at an annual rate of 4%. What is the growth factor?

a)

.96

b)

1.4

c)

1.04

d)

$3000

88.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

89.

Determine the graph for the following function:

$f\left(x\right)=\frac{4}{x+1}-1$

a)

b)

c)

90.

What is the 20^thterm of the arithmetic sequence shown below.

7, 4, 1,...

a)

-49

b)

50

c)

-50

d)

-51

91.

Find the common ratio for the geometric sequence.

a)

10

b)

1/2

c)

2

d)

4

92.

Write the explicit formula for the geometric sequence.

a)

a_n = 10(2)^n-1

b)

a_n = 2(10)^n-1

c)

a_n = 10(2)ⁿ

d)

a_n = 2(10)ⁿ

93.

Which equation best represents the relationship between x and y in the table shown?

a)

y= 5x+5

b)

y=1/5x+5

c)

y=15x+5

d)

y=10x+5

94.

Write the explicit formula for the sequence given by 3, 6, 12, 24, …

a)

^a_n= 3(2)^n-1

b)

^a_n= 3+(2)ⁿ

c)

^a_n= 3(2)ⁿ

d)

^a_n= 3+(2)^n-1

95.

What is the common ratio for the sequence:
28, -14, 7, -3.5...

a)

1/2 (or 0.5)

b)

- 1/2 (or -0.5)

c)

-14

d)

-7

96.

Which of the the following are examples of arithmetic sequence?

a)

$\frac{1}{4},\frac{1}{2},\frac{3}{4},1$

b)

$6,11,16,21,...$

c)

$100,95,90,85,80,75$

d)

$100,50,25,\ ...$

97.

Find the next three terms for the arithmetic sequence
12, 7, 2, -3, ...

a)

8, 13, 18

b)

-8, -13, -18

c)

-7, -11, -15

d)

7, 11, 15

98.

Find the given term for the sequence.
Find the 30th term of 20, 11, 2, -7, -16, ...

a)

29

b)

-261

c)

-241

d)

cannot be determined

99.

The axis of symmetry line passes through which point?

a)

y-intercept

b)

any random point

c)

vertex

d)

symmetrical point for the vertex

100.

In the picture, what does the coordinate (0, -2), where the parabola crosses over the y-axis, represent?

a)

the x-intercept

b)

the minimum

c)

the axis of symmetry

d)

the y-intercept

101.

If the vertex of this graph is (2, -1), what is the axis of symmetry?

a)

y= 2

b)

x = 2

c)

y = -1

d)

x = -2

102.

What is the vertex of y=x²+4x+3?

a)

(2,1)

b)

(-2,1)

c)

(0,0)

d)

(-2,-1)

103.

Given the equation y = 3(x + 5)² - 4,

what is the vertex of the parabola?

a)

(5, -4)

b)

(-5, -4)

c)

(-15, -4)

d)

(15, -4)

104.

What is the quadratic for the following factored form: (x - 7)(x + 7)?

a)

x² + 7x - 49

b)

x² - 7x + 49

c)

x² - 49

d)

x² + 49

105.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

106.

Maggie is knitting blankets for the residents of a local nursing home. She already has 6 blankets completed. After one week, Kay has 8 blankets. After two weeks, Kay has 10 blankets. Kay's scenario is best represented by a _______________ function.

a)

Linear

b)

Quadratic

c)

Exponential

d)

None of the above

107.

In the first year of an annual 5K run there were 120 participants. In the 2nd and 3rd year of the 5K run, there were 180 and 270 participants respectively. This situation is best modeled by a(n) ________________ function.

a)

linear

b)

quadratic

c)

exponential

d)

none of the above

108.

Given the following table of values, construct the function that represents the sequence.

a)

y = 3(4)^x

b)

y = 3x + 4

c)

y = 4(3)^x

d)

y = 4x + 3

109.

Which of the following statements is true about the functions f(x) and g(x)?

a)

The y-intercept of the function f(x) is less than the y-intercept of the function g(x).

b)

The y-intercept of the function f(x) is greater than the y-intercept of the function g(x).

c)

The y-intercept of the function f(x) is equal to the y-intercept of the function g(x).

d)

The y-intercepts cannot be determined.

110.

What function model best represents the data in the table?

a)

linear

b)

exponential

c)

quadratic

111.

Put these functions in order from least to greatest based on their Y-INTERCEPT.

a)

B C A

b)

B A C

c)

C A B

d)

C B A

112.

Monica did an experiment to compare two method of warming an object. The results are shown in the table above. Which statement best describes her results?

a)

The temperature using both methods changed at a constant rate.

b)

The temperature using both methods changed at an exponential rate.

c)

The temperature using Method 2 changed at a constant rate.

d)

The temperature using Method 2 changed at an exponential rate.

113.

Pick a function that best models the following situation: A babysitter getting paid hourly.

a)

Exponential

b)

Linear

c)

Quadratic

d)

Neither

114.

Slope is another word for:

a)

Initial Value

b)

Rate of Change

c)

Change in Y's

d)

Y-intercept

115.

What variable is commonly used for domain?

a)

A

b)

X

c)

?

d)

Y

116.

The graph below describes a ball that was kicked. Which of the following is a true statement describing the graph?

a)

The ball was kicked from 500 centimeters from the ground and it traveled for 4 seconds.

b)

The ball was kicked from the ground and it was in the air for 4 seconds.

c)

The ball had a maximum height of 2000 centimeters and it was in the air for a total of 2 seconds.

d)

The ball had a maximum height of 1000 centimeters and it was in the air for 4 seconds.

117.

Identify the domain and range of the function.

a)

Domain: -6 ≤ x ≤ 2
Range: -3 ≤ y ≤ 5

b)

Domain: All real numbers.

Range: $y>-3$

c)

Domain: All real numbers
Range: y ≥ -3

d)

Domain: All real numbers Range: y ≤ -3

118.

Which function best models the data in the given table?

a)

y = -3x + 9

b)

y = 4x² - 3x + 1

c)

y = 5.2(.75)^x

d)

y = -3x² + 4x + 1

119.

What is the probability that a randomly selected student plays sports given that they do not do community service?

a)

$\frac{4}{27}$

b)

$\frac{4}{12}$

c)

$\frac{4}{9}$

d)

$\frac{4}{5}$

120.

What is the probability that a randomly selected student plays sports and does not participate in community service?

a)

$\frac{4}{9}$

b)

$\frac{4}{12}$

c)

$\frac{4}{27}$

d)

$\frac{9}{27}$

121.

What is the probability that a student takes Latin given that they participate in a club?

a)

$\frac{59}{378}$

b)

$\frac{41}{59}$

c)

$\frac{41}{378}$

d)

$\frac{41}{240}$

122.

Units of the population are grouped; one or more groups are selected at random. All units of that group are included in the sample.

a)

cluster sample

b)

simple random

c)

stratified

d)

proportional

123.

Cluster, stratified, simple random, systematic, and proportional are all types of

a)

convenience samples

b)

biased samples

c)

haphazard samples

d)

unbiased samples

124.

Identify the sampling design: The LFCC registrar wants to investigate attitudes of their graduates. The registrar randomly selects 100 names from each of the four past graduating classes.

a)

cluster

b)

volunteer

c)

stratified

d)

simple random

125.

Identify the sampling design: School admin conducted a survey on post-graduation plans. Students of senior class 2018 were listed in order by class rank. The school selected a random number between 1 and 15, obtaining a number 11. Then, they selected every 11th student for the survey.

a)

cluster

b)

volunteer

c)

systematic

d)

simple random

126.

Identify the sampling design: Mr. Rhoades puts all of his students' names in a hat and randomly selects one without looking.

a)

cluster

b)

volunteer

c)

systematic

d)

simple random

127.

A researcher randomly assigned students to two groups. One group was assigned to watch a violent television program while the other group watched a nonviolent program. The student's behavior was then recorded for incidences of aggressive behavior. Which research method is most appropriate?

a)

experimental

b)

census

c)

sample survey

d)

observational study

128.

Jane Goodall lived among wild chimpanzees intermittently for decades, studying their social and family systems while keeping her interaction with the chimpanzees to a minimum. Which research method is most appropriate?

a)

biased study

b)

census

c)

experiment

d)

observational study

129.

Ghala wanted to know what the most popular book was in the whole school, so she asked everybody in 11th grade what their favorite book was. Which research method is most appropriate?

a)

Sample Survey

b)

Census

c)

Experiment

d)

Biased Sample

130.

This research method is a technique for ascertaining the self – reported attitudes or behaviors of a particular group, usually by questioning a representative, random sample of the group.

a)

Survey

b)

Observational

c)

Correlational

d)

Experiments

e)

Case Study

LAM2--Final Exam Review

Total questions: 130

Worksheet time: 7hrs 30mins

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