Free Printable Principles Of Algebra 2025 Study Guide

1.

12k + 15 = 35 +2k

a)

k = 2

b)

k = 4

c)

k = -2

d)

k = -4

2.

3 ( a + 22 ) = 12a + 30

a)

a = 8

b)

a = 2

c)

a = 4

d)

a = -2

3.

6x + 5 = 10 + 5x

a)

x = -5

b)

x = 6

c)

x = 4

d)

x = 5

4.

Solve for x:
5x - 14 = 8x + 4

a)

x = 6

b)

x = -6

c)

x = -18/13

d)

x = 10/3

5.

What is the first step in solving the equation 2a - 4(a - 5) = 10

a)

Add 4 to both sides

b)

Add the 2a and a

c)

Distribute 4 to a and -5

d)

Distribute -4 to a and -5

6.

The goal of solving a one, two, or multi-step equations is to:

a)

Find the value of the variable

b)

Find the constant

c)

Be confused

d)

Find the coefficient

7.

10x + 9 = 4x - 9

a)

x = 0

b)

x = 3

c)

x = -3

d)

x = -18

8.

8x - 8 = -4x + 16

a)

x = 8

b)

x = 16

c)

x = 24

d)

x = 2

9.

7w + 5 = 3w - 15

a)

w = 5

b)

w = -2

c)

w = 2

d)

w = -5

10.

7x = 4x + 33

a)

x = 3

b)

x = 11

c)

x = 21

d)

x = 88

11.

Solve for x:

3x - 7 = -5x + 17

a)

x = 5

b)

x = 12

c)

x = 3

d)

x = 1.2

12.

2x - 3 + 4x = 27

a)

12

b)

4

c)

5

d)

15

13.

8v - 4(v + 8) = 8

a)

2

b)

10

c)

4

d)

-4

14.

-8(-8x - 6) = -6x - 22

a)

2/5

b)

-1

c)

8/7

d)

2

15.

Find the error in the problem below
19 - 2k = 3k - 1
+3k +3k
19 + 1k = -1
-19 -19
k = -20

a)

They should have divided by 1 for the last step

b)

They should add 19 instead of subtracting 19

c)

I can not find an error

d)

Instead of adding 3k they should subtract 3k

16.

The four regions on the coordinate plane are called_________________

a)

origins

b)

ordered pairs

c)

quadrants

d)

coordinates

17.

The vertical number line is called the _______.

a)

x-axis

b)

y-axis

c)

ordered pair

d)

quadrant

18.

The horizontal number line is called the _________ .

a)

x-axis

b)

y-axis

c)

ordered pair

d)

origin

19.

An _________ is the set of numbers used to locate a point on the coordinate plane.

a)

quadrant

b)

ordered pair

c)

origin

d)

y-axis

20.

What are the coordinates of Point C?

a)

(-4, -2)

b)

(-2,-4)

c)

(2, -4)

d)

(-2, 4)

21.

Which quadrant has both positive coordinates?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

22.

Which quadrant has both negative coordinates?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

23.

What is the distance between points (3, -5) and (3, -8)?

a)

1 unit

b)

2 units

c)

3 units

d)

4 units

24.

What is at (1,2)?

a)

the moon

b)

the sun

c)

a blue planet

d)

a robot

25.

Where is point A located?

a)

( 7 , 2 )

b)

( 2 , 6 )

c)

( - 2 , 7 )

d)

( 2 , 7 )

26.

How do you correctly write an ordered pair?

a)

(y,x)

b)

(x,y)

c)

(0,0)

d)

(yy,x)

27.

Graph the point (-6, 4)

28.

Graph the point (0,-5)

29.

Match the following ordered pairs with the quadrant where they can be found.

a)

(4,3)

1.

Quadrant I

b)

(-9,7)

2.

Quadrant II

c)

(-5,-2)

3.

Quadrant III

d)

(8,-5)

4.

Quadrant IV

30.

When plotting the point, (-4, 3), which describes the movement along the x-axis and y-axis in the correct order?

a)

4 units right then 3 units up

b)

4 units down then 3 units left

c)

4 units left then 3 units up

d)

4 units up then 4 units right

31.

Give the coordinates for POINT I.

a)

(-2, 5)

b)

(-2, -5)

c)

(2, 5)

d)

(2, -5)

32.

Ordered pair (0,0) is also known as the ___.

a)

y-axis

b)

x-axis

c)

origin

33.

Where is point B located?

a)

( -4, 6 )

b)

( 6 , -4 )

c)

( 2 , 6 )

d)

( -3 , -3 )

34.

What point is at (-3,3)?

a)

F

b)

H

c)

J

d)

C

35.

Give the coordinates for POINT C.

a)

(4, -2)

b)

(-2, 4)

c)

(-2, -4)

d)

(4, 2)

36.

What is the ordered pair for the hat?

a)

(-1,-3)

b)

(3,1)

c)

(-3,-1)

d)

(1,3)

37.

Find the slope

a)

-3/4

b)

4/3

c)

3/4

d)

-4/3

38.

Find the slope

a)

5/2

b)

-5/2

c)

2/5

d)

-2/5

39.

Find the slope of the line.

a)

1/2

b)

-1/2

c)

2/1

d)

-2/1

40.

Find the slope of the line.

a)

1/4

b)

-1/4

c)

-4/1

d)

4/1

41.

Find the slope of the line.

a)

4/2

b)

-4/2

c)

2/1

d)

-2/1

42.

What type of slope?

a)

negative

b)

positive

c)

zero slope

d)

downward slope

43.

Find the slope

a)

-3/4

b)

4/3

c)

3/4

d)

-4/3

44.

Find the slope

a)

4/5

b)

5/4

c)

-5/4

d)

-4/5

45.

Find the slope of the line.

a)

4/2

b)

-4/2

c)

2/1

d)

-2/1

46.

What is the slope in the picture?

a)

Positive

b)

Negative

c)

Zero

d)

Undefined

47.

What type of slope does the following graph have?

a)

Postive

b)

Negative

c)

Zero Slope

d)

Undefined

48.

What type of slope does the graph have?

a)

Zero

b)

Undefined

c)

Negative

d)

Positive

49.

Find the slope of the line.

a)

-2/1

b)

2/1

c)

-1/2

d)

1/2

50.

a)

2/3

b)

3/2

c)

-2/3

d)

-3/2

51.

a)

undefined

b)

1/1

c)

-1/1

d)

2/1

52.

Find the slope:

a)

2

b)

-2

c)

1/2

d)

-1/2

53.

Find the slope of the line.

a)

0

b)

1

c)

undefined

d)

-1

54.

Find the slope of the line.

a)

undefined

b)

1

c)

zero

d)

-1

55.

What is the slope in this picture?

a)

Positive

b)

Negative

c)

Zero

d)

Undefined

56.

a)

undefined

b)

0

c)

positive

d)

negative

57.

a)

-5/2

b)

5/2

c)

-2/5

d)

2/5

58.

a)

2/3

b)

-3/2

c)

-2/3

d)

3/2

59.

a)

Slope guy

b)

Crazy man who has nothing to do with math

c)

Ms. Warns's husband

d)

The janitor the day before christmas break

60.

What formula do we use when counting slope on a graph?

a)

Rise/Run

b)

Run/Rise

c)

Run/Race

d)

Walk/Run

61.

Find the slope of the line.

a)

1/2

b)

-1/2

c)

1

d)

-1

62.

Determine what type of slope is portrayed in the image

a)

Positive

b)

Negative

c)

Zero

d)

Undefined

63.

How do you calculate slope using a graph?

a)

rise over run

b)

run over rise

c)

look at the y intercept

d)

look at the x intercept

64.

Match the following:

a)

1.

Positive

b)

2.

Negative

c)

3.

Zero

d)

4.

Undefine

65.

What is the slope of this graph?

(a)

66.

What is the slope of this graph?

(a)

67.

Which graph shows an undefined slope?

a)

b)

c)

d)

68.

Which graph or graphs show a positive slope?

a)

b)

c)

d)

e)

69.

What is the slope of this line?

(a)

70.

I am confident with identifying types of slopes and finding slope from tables, graphs, and ordered pairs and will score 80% on my quiz.

a)

I GOT THIS!!

80-100%

b)

I'm not quite ready.

60-75%

c)

I have no idea what to do.

50% and below

Principles Of Algebra 2025 Study Guide

Total questions: 70

Worksheet time: 3hrs 34mins

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