Free Printable Applied Algebra Semester 1 Final Practice Test

1.

What is the y-intercept in the equation?

y = 5x - 4

(a)

2.

Find the equation of the line in slope-intercept form.

a)

y = - 1/4x - 3

b)

y = 3x + 3

c)

y = -1/3x + 3

d)

y = 1/3x - 3

e)

y= 3x -3

3.

Which is the graph of y=-x+2?

a)

A

b)

B

c)

C

d)

D

4.

Select the correct graph for each inequality.

a)

A

b)

B

c)

C

d)

_D

5.

which equation best represents this graph?

a)

y < 1/2x + 1

b)

y < 1/2x + 2

c)

y >1/2x + 2

d)

y > 2x

e)

y> 3/2x +2

6.

Which point below is NOT part of the solution set?

a)

(0, 0)

b)

(5, 1)

c)

(-1, -3)

d)

(20, -5)

7.

Identify the inequality.

a)

y > 2

b)

y ≤ 1

c)

x ≥ 2

d)

y ≥ 1

8.

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)

9.

Which system of inequalities matches the graph?

a)

y > 2x - 4

y < 2

b)

y < 2x - 4

y < 2

c)

y > 2x - 4

y < 2

d)

y < 2x - 4

y < -2

10.

Which point is a solution?

a)

(0, 6)

b)

(-3, 4)

c)

(1, 0)

d)

(-4, 3)

11.

a)

(2.5, 1)

b)

(1, 2.5)

c)

(-2.5, -1)

d)

(-1, -2.5)

12.

Parallel Lines never intersect because...

a)

they have the same slopes.

b)

they have the same y-intercept.

c)

they have different slopes.

d)

they have different y-intercepts.

13.

Which of the following graphs best describes a system with no solution?

a)

b)

c)

d)

14.

Which inequality is equivalent to 7x - 2y > 8 ?

a)

b)

c)

d)

15.

-4x + 14 ≤ 54

a)

x ≥ - 10

b)

x ≤ -10

c)

x ≥ 10

d)

x ≤ 10

16.

Find the slope of the line that passes through the points (2, 4) and (6, 12)

a)

1/2

b)

-1/2

c)

2

d)

-2

17.

a)

b)

c)

d)

18.

Which graph matches the inequality

-2 ≥ n?

a)

A

b)

B

c)

C

d)

D

19.

Which inequality matches the graph?

a)

A

b)

B

c)

C

d)

D

20.

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.

21.

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)

22.

For the function f(x) = -3x + 3 find f(0).

a)

0

b)

-3

c)

3

d)

-1

23.

Given f(x) = -4x - 10 and f(x) = 10. Find x

a)

x = -5

b)

x = 5

c)

x = -50

d)

x = 30

24.

Solve: 2(4x - 3) - 8 = 4 + 2x

a)

5/3

b)

3

c)

1

d)

2

25.

How many solutions does the following equation have?

4x - 8 = -2(-2x + 4)

a)

No solutions

b)

1 solution

c)

Infinitely many solutions

26.

Solve m - n = 5 for m.

a)

m = 5 + n

b)

m = -5 - n

c)

m = -5 + n

d)

m = 5 - n

27.

Solve for the indicated variable.

a)

A = l/w

b)

w = l/A

c)

w = A

d)

w = A/l

28.

Seven times a number plus three is less than the product of the number and 9.

a)

7x + 3 < 9x

b)

7x + 3 > 9x

c)

7x + 3 < x/9

d)

7x + 3 > x/9

29.

Solve by elimination:

4x+9y=28

-4x-y=-28

a)

(-7,0)

b)

(6,0)

c)

(-6,0)

d)

(7,0)

30.

Solve by elimination:

7x-9y=29

7x+2y=-15

a)

(-4,-1)

b)

(-1.-4)

c)

(-1,4)

d)

(-1,6)

31.

In order to join a dancing club, there is a $30 startup fee and a $4 monthly fee. Write an equation in slope-intercept form that models this situation. After how many months will the total cost be $58?

a)

7 months

b)

6 months

c)

5 months

d)

4 months

32.

What is the value of x in the solution to the system of equations?

a)

1

b)

5/3

c)

8/3

d)

7/3

33.

Which graph does not represent y as a function of x?

a)

b)

c)

d)

34.

An architect is designing an office building with n floors that will have an FM radio antenna 15.85 meters tall on its roof. Each floor of the building will be 3.9 meters high. Which function can be used to find the total height of the building in meters, including the FM antenna?

a)

h(n) = 15.85n + 3.9

b)

h(n) = 3.9n + 15.85

c)

h(n) = 3.9n - 15.85

d)

h(n) = 19.75n

35.

What is the range of the function shown?

a)

{-7, -2, 0, 5}

b)

{-9, -4, -1}

c)

{-9, -7, -4, -2, -1, 0, 5}

d)

{-1}

36.

Which of the following is equivalent to 3x - 4y = 6?

a)

y = -6/7x

b)

y = -3/4x

c)

y = 4/3x + 2

d)

y = 3/4x - 3/2

37.

If y = -4/5x - 2, what is the value of x when y = -9?

a)

-35/4

b)

-55/4

c)

35/4

d)

55/4

38.

The table represents points on the graph of a linear function. What is the rate of change of y with respect to x for this function?

a)

2/9

b)

-9/2

c)

9/2

d)

-2/9

39.

Which inequality describes all of the solutions to the given inequality?

a)

x < -9

b)

x > 3

c)

x < -3

d)

x > 7

40.

Which is the solution to 5+2x>7?

a)

A

b)

B

c)

C

d)

D

41.

A furnace repair person charges an initial fee of $80 plus $30 per hour to do repairs. After how many hours would the cost of the repair be at least $320?

a)

6 hours

b)

7 hours

c)

8 hours

d)

9 hours

42.

Which compound inequality is represented by the graph?

a)

-1 < x - 1 < 4

b)

-1 < x + 1 < 4

c)

-2 < x - 1 < 3

d)

-2 < 2x < 3

43.

Determine the number of solutions to the equation.

a)

x = -6

b)

y = 6

c)

no solution

d)

infinitely many solutions

44.

-6x + 5 = -6x + 5

a)

no solution

b)

two solutions

c)

one solution

d)

infinitely many solutions

45.

Which of the following lines are parallel to y = -1/2x + 4?

a)

y = 2x + 4

b)

y = 1/2x + 2

c)

y = 1/2x + 4

d)

y = -1/2x + 7

46.

Solve:

3(x - 6) = 4x - (8 + 6x)

a)

2

b)

0

c)

No Solution

d)

Identity

47.

If f(x) = 27 - 15x - 3x², find f (-6).

a)

9

b)

-171

c)

-9693

d)

No Solution

48.

What is the domain of the function shown on the graph?

a)

-2 < x ≤ 2

b)

-2 ≤ x < 2

c)

-4 ≤ f(x) < 4

d)

-4 < f(x) ≤ 4

49.

Ms. Law is on leave from work and she has a savings account. She is not getting any extra income and her bills are $899 a week. Her account can be represented by the following equations

y = 11,000 - 899x

where x is the number of weeks and y is the amount left in the account. What is a reasonable domain for this situation?

a)

{0, 1, 2, 3, 4, 5}

b)

{11000, 10911, 10822, 10733, 10644, 10555}

c)

0 ≤ x ≤ 5

d)

10555 ≤ f(x) ≤ 11000

50.

Oceanside Bike Rental Shop charges 16 dollars plus $8.36 an hour for renting a bike. Write the equation that represents the total cost, C, in terms of the number of bike rental hours, h, purchased.

a)

C = 8.36h + 16

b)

h = 8.36C + 16

c)

C = 16h + 8.36

d)

h = 8.36C + 16

51.

Alondra sells toy trucks and toy cars. The trucks are $3.50 and cars are $6. She earned $319. Alondra represented this situation with the following equation:

3.50x + 6y = 319

Where x is the number of trucks and y is the number of cars. What would be a reasonable domain for this equation?

a)

{0,1,2,3,…89,90,91}

b)

0 < x < 91

c)

1 < y < 53

d)

{0,1,2,3,…51,52,53}

52.

Alondra sells toy trucks and toy cars. The trucks are $3.50 and cars are $6. She earned $319. Alondra represented this situation with the following equation:

3.50x + 6y = 319

Where x is the number of trucks and y is the number of cars. What would be a reasonable range for this equation?

a)

{0,1,2,3,…89,90,91}

b)

0 < x < 91

c)

1 < y < 53

d)

{0,1,2,3,…51,52,53}

53.

Solve for h.
V = πr²h

a)

h = V/(πr²)

b)

h = V - πr²

c)

h = πr²V

d)

h = V + πr²

54.

Which property is demonstrated here?
3(x - 2) = 3x - 6

a)

Multiplication Property of Equality

b)

Distributive Property

c)

Associative Property

d)

Commutative Property

55.

Solve the system. What is the value of x?
2x + 3y = 13
x - 2y = 3

a)

x = 1

b)

x = 3

c)

x = -2

d)

x = 5

56.

(x + 7)(x - 2) =

a)

x² + 9x - 14

b)

x² + 5x - 14

c)

x² + 5x + 9

d)

x² + 7x - 2

57.

The graph shows the height (cm) of a candle as it burns, what is the y intercept and what does the y-intercept mean?

a)

b=9, Candle starts at 9 cm.

b)

b=9, the candle burns 9 inches per hour.

c)

b=2, the candle burns 2 inches per hour.

d)

b = 5, The candle ends at 5 cm

58.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(0, 1)

59.

Solve for x and y
3x + 2y = 16
7x + y = 19

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

60.

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

a)

1.5x+0.5y=78.5
x+y=87

b)

1.5x+0.5y=78.5
1.5x+0.5y=87

c)

x+y=78.5
1.5x+0.5y=87

d)

x+y=78.5
x+y=87

61.

If $f\left(x\right)=2x+5$ , what is the value of $f\left(8\right)$

a)

$f\left(8\right)=15$

b)

$f\left(8\right)=21$

c)

$f\left(8\right)=24$

d)

$f\left(8\right)=19$

62.

Which of the following represents a relation that IS a function

a)

b)

c)

d)

63.

What is the value of $f\left(2\right)$ when $f\left(x\right)=x^2+2x+2$

a)

8

b)

10

c)

12

d)

14

64.

If the function $f\left(x\right)=x^2-2$ has a domain of $\left\{1,2,3,4,5\right\}$ what is the range?

a)

$\left\{-1,2,8,17,21\right\}$

b)

$\left\{-1,5,15,22,54\right\}$

c)

$\left\{-1,15,22,36,56,88\right\}$

d)

$\left\{-1,2,7,14,23\right\}$

65.

Solve for x: $x-3\left(4-x\right)=8$

a)

$x=5$

b)

$x=-1$

c)

$x=-5$

d)

$x=-2$

66.

Solve for x: $3\left(x+5\right)=5\left(x+12\right)-13\left(x+1\right)-2$

a)

$x=5$

b)

$x=6$

c)

$x=7$

d)

$x=8$

67.

Solve the system of equations by substitution:

a)

$\left(5,-1\right)$

b)

$\left(2,-1\right)$

c)

$\left(6,-1\right)$

d)

$\left(3,2\right)$

68.

Solve the system of equations by elimination:

a)

$\left(-\frac{1}{3},\frac{4}{3}\right)$

b)

$\left(\frac{1}{9},\frac{4}{3}\right)$

c)

$\left(-\frac{1}{3},\frac{16}{3}\right)$

d)

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

69.

Solve for x: $-5\left(x-1\right)=5+5\left(4-3x\right)$

a)

$x=4$

b)

$x=3$

c)

$x=2$

d)

$x=-3$

70.

What is the value of x in the solution to the system of equations?

a)

1

b)

5/3

c)

8/3

d)

7/3

71.

Which coordinate pair is in the solution set for y<1-6x?

a)

(1, 0)

b)

(1, -1)

c)

(0, 1)

d)

(-1, 1)

72.

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

73.

Match the system to the graph.

a)

y ≥ -x - 1 and y < x + 4

b)

y < -x - 1 and y ≥ x + 4

c)

y > -x - 1 and y ≥ x + 4

d)

y > -x - 1 and y ≤ x + 4

74.

a)

f = (w - k) / Z

b)

f = (w + k) / Z

c)

f = (wk) / Z

d)

f = Zw-Zk

75.

Solve the system of equations.
3x + 2y = 16
7x + y = 19

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

76.

Simplify by combining like terms.

7c -8a + 9a + 11c

a)

18c + 1a =

b)

-4c +17a

c)

78911ca =

d)

-1+ 20c

77.

Simplify the following expression:

(5 + 4x) + (2x - 8)

a)

13 + 6x

b)

6x - 3

c)

6x - 13

d)

6x + 3

78.

Simplify the expression:

3f + 4(2f - 5)

a)

3f + 8f - 20

b)

11f - 20

c)

11f - 5

d)

11f + 5

79.

Simply:

a)

-8

b)

-4

c)

-2

d)

6/5

e)

2

80.

Find the value of the expression below when x=-4 and y=2

-3x²y+4x

a)

-112

b)

-88

c)

40

d)

-12x³y

e)

The expression is already simplified

81.

Which of the following is equivalent to the expression below?

4x + 3(2x - 1) - 4x

a)

6x - 3

b)

6x + 3

c)

14x - 3

d)

14x + 3

e)

3x

82.

1-4x≤21 or 5x≥25

a)

x≥ -5 or x≥5

b)

x≤ -4 and x≤ 8

c)

No Solutions

d)

All Real Numbers

e)

None of the above

83.

Elber bought 11 binders and notebooks from the store and spent $45. Binders cost $6 each and notebooks cost $2.50 each. Which equations would you use to find the numbers of binders, b, and notebooks, n, she purchased

a)

b+n=11

b)

b+n=45

c)

6b+2.5n=11

d)

6b+2.5n=45

e)

2.5b+6n=11

84.

Valley Video charges a $15 annual fee plus $3 per movie for rentals. Last year, Jennifer spent $99 at the video store. How many movies did she rent? Write the linear equation and solve for the number of movies.

a)

15x + 3x = 99 and 6 movies

b)

15x + 3 = 99 and 6 movies

c)

3x + 15 = 99 and 28 movies

d)

3x + 99 = 15 and 28 movies

e)

15x+99= 3 and 6 movies

85.

(3 + 4)² - 32

a)

7

b)

112

c)

17

d)

-7

86.

6 + 3² x 4 - 2² ÷ 4 =

a)

51

b)

41

c)

14

d)

18

87.

Which situation can be represented by
y = 17x - 8?

a)

The number of seeds, y, needed to feed 8 hamsters 17 seeds each.

b)

The earnings from a lemonade stand, y, selling glasses at 17 dollars each with $8 in the tip jar.

c)

The cost, y, of buying 17 movie tickets that sell for $8 each.

d)

The cost, y, of buying Star Wars figurines at $17 each with an $8 discount.

88.

Solve.

z + 3(2 + 4z) = 6(z+1) + 5z

a)

0

b)

2

c)

No solution

d)

All real numbers

89.

Solve the following equation for x:

3x + 8 = 8 + 3x

a)

x = 3

b)

x = 8

c)

infinite solutions

d)

x = 0

90.

Solve the following equation for x:
10x + 2x + 5 = 8x + 4x + 7

a)

no solution

b)

infinite solutions

c)

x = 12

d)

x = 0

91.

a)

x ≥ -154

b)

x ≤ -154

c)

x ≤ 154

d)

x ≥ 154

92.

You and your friend are planning to walk across an old bridge. The bridge can hold at most 1000 pounds. The total weight of the people currently on the bridge is 675 pounds. You weigh 156 pounds.Write and solve an inequality that represents how much your friend can weigh within the limits of the bridge.

a)

X ≤ 169

b)

X < 169

c)

X < 156

d)

X > 156

93.

Yellow Cab Taxi charges a $1.75 flat rate in addition to $0.65 per mile. Katie has no more than $10 to spend on the taxi ride.

a)

1.75 + 0.65m < 10

b)

1.75 + 0.65m > 10

c)

1.75m + 0.65 < 10

d)

1.75m + 0.65 > 10

94.

The Starlight Bowling Alley charges $6 to rent shoes and $8 per game. Cameron has only $42 to spend. Which inequality represents this scenario if “x” represents the number of games Cameron can play?

a)

6x + 8 ≥ 42

b)

8x + 6 ≤ 42

c)

6x + 8 > 42

d)

8x + 6 < 42

95.

Write an inequality for the situation:
George rented a bike for 4 hours. There was a $10 dollar deposit to pay in addition to the hourly rate. What was the hourly rate if the total came to less than or equal to $65?

a)

10x + 65 ≥ 40

b)

4x + 10 ≤ 65

c)

4x - 10 ≤ 65

d)

65 + 4x ≥ 40

96.

Select ALL the values of x that make the following inequality true.

-3(x+1)>15

a)

0

b)

-5

c)

-6

d)

-6.5

e)

-12

97.

Which of the following equations match the given graph?

a)

y ≤ -3/4 x + 3

b)

y ≥ -3/4 x + 3

c)

y < -3/4 x + 3

d)

y > -3/4 x + 3

98.

Find the value of x:

\sqrt{x}=4

(a)

99.

Solve by square roots (SADMEP)
x² - 64 = 0

a)

64

b)

8

c)

8 or -8

d)

1 or -64

100.

x²= 100

a)

10

b)

10 or -10

c)

50

d)

50 or -50

Applied Algebra Semester 1 Final Practice Test

Total questions: 100

Worksheet time: 2hrs 40mins

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