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FINAL EXAM - FOUNDATIONS

Total questions: 79

Worksheet time: 15hrs 51mins

Name
Class
Date
1.

The number is a/an...

a)

Rational Number

b)

Irrational Number

c)

Integer

d)

Whole Number

2.

The number is a/an...

a)

Rational Number

b)

Irrational Number

c)

Integer

d)

Whole Number

3.

Which of the following numbers is irrational?

a)

√8

b)

¾

c)

2

d)

-1.325

4.

Which number is an irrational number?

a)

2.5

b)

5.72314.....

c)

-17

d)

1/2

5.

Which answer choice correctly shows the expression in exponential form? 
5x3^5\sqrt{x^3}

a)

x35x^{\frac{3}{5}}  

b)

x53x^{\frac{5}{3}}  

c)

3x3x  

d)

5x5x  

6.

Which answer choice correctly shows the expression in exponential form? 
4a3^4\sqrt{a^3}

a)

3a4\frac{3a}{4}  

b)

a34a^{\frac{3}{4}}  

c)

a43a^{\frac{4}{3}}  

d)

4a3\frac{4a}{3}  

7.

Rewrite the polynomial in standard form: -5 + 4m

a)

-5 + 4m

b)

4m - 5

c)

-4m + 5

d)

4m2 - 5

8.

Which of the following polynomials is written in standard form?

a)

9 + 8x - 2x2

b)

10x + x3 - 4x2 - 11

c)

x4 + 5x3 - 6x +1

d)

4x3 + 3x4 + 2x + 1

9.

The product of seven and j..

a)

7j

b)

j+3

c)

j-3

d)

j/3

10.

5 less than the product of 7 and s

a)

7s - 5

b)

5 - 7 + s

c)

7(s - 5) 

d)

5 - 7s

11.

5 less than a number is 15.

a)

x - 5 = 15

b)

5 - x = 15

c)

15 - x = 5

12.

Translate the sentence into an inequality.
Seven subtracted from n is greater than or equal to 18.

a)

n - 7 > 18

b)

7 - n ≥ 18

c)

n - 7 ≥ 18

d)

n + 7 ≥ 18

13.

Simplify the expression by combining like terms:

5x + 3y + 5 + 4x + 3y + y + 8

a)

9x + 7y + 13

b)

6x + 2y + 2

c)

25x + 2y + 3

d)

x + 7y + 12

14.

Simplify the expression by combining like terms:


3x2y + 4x - 6y + 4x2y -2y

a)

11x2y - 8y

b)

3y

c)

7x2y - 4y

d)

7x2y + 4x - 8y

15.

What is the perimeter of this triangle?

*hint: To find perimeter, add all sides.

a)

2x - 2

b)

4x - 2

c)

2x + 8

d)

4x + 8

16.

What is the degree classification of this polynomial?
x²+4x-8

a)

binomial

b)

trinomial

c)

quadratic

d)

cubic

17.

What is the term classification of the following polynomial?
x³-7x²+3

a)

monomial

b)

binomial

c)

trinomial

d)

polynomial

18.

What is the classification of the following polynomial?
x²-8x+10

a)

quadratic binomial

b)

cubic trinomial

c)

linear binomial

d)

quadratic trinomial

19.

5 + 2(n + 1) = 2n
Bill says the first step is to add and get
7(n + 1) = 2n

a)

Bill is correct

b)

Bill is wrong; he should have distributed the 2 first.

c)

Bill is wrong; he should have subtracted 5 from both sides first.

d)

Bill is wrong; he should have divided by 2 firat.

20.

Is there a mistake on the equation solved? If so where was the mistake made?

a)

This equation is solved correctly.

b)

The mistake was made on the first step of moving the variable to the right side.

c)

The mistake was made on the second step of moving the constant to the left side.

d)

The mistake was made on the last step when isolating the variable by removing the coefficient

21.

Which property of real numbers justifies the work shown from Step 1 to Step 2?

a)

Distributive Property

b)

Commutative Property

c)

Identity Property

d)

Associative Property

22.

Which property justifies the work in solving this equation?

a)

Addition Property of Equality

b)

Additive Inverse Property

c)

Identity Property of Addition

d)

Subtraction Property of Equality

23.

Which property justifies the work shown?

a)

Multiplication Property of Equality

b)

Subtraction Property of Equality

c)

Division Property of Equality

d)

Addition Property of Equality

24.

Do I need to flip my sign?
-3x  ≥ 12

a)

Yes, because I'll be dividing by a negative number

b)

No, because you never flip the sign. 

25.

Write the phrase as an expression.
twice a number x plus 8 is greater than 12

a)

2 + 8x < 12

b)

2x + 8 > 12

c)

2(x+8) ≠ 12

d)

8(2+x) 

26.

Which sentence represents m > 41?

a)

Mary’s points, m, totaled more than 41

b)

Calvin ran no less than 41 miles, m

c)

The temperature, m, was less than 41°F

d)

The magazines’ cost, m, was not more than $41.

27.

The steps in solving 5b - 6 > 24 are:

a)

Add 6 to both sides and divide both sides by 5

b)

Add 6 to both sides and multiply both sides by 5

c)

Subtract 6 from both sides then multiply both sides by 5

d)

Subtract 6 from both sides then divide both sides by 5

28.

Graph the solution set of the inequality.


–4n + 1 > –23

a)
b)
c)
d)
29.

Graph the solution set of the inequality.


–4a ≤ –28

a)
b)
c)
d)
30.

Which of the following are solutions to the inequality  x+6≥10x+6\ge10  ?

a)

3

b)

4

c)

5

d)

6

31.

Solve I = prt for r.

a)

r = I/pt

b)

r = pt/I

c)

r = I - pt

d)

r = pt - I

32.

-2 = 4r + s solve for s.

a)

s = -2 + 4r

b)

s = 2 - 4r

c)

s = -2 - 4r

d)

s = 2 + 4r

33.

Solve the formula for y. What is the 1st step?

a)

Subtract B from each side.

b)

Divide each side by Ax.

c)

Divide each side by B.

d)

Subtract Ax from each side.

34.

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.

35.
a)

It is a function because no vertical lines hit it twice.

b)

It's not a function because a vertical line hits it twice.

c)

It's not a function because no vertical lines hit it twice.

d)

It is a function because a vertical line hits it twice.

36.
a)
It is a function because no vertical lines hit it twice.
b)
It's not a function because a vertical line hits it twice.
c)
It's not a function because no vertical lines hit it twice.
d)
It is a function because a vertical line hits it twice.
37.

Which set of values is a function?

a)

(9,5) (10,5) (9,-5) (10,-5)

b)

(3,4) (4,-3) (7,4) (3, 8)

c)

(6,-5) (7, -3) (8, -1) (9, 1)

d)

(2, -2) (5, 9) (5, -7) (1, 4)

38.

Is this set of ordered pairs a function and how can you tell?

a)

Yes its a function because no y values repeat

b)

No it's not a function because there are negative numbers

c)

No it isn't a function because an x value repeats but has different y values 

d)

No it isn't a function because an y value repeats but has different x values

39.

  1. Consider the function given below.

  2. (−𝟔, 𝟕), (−𝟑, 𝟎), (𝟎, 𝟖), (𝟑, 𝟑), (𝟕, −𝟏𝟎)

  3. What point could be added so that it still represents a function?

a)

(−5, 0)

b)

(−3, 2)

c)

(0,6)

d)

(3, −10)

40.

Which of the following best describes a reasonable range for this situation?

a)

All real numbers greater than or equal to 0 and less than or equal to 400

b)

All real numbers greater than or equal to 0 and less than or equal to 25

c)

All real numbers less than or equal to 25

d)

All real numbers greater than or equal to 400

41.

What is the range of the table?

a)

{-4, 0, 1, 3}

b)

{-2, 0, 2, 3}

c)

{-4, -2, 0, 1, 2, 3}

d)

{ (0, 0), (2, -4), (3, 3), (-2, 1) }

42.

Identify the domain of the following relation:

a)

-6, 14, 2, 28

b)

(-6,14), (0,32), (2,38), (4,44)

c)

-6, 0, 2, 4

d)

14, 32, 38, 44

43.

Identify the solutions of the graph?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

44.

Find the zero(s) of the function.

a)

x = -3

b)

x = 1

c)

x = {-3, 1}

d)

y = 1

45.

Find the root(s) of the function.

a)

x = 3

b)

x = {-3, -1, 2}

c)

x = {-3, 2}

d)

x = -1

46.

  1. Find the zeros

f(x)=−x3+7x2+18xf\left(x\right)=-x^3+7x^2+18x

a)

x= 0, 9, 2

b)

x= 0, -9 ,2

c)

x= 0, 9 ,-2

d)

x= 9, -2

47.

  1. Find the zeros

f(x)=x4−36x2f\left(x\right)=x^4-36x^2

a)

x= 0, 0, 6, -6

b)

x= 0, 6

c)

x= 0, 6, -6

d)

x= 6, -6

48.

Find the rate of change.

a)

-2 minutes per gallon

b)

-20 minutes per gallon

c)

-2 gallons per minute

d)

-20 gallons per minute

49.

This graph represents Matthew taking his dogs out for a walk.  Along which section of the graph is Matthew moving the fastest? 

a)

A

b)

B

c)

D

d)

E

50.

Which statement below accurately represents the graph?

a)

$100 is earned for each hour worked

b)

$100 is earned for every 2 hours worked

c)

$500 is earned for every 8 hours worked

d)

$150 is earned for every 3 hours worked

51.

What is the equation of a line with a slope of 4 and a y-intercept of 2?

a)

y = -4x + 2

b)

y = -2x + 4

c)

y = 4x + 2

d)

y = 2x + 4

52.

Determine the slope and y-intercept.         y = 3/2x + 3

a)

slope: 5   y-intercept:  (0,3) 

b)

slope: 3/2   y-intercept:  (0,3) 

c)

slope:  4  y-intercept:  (0,3/2)

d)

slope: 1/5   y-intercept:  (0,5) 

53.

What is the slope-intercept form of a line?

a)

Ax + By = C

b)

y = mx + b

c)

y - y1 = m(x - x1)

d)

y = Ax + By

54.

What is the formula for standard form?

a)

y=mx+b

b)

y-y1=m(x-x1)

c)

Ax+By=C

d)

rise÷run

55.

An airplane 30,000 feet above the ground begins descending at a rate of 2,000 feet per minute. Write an equation to model the situation.

a)

y = - 2,000x + 30,000

b)

y = - 2,000x - 30,000

c)

y = 30,000x + 2,000

d)

y = -30,000x + 2,000

56.

A canoe rental service charges a $20 transportation fee and $30 dollars an hour to rent a canoe. Write an equation representing the cost, y, of renting a canoe for x hours.

a)

y = 30x + 20

b)

y = 20x + 30

c)

y = 50x

d)

y = 60x

57.

For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. Write an equation for the cost, C, after h hours of babysitting. 

a)

C = 5h + 3

b)

C = 3h + 5

c)

H = 5c + 3

d)

H = 3c + 5

58.

Two relationships are described:


Relationship A: John walked 6 miles in 2 hours, then he walked 12 miles in 4 hours.


Relationship B: Adam baked 200 cookies in 2 hours, then he baked 500 cookies in 3 hours.


Which statement is true about these relationships?

a)

Neither relationship is a direct variation.

b)

Both relationships are direct variations.

c)

Only Relationship A is a direct variation.

d)

Only Relationship B is a direct variation.

59.

Which of the given graphs is a direct variation?

a)

A

b)

B

c)

C

d)

D

60.

Which table represents a direct variation?

a)
b)
c)
d)
61.

The amount of money earned on a job is directly proportional to the number of hours worked.  If $70.00 is earned in 5 hours, how much money is earned in 22 hours of work?

a)

$2

b)

$308

c)

$1.57

d)

$265

62.

The interest received on a savings account varies directly with the amount deposited. Daniel received $55.35 in interest on $1230 he deposited. How much interest would Daniel have received if he had deposited $2000 into his account?

a)

34.04

b)

90.00

c)

1,285.35

d)

44,444.44

63.

The width of a rectangle varies inversely with its length. If the width is 4 when the length is 18, what is the width when the length is 8?

a)

4

b)

5

c)

9

d)

12

64.

Is the sequence arithmetic: 37, 31, 25, 19, ...

a)

Yes

b)

No

65.

Find the common difference: -34, -29, -24, -19, ...

a)

d = -5

b)

d = 5

c)

d = -6

d)

d = 6

66.

Is the sequence arithmetic: 17, 9, 1, -7, ...

a)

Yes

b)

No

67.

Find the common difference: 29, 21, 13, 5, ...

a)

d = -10

b)

d = -9

c)

d = -8

d)

d = -7

68.

Write an equation for the nth term given the sequence:
2, 8, 14, 20, ...

(Hint:  Use the formula an = a1 + d(n - 1)

a)

an = 2 + 6n

b)

an = -6 + 6n

c)

an = 6n - 4

d)

an = 4 - 6n

69.

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  How many minutes does it take for Alexandria to finish each type of job?

Select which system of equations represents the situation and select the correct answer.

You must have TWO responses.

a)

System:

3x + 2y = 315
2x + 4y = 450

b)

System:

3x + 2y = 450
2x + 4y = 315

c)

System:

2x + 2y = 315
3x + 4y = 450

d)

Answer:

45 minutes for a haircut and 90 minutes for a hair dye

e)

Answer:

90 minutes for a haircut and 45 minutes for a hair dye

70.

Josh is thinking of two numbers.  Their sum is -10 and their difference is -2. What are the two numbers?

Select which system of equations represents the situation and select the correct answer.

You must have TWO responses.

a)

System:

x - y = -10
x + y = -2

b)

System:

x + y = -2
x - y = -10

c)

System:

x + y = -10
x - y = -2

d)

Answer:

The first number is -6 and the 2nd number is -4.

e)

Answer:

The first number is -6 and the 2nd number is 4

71.

The cost of 5 squash and 2 zucchini is $1.32. Three squash and one zucchini cost $0.75. Write a system of equations.

Select which system of equations represents the situation and select the correct answer.

You must have TWO responses.

a)

System:

5x + 2y = 1.32
3x + 1y = 0.75

b)

System:

1x + 1y = 1.32
1x + 1y = 0.75

c)

System:

5x + 1y = 1.32

3x+ 2y = 0.75

d)

Answer:

Each squash costs 18 cents and zucchini costs 21 cents

e)

Answer:

Each squash costs 21 cents and zucchini costs 18 cents

72.

The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. How much is the cost for each type of ticket?

Select which system of equations represents the situation and select the correct answer.

You must have TWO responses.

a)

System:

1x + 3y = 38
2x + 3y = 52

b)

System:

3x + 1y = 38
3x + 2y = 52

c)

System:

3x + 3y = 38
1x + 2y = 52

d)

Answer:

A senior citizen ticket costs $8 and a Child ticket costs $14

e)

Answer:

A senior citizen ticket costs $14 and a child ticket costs $8

73.

Complete the box.

a)-6x
b)2x
c) x2x^2
d)6x
e)-2x
f)-12
1
2
3
4
1)
2)
3)
4)
74.

Complete the box.

a)7
b)-3
c) x2x^2
d)10x
e)-3x
f)-30
1
2
3
4
1)
2)
3)
4)
75.

Mr.Ben used the box method to solve (3x−1)(x+4)\left(3x-1\right)\left(x+4\right) Which of the following will Mr.Ben get if he simplifies correctly?  

a)

3x2+11x−43x^2+11x-4  

b)

3x2+13x−43x^2+13x-4  

c)

3x2+11x+43x^2+11x+4  

d)

3x2−11x+43x^2-11x+4  

76.

Find the product:
(3x – 1)(x + 5) 

a)

3x2 + 4x + 5

b)

3x2 + 4x - 5

c)

3x2 + 14x + 5

d)

3x2 + 14x - 5

77.

If the point (2, −10)\left(2,\ -10\right)   lies on the graph of an inverse variation, which represents the inverse variation equation?

a)

y=−20xy=-20x  

b)

y=−5xy=-5x  

c)

y=−20xy=-\frac{20}{x}  

d)

y=−5xy=-\frac{5}{x}  

78.
What type of variation does this scenario represent?
The length of time you charge your cell phone
and the battery power 
a)
direct variation
b)
inverse variation
c)
joint variation
d)
none of these
79.
The amount of money earned on a job is directly proportional to the number of hours worked.  If $70.00 is earned in 5 hours, how much money is earned in 22 hours of work?
a)

$2

b)

$308

c)

$1.57

d)

$265

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