Free Printable Algebra 1 Winter Final Review

1.

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

a)

b)

c)

d)

2.

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

a)

b)

c)

d)

3.

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

4.

What is the equation in standard form of the line that passes through the point (1, 24) and has a slope of -0.6.

a)

3x+5y=125

b)

3x+5y=77

c)

3x+5y=123

d)

3x+5y=115

5.

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

a)

b)

c)

d)

6.

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

7.

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}

8.

What value of x makes the equation true?

9.

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

10.

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?

11.

Which graph represents -3x + 5y = -15

a)

b)

c)

d)

12.

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

a)

x < -9

b)

x > 3

c)

x < -3

d)

x > 7

13.

What is the equation for the line?

a)

y=-2x-2

b)

y=x+2

c)

y=3x-1

d)

y=2x+3

14.

What is the equation of the line that passes through the points: (2, 9) and (22,-1)

a)

y= -8x

b)

y= -2/3x + 3

c)

y= -1/2x +10

d)

y= -5x + 12

e)

No solution

15.

What is the inequality of the line shown?

a)

$y\le-\frac{1}{3}x-1$

b)

$y>-\frac{1}{3}x-1$

c)

$y<-\frac{1}{3}x-1$

d)

$y\ge-\frac{1}{3}x-1$

16.

What is the error?
3x -9 = 36
-9 -9
___________
3x = 27
divide divide
3 3
x = 9

a)

Nothing is wrong

b)

Did not divide by the correct coefficient

c)

Did not perform the correct inverse operation to isolate 3x

d)

Did not add correctly

17.

Tonia purchased 6 yards of red fabric and 3 yards of black fabric for a total of $24. If the red fabric cost $2.50 per yard, How much was the cost of the black fabric. Answer in dollars ($x), or dollars and cents ($x.xx) and no spaces.

(a)

18.

Which equation matches the graph? (Click me to see the image)

a)

y = 2x

b)

y = 1/4 x + 2

c)

y = 1x + 4

d)

y = -2x

19.

Does the system have no solution or infinitely many solutions? y = (2/3)x + 2 and -2x + 3y = 6

a)

No solution

b)

Infinitely many solutions

20.

What is the solution of the system? 2x + 5y = 14 and x + 3y = 16

a)

(-38, 18)

b)

(18, -38)

c)

(14, 16)

d)

(0, 14)

21.

What is the solution of the system? 5x + 2y = 9 and 4x - 3y = 44

a)

(5, -8)

b)

(-8, 5)

c)

(9, 44)

d)

(0, 9)

22.

The price of 6 slices of pizza and 4 drinks is $37. The price of 4 slices of pizza and 6 drinks is $33. How much does one drink cost?

a)

$1.75

b)

$2.50

c)

$3.50

d)

$4.50

23.

If you graph the inequality y > 3x + 3. Which description matches the correct graph of this inequality?

a)

A dashed boundary line y = 3x + 3 with the region above the line shaded

b)

A dashed boundary line y = 3x + 3 with the region below the line shaded

c)

A solid boundary line y = 3x + 3 with the region above the line shaded

d)

A solid boundary line y = 3x + 3 with the region below the line shaded

24.

Which inequality does the graph represent?

a)

y < 2.5x − 2

b)

y > 2.5x − 2

c)

y ≤ 2.5x − 2

d)

y ≥ 2.5x − 2

25.

What system of inequalities is shown in the graph?

a)

y < −2 and y < x − 3

b)

x < −2 and y < x − 3

c)

y ≤ −2 and y ≤ x − 3

d)

y ≤ −1 and y ≤ x − 3

26.

What is the Domain of this linear function?

a)

-6 ≤ x ≤ 6

b)

0 ≤ x ≤ 7

c)

2 ≤ x ≤ 7

d)

No Solution

27.

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

28.

Level 3

Given the line 2x-3y=9, write the equation of a line parallel to it that passes through the point (4, -1)

a)

y = 2/3x - 3

b)

y = 2/3x - 11/3

c)

y = 2/3x - 4

d)

y = 2/3x - 5/3

29.

Level 2

Select ALL of the lines that are PERPENDICULAR to y = 3/4x + 9

a)

y = 3/4x - 3

b)

y = -3/4x + 9

c)

y = -4/3x + 8

d)

3y = -4x + 5

e)

4y = -3x + 7

30.

Solve for v (just enter the number for your answer)

31.

Solve for k (just enter the number for your answer)

32.

Solve for b (just enter the number for your answer)

33.

Solve for b (just enter the number for your answer)

34.

What inequality is graphed?

a)

x > 2 and x < 4

b)

2 ≤ x ≤ 4

c)

x > 2 or x < 4

d)

x ≥ 2 or x ≤ 4

35.

Write an inequality for Graph 3.

a)

x ≤ -2 AND x > 5

b)

x ≤ -2 OR x > 5

c)

x ≥ -2 OR x < 5

d)

-2 ≤ x < 5

36.

Which graph represents $x\le-4$ or $x>0$ ?

a)

b)

c)

d)

e)

37.

What are the equation and the slope of the line?

Move the correct answer to each box. Not all answers will be used.

Equation: (a)

Slope: (b)

Choose from the below words

x = 5

undefined

0

5

y = 5x

y = 5

38.

Let w(x) = 3x - 7. If w(x) = 14, find x.

39.

Evaluate f(x)=12 if f(x) = x+3

40.

If f(x) = -4x - 5

what is f(x)=11?

41.

Given h(x) = 5 - 9x, find h(8).

42.

Evaluate f(-5) if f(x) = -2x - 12

43.

Convert the equation of the line

y + 5 = -3(x - 6)

into slope intercept form.

a)

y = -3x - 23

b)

y = -3x - 13

c)

y = -3x - 11

d)

y = -3x + 13

44.

For the equation
y - 3 = 2(x + 4),
the line has a slope of 2 and contains what point?

a)

(-4, 3)

b)

(3, -4)

c)

(-3, -4)

d)

(-4, -3)

45.

Write the equation in point-slope form of the line that passes through the given point and has the given slope.

(4, -7); m = -1/4

a)

y + 7 = -1/4(x - 4)

b)

y - 4 = -1/4(x + 7)

c)

y + 7 = 4(x - 4)

d)

y - 7 = -1/4(x - 4)

46.

What is the point slope form equation for the given line?(Use blue point for formula)

47.

What is the point slope form equation of the graph given(use blue point in equation)

48.

Solve and graph

a)

A

b)

B

c)

C

d)

D

49.

Solve and graph

a)

A

b)

B

c)

C

d)

D

50.

Solve for n
$h\ =\ ac\ +\ mn$

a)

$n\ =\ \frac{h\ +\ ac}{m}$

b)

$n\ =\ \frac{m}{h\ -\ ac}$

c)

$n\ =\ m\left(h\ -\ ac\right)$

d)

$n\ =\ \frac{h\ -\ ac}{m}$

51.

Solve $A=\frac{1}{2}bh$ for $b.$

a)

$b=\frac{2A}{h}$

b)

$b=\frac{h}{2A}$

c)

$b=\frac{A}{2h}$

d)

$b=\frac{2h}{A}$

52.

Solve $ax+bx=c$ for $x.$

a)

$x=\frac{c}{a+b}$

b)

$x=\frac{c}{a-b}$

c)

$x=\frac{a+b}{c}$

d)

$x=\frac{a-b}{c}$

53.

Solve for x:
3(5x + 10) + 10 = 6x - (x + 10)

54.

This equation, 3x + 2 = 3x + 2, has (a) solutions.

Choose from the below words

One Solution

No Solution

Infinite Solutions

55.

Solve for x:

a)

x = yb - v

b)

x = by - v

c)

x = by + v

56.

y = -2/3x + 2
y = 3/2x + 9
These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

57.

Slopes of parallel lines are...

a)

negative reciprocals.

b)

opposites.

c)

the same.

d)

always 7.

58.

A line is perpendicular to y = 2x - 7.
What is the slope of this line?

a)

-2

b)

1/2

c)

-1/2

d)

2

59.

Write the equation of a line PERPENDICULAR to the line y = 3x + 2 that passes through the point (9, -2)

a)

y = -1/3x - 5

b)

y = 3x-29

c)

y = 1/3x -5

d)

y = -1/3x +1

60.

Write the equation of the line PARALLEL to the line y = 4x - 9 that passes through the point (-2, 4)

61.

Andrew opens a savings account at Students First Credit Union. He receives $50 for just signing up. He earns $0.60 for each month he leaves money in the account. He needs at least $200 for a new Chromebook. Write an inequality representing x, the number of months he needs to keep money in his savings account to afford his Chromebook.

62.

(-3y^-5)^-2

a)

y¹⁰ / 9

b)

9 / y^-7

c)

6 / y¹⁰

d)

6 / y³

63.

(34x⁵y⁶z^-7)⁰

a)

34x⁵y⁶ / z⁷

b)

34x⁵y⁶ / x^-7

c)

0

d)

1

64.

Simplify.
(x³ ⋅ y⁴ ⋅ z)³ ⋅ (x⁵ ⋅ y ⋅ z³)²

a)

x¹⁹y¹²z⁹

b)

x¹⁹ y¹⁴z⁹

c)

x¹³y¹⁰z⁹

d)

x²³y⁴²z¹¹

65.

a)

A

b)

B

c)

C

d)

D

66.

a)

A

b)

B

c)

C

d)

D

67.

a)

A

b)

B

c)

C

d)

D

68.

a)

A

b)

B

c)

C

d)

D

69.

a)

A

b)

B

c)

C

d)

D

70.

Simplify

(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

8a⁶b⁸z⁵

d)

12a⁵b⁶z⁶

71.

$\frac{\left(2x^4y^4\right)\left(2x^3y\right)}{3y^2}$

Simplify

a)

$\frac{4x^7y^3}{3}$

b)

$\frac{4x^7}{3y^3}$

c)

$12x^7y^3$

d)

$4x^{12}y^2$

72.

Simplify completely.

a)

b)

c)

d)

73.

Simplify:

a)

b)

c)

d)

74.

Simplify:

a)

b)

c)

d)

75.

Simplify completely.

a)

b)

c)

d)

76.

Simplify completely.

a)

b)

c)

d)

77.

Simplify the radical:
$\sqrt{98}$

a)

$2\sqrt{7}$

b)

$7\sqrt{2}$

c)

$14\sqrt{2}$

d)

$49\sqrt{2}$

78.

Simplify:

$\sqrt[]{12}+3\sqrt[]{27}$

A decimal will be marked incorrect.

79.

2√5 + 4√5 =

a)

6√10

b)

8√10

c)

8√5

d)

6√5

80.

Simplify: 6√3 + 2√75 - 4√27

a)

16√3 - 12√2

b)

2√15

c)

28√3

d)

4√3

81.

Simplify: 6√8 * 3√24

a)

18√3

b)

144√3

c)

72√12

d)

18√8

82.

Alina has $500 in her bank account. Every week she withdraws $45. Write an equation where x represents the number of weeks and y represents the amount of money in her bank account.

83.

Write the inequality of the graph given. (Slope intercept form)

84.

Maddie plants a tree that is 6 feet tall outside her house. The label on the tree says it should grow $\frac{3}{4}$ of a foot every year. Write an equation to model y the height of the tree after x years.

85.

Match the following equations to the type of equation

a)

Slope Formula- Used to find the slope given two points

1.

m = (y2 - y1) / (x2 - x1)

b)

Standard Form- Graphing using intercepts or convert to slope intercept form

2.

Ax + By = C

c)

Slope Intercept Form- Used to graph using the slope and y-intercept

3.

y=mx+b

d)

Point Slope Form- Used to get the equation of a line given the slope and one point

4.

y-y1=m(x-x1)

86.

A university will spend at most $4,500 to buy monitors and keyboards for a computer lab. Each monitor will cost $250 and each keyboard will cost $50.

Write an inequality that represents all possible combinations of x, the number of monitors and y, the number of keyboards.

(a) x + (b) y (c) (d)

Choose from the below words

250

50

$\le$

4,500

=

200

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Algebra 1 Winter Final Review

Total questions: 86

Worksheet time: 6hrs 44mins

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