Free Printable Alg 2 9 week test

1.

If (n³ - 2) is a factor of

2n⁴ + 7n³ - 4n - 14. Which is the other factor. (Factor Theorem)

a)

(n - 2)

b)

(n - 1)³

c)

(2n + 7)

d)

(n + 1)

2.

If (k² - 13) is a factor of

k⁴ - 10k² - 39. What is the other factor? (Remainder Theorem)

a)

(k² + 3)

b)

(k + 3)

c)

(x²-4)

d)

(k - 5)

3.

Factor out the GCF then apply x-method to factor completely.
3x² + 18x +15

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

4.

The number of hours to paint a house varies inversely with the number of painters working. A house can be painted in 27 hours by 6 painters. How many painters would need to work in order to paint the house in 18 hours?

a)

8 painters

b)

10 painters

c)

9 painters

d)

Before answering, watch video first.

5.

The value of y varies directly with x. Which function represents the relationship between x and y if y = 14 when x = 6.

a)

y=20x

b)

y=84x

c)

y=7/3x

d)

y=3/7x

6.

The variables $x$ and $y$ vary inversely. Use the given values to write an inverse variation equation:

$x=8,\ \ y=5$

a)

$y=\frac{40}{x}$

b)

$y=\frac{0.625}{x}$

c)

$y=40x$

d)

$y=0.625x$

7.

$Log_32x=5$ can be rewritten as...

a)

$2x=3^5$

b)

$5=3^{2x}$

c)

$2x=5^3$

8.

$Log_{6x}4=-9$ can be rewritten as...

a)

$4=6x^{-9}$

b)

$6x=4^{-9}$

c)

$4=-9^{6x}$

9.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

10.

14² = 196

a)

log₁₄196 = 2

b)

log₂ 14 = 196

c)

log₂ 196 = 14

d)

log₁₄ 14 = 2

11.

Solve using nsolve menu 3, 1

$\log_8\left(3x+7\right)=\log_8\left(7x+4\right)$

a)

$x=\frac{3}{4}$

b)

$x=3$

c)

$x=6$

d)

$x=\frac{4}{3}$

12.

Solve using nsolve menu 3, 1

$\log_6x+\log_69=\log_654$

a)

x=6

b)

x=45

c)

x=7

d)

x=36

13.

Solve using nsolve menu 3, 1

log₄(3x-1)=log₄(2x+3)

a)

4

b)

3

c)

1

d)

8

14.

Solve using nsolve menu 3, 1
2^-2n = 2⁶

a)

-1

b)

-7

c)

5

d)

-3

15.

Solve using nsolve menu 3, 1

3³ = 3^{4x + 2}

a)

¼

b)

-¼

c)

½

d)

-½

16.

Solve using nsolve menu 3, 1

8 = 2^5x+7

a)

⅘

b)

¼

c)

-⅘

d)

-¼

17.

Solve using nsolve menu 3, 1

2^x+1 = 512

a)

x = 255

b)

x = 8

c)

x = 256

d)

x = 9

18.

Which expression is equivalent.

Hint: Plug in a value on original expression and evaluate. Then plug in the same value you plugged in on original expression on answer choices and evaluate each to find matching outcome.

a)

(x + 9)

b)

(x - 3) / (x + 2)

c)

(x + 9) / (x + 2)

19.

$Simplify:\ \ \frac{x^2+7x+10}{x^2-4}$

Hint: Plug in a value on original expression and evaluate. Then plug in the same value you plugged in on original expression on answer choices and evaluate each to find matching outcome.

a)

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

b)

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

c)

$\frac{x+5}{x-2}$

20.

Subtract the expressions

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

Hint: Plug in a value on original expression and evaluate. Then plug in the same value you plugged in on original expression on answer choices and evaluate each to find matching outcome.

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)

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

21.

Add
$\frac{8n}{n-3}+\frac{3n}{5n-6}$

Hint: Plug in a value on original expression and evaluate. Then plug in the same value you plugged in on original expression on answer choices and evaluate each to find matching outcome.

a)

$\frac{43n^2-9}{\left(5n-6\right)\left(n-3\right)}$

b)

$\frac{11n}{6n-9}$

c)

$\frac{43n^2-57n}{\left(n-3\right)\left(5n-6\right)}$

22.

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

Steps on Calculator

Menu 6, 1, then select Linear Regression and input the data. Do not forget to put the set notation {......}

a)

y = 1.5x + 12

b)

y = 12x + 1.5

c)

y = 0.67x - 8

23.

The linear regression equation is y = 61.93x - 1.79. Use the equation to predict how far this person will travel after 10 hours of driving.

Hint: Plug in the given value 10 in the correct variable and evaluate.

a)

10 miles

b)

617.5 miles

c)

0.19 miles

24.

The linear regression equation is y = 61.93x - 1.79. According to the model, the slope can be interpreted as:

a)

After 0 hours of driving, they went 61.93 miles.

b)

They drove at a speed of 61.93 miles per hour.

c)

They drove 61.93 miles total.

d)

They drove 61.93 hours total.

25.

Based on the table, which quadratic function can best be used to model this situation?

Menu 6, 1, then select Quadratic Regression and input the data. Do not forget to put the set notation {......}

a)

h(t) = 99t² + 858

b)

h(t) = -4.9t² + 295t + 0.6

c)

h(t) = -4.9t² + 295t + 2

26.

Which of the following quadratic equations best represents the following data?

Menu 6, 1, then select Quadratic Regression and input the data. Do not forget to put the set notation {......}

a)

y = 7x² - 3x

b)

y = 3x² - 2x + 1

c)

y = 6x² + 3x - 2

27.

What is the exponential equation of this table?

a)

y=512(1/4)^x

b)

y=32(4)^x

c)

y=32(1/4)^x

28.

Which equation is represented by the table?

a)

y = 40(2)^x

b)

y = 40(1/2)^x

c)

y = 40 - 2x

d)

y = 40 - 1/2x

29.

A chemist has a 100-gram sample of a radioactive material. He records the amount of radioactive material every week for 6 weeks and obtains the following data: How much is left after 12 weeks?

Hint: Find exponential equation the plug in the 12 into x and evaluate.

a)

15

b)

21

c)

17

30.

Match the following. #44

a)

1.

Non-linear Correlation

b)

2.

No Correlation

c)

3.

Positive, Linear Correlation

d)

4.

Negative, Linear Correlation

31.

Which equation best represents the table?

Graph each given equation than get the table by pressing ctrl t

a)

y=2x-3

b)

y=x²-5

c)

y=(2)^x

32.

Which function matches the following table?

Graph each equation then pull up table by pressing ctrl t

a)

y=4x²-0.5x+1.27

b)

y=1.257x-2

c)

y=2(.707107)^x

33.

Which function family matches the following table.

a)

Linear

b)

Quadratic

c)

Exponential

d)

Neither

34.

Which of the following transformations are present (select all that apply)?

g(x)= -2f(x - 1)) + 2

a)

reflection over x axis

b)

1 unit to the right

c)

vertical Stretch by a factor of 2

d)

2 units up

e)

Vertical Compression by factor of 2

35.

Describe the transformation of the equation below from the absolute value parent function. SELECT ALL THAT APPLY $g\left(x\right)=\frac{1}{2}f\left(x+3\right)-2$

a)

right 3

b)

left 3

c)

Down 2

d)

Vertical Compression by 1/2

e)

stretch by 2

36.

The function $f\left(x\right)$ was reflected over the y-axis and vertically stretched with a scale factor of 5 and shifted 4 units down. Which rule describes this transformation?

a)

$g\left(x\right)=f\left(-5x\right)-4$

b)

$g\left(x\right)=5f\left(-x\right)+4$

c)

$g\left(x\right)=-5f\left(x-4\right)$

d)

$g\left(x\right)=5f\left(-x\right)-4$

37.

The function $f\left(x\right)$ was reflected over the x-axis and vertically stretched with a scale factor of 3 and shifted 8 units up. Which rule describes this transformation?

a)

$g\left(x\right)=f\left(-3x\right)+8$

b)

$g\left(x\right)=3f\left(-x\right)+8$

c)

$g\left(x\right)=-3f\left(x-8\right)$

d)

$g\left(x\right)=-3f\left(x\right)+8$

38.

What are the transformations of this functions compared to the parent function?

$f\left(x\right)=-2\sqrt[]{x-5}$

a)

Shifted right 5, shifted down 2, and reflected over the x-axis

b)

Reflected over the x-axis, vertical stretch, and shifted right 5

c)

Reflected over the x-axis, vertical stretch, and shifted left 5

d)

Shifted right 5, shifted down 2

39.

What are the transformations for the graph of

$f\left(x\right)\ =\ 2\sqrt[]{x}-5$

a)

Vertical Stretch by a factor of 2; translated down 5 units

b)

Shifted right 2 units and down 5 units

c)

Vertical stretch by a factor of 2; translated left 5 units

d)

Vertical stretch by a factor of 2; translated right one unit

40.

Solve for r by using nsolve menu 3, 1

a)

5

b)

- 5, 4

c)

- 5

d)

5, 4

41.

Solve by using nsolve menu 3, 1

a)

x = 5

b)

x = -3

c)

x = 3

d)

x = -5

42.

Solve by using nsolve menu 3, 1

a)

x = 4.5

b)

x = -4.5

c)

x = 3

d)

x = -3

43.

Solve the equation for x by using nsolve menu 3, 1

a)

6

b)

12

c)

0

d)

3

44.

Solve for x by using nsolve menu 3, 1

a)

x = 10

b)

x = -30/13

c)

x = 6

d)

no solution

45.

Which of the following is true.

a)

Inverse graphs reflect over the diagonal line y=x

b)

inverse graphs reflect over the x-axis

c)

inverse graphs reflect over the y-axis

46.

Which graphs are inverse ?

a)

b)

c)

none

d)

47.

Are these functions inverses?

a)

Yes, they are a reflection over the diagonal dotted line.

b)

No, they are not a reflection over the diagonal dotted line.

48.

Are these inverse graphs?

a)

no, bc they are a reflection over the y-axis instead of the diagonal line.

b)

yes, they are inverse graphs?

c)

no way to tell

49.

What's the best description?

a)

They are both functions, but not inverse functions.

b)

They are reflected over y=x, but they are not both functions.

c)

They are not reflected over y=x, and they are not both functions.

d)

They are inverse functions.

50.

Graph the inverse

a)

b)

c)

d)

51.

Which is the inverse of the table?

a)

b)

c)

d)

52.

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

a)

(1, 4) and (4, 6)

b)

(-4, -1) and (-6, -4)

c)

(-1, -4) and (-4, -6)

d)

(4, 1) and (6, 4)

53.

Find the inverse function of $f\left(x\right)=\sqrt{x}-6$ and the restricted domain.

a)

$y=\left(x+6\right)^2$ with a restricted domain of ( -∞, -6)

b)

$y=\left(x+6\right)^2$ with a restricted domain of (-6, ∞)

54.

Find the inverse function of $y=x^2+9$ with a restricted domain of (-∞,0)

a)

$y=-\sqrt{x-9}$

b)

$y=\sqrt{x-9}$

55.

Find the inverse function of $y=\sqrt{x+11}$

a)

$y=x^2-11$ with a restricted domain of (0, ∞)

b)

$y=x^2+11$ with a restricted domain of (-∞,0)

56.

Find the inverse of $f\left(x\right)=-4\left(5\right)^{x-7}+12$

a)

$f^{-1}\left(x\right)=\log_5\left(-\frac{1}{4}x+3\right)+7$

b)

$f^{-1}\left(x\right)=7\log_5\left(-\frac{1}{4}x+3\right)$

c)

$f^{-1}\left(x\right)=\log_5\left(x-3\right)-7$

57.

Find the inverse of $f\left(x\right)=\left(10\right)^{6x+18}-7$

a)

$f^{-1}\left(x\right)=\frac{1}{6}\log_{10}\left(x+7\right)-3$

b)

$f^{-1}\left(x\right)=1\log_{10}\left(x+7\right)$

c)

$f^{-1}\left(x\right)=6\log_{10}\left(x-7\right)+3$

58.

Find the inverse of y = e^x+1 - 4

a)

f^-1(x)= ln (x + 4) - 1

b)

f^-1(x)= ln (x + 1) - 4

c)

f^-1(x)= ln (x + 4 + 1)

59.

Inverse of y = ln (x+5) - 7

a)

f^-1(x) = e^x+7 - 5

b)

f^-1(x) = e^x+5 - 7

c)

f^-1(x) = x + 2

60.

Solve. Select BOTH solutions.
$\left|-4+x\right|=10$
Hint: You can also plug in the given values into the x, evaluate, and find the ones with a True outcome.

a)

$6$

b)

$14$

c)

$\frac{5}{2}$

d)

$-6$

61.

Solve. Select BOTH solutions.
$5\left|7+x\right|+2=17$

Hint: You can also plug in the given values into the x, evaluate, and find the ones with a True outcome.

a)

$-10$

b)

$3$

c)

$4$

d)

$-4$

62.

Solve the following equation:

|6 − 2k| = 18

Hint: You can also plug in the given values into the x, evaluate, and find the ones with a True outcome.

a)

k = −6, k = 6

b)

k = −6, k = 12

c)

k = −6, k = −12

d)

k = −6, k = 5

63.

Solve for x: $10+9\left|x+8\right|<55$

Plug in a number in the solution set into the x, evaluate, and find the one with a True outcome.

a)

$18<x<30$

b)

$-13<x<-3$

c)

$-50<x<-32$

64.

Solve for x:
$-5\left|4+x\right|<-15$

Plug in a number in the solution set into the x, evaluate, and find the one with a True outcome.

a)

$x>-1\ \ \ or\ \ \ x<-7$

b)

$-7<x<-1$

c)

no solution

65.

Match the system to the graph (solution set is on the left)

a)

y ≤ 3x and y ≤ -2x + 4

b)

y > 3x and y > -2x + 4

c)

y < 3x and y > -2x + 3

d)

y > 3x and y < -2x + 4

66.

Which of the following is not a solution to this system of inequalities?

a)

(0,-1)

b)

(0,3)

c)

(4,0)

d)

(6,-2)

67.

Which of the following points is a solution to the system of equations below?
x + 2y ≥ 4
3x − 2y < 4

a)

(0, 0)

b)

(2, 1)

c)

(2, 2)

d)

(-1, 1)

Alg 2 9 week test

Total questions: 67

Worksheet time: 5hrs 13mins

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