Free Printable Algebra 1st Semester Study Guide 2023

1.

An example of an integer is...

a)

9.1

b)

$\frac{8}{9}$

c)

-9

d)

-2.3

2.

Identify ALL the subsets to which the number belongs:

-12

a)

real

b)

rational,

real

c)

natural,

rational,

real

d)

integer,

rational,

real

3.

Which of the following is a whole number?

a)

9

b)

$\frac{10}{9}$

c)

$-3\ \frac{1}{2}$

d)

$2\ \frac{2}{3}$

4.

The number is a/an...

a)

Rational Number

b)

Irrational Number

c)

Integer

d)

Whole Number

5.

7 + 9 = 9 + 7
This is an example of which property?

a)

Commutative

b)

Associative

c)

Identity

6.

3 + ( 9 + 5) and (3 + 9) + 5
This is an example of which property?

a)

Commutative

b)

Associative

c)

Identity

7.

2(3x + 4) = 6x + 8 is an example of which property?

a)

Community Property of Multiplication

b)

Distributive Property

c)

Commutative Property of Addition

d)

Associative Property of Addition

8.

Which property says that if k = 3, then 3 = k?

a)

Substitution Property

b)

Reflexive Property

c)

Symmetric Property

d)

Transitive Property

9.

Which property states that 4 = 4?

a)

Substitution Property

b)

Reflexive Property

c)

Symmetric Property

d)

Transitive Property

10.

Which property states that if 10a = 2b and 2b = c, then 10a = c?

a)

Substitution Property

b)

Reflexive Property

c)

Symmetric Property

d)

Transitive Property

11.

Identify the terms (select all that apply)

10a + 4 + 5a

a)

10a

b)

4

c)

5a

d)

1

e)

7

12.

Simplify

4a + 9 + a

a)

5a + 9

b)

14a

c)

3a + 9

d)

5a - 9

13.

Use the Distributive Property to Rewrite the Expression

2(c - 8)

a)

2c - 16

b)

2c + 16

c)

2c - 8

d)

c - 16

14.

Simplify

5(y + 6) + 4

a)

5y + 15

b)

5y + 34

c)

5y + 10

d)

y + 34

15.

Simplify: 6b + 7b - 10

a)

3b

b)

13b - 10

c)

13b+10

d)

42b+10

16.

Simplify the expression.

14 - 3z + 8 + z

a)

-2z + 22

b)

2z + 22

c)

4z + 22

d)

-4z + 22

17.

Simplify the expression.

3(q + 1) - 4

a)

3q - 1

b)

3q + 7

c)

3q + 1

d)

3q - 3

18.

Simplify the expression.

-2(g + 4) + 7g

a)

9g - 8

b)

9g + 4

c)

5g + 4

d)

5g - 8

19.

Evaluate 2a + 4b
if a = 10 and b = 6

a)

20

b)

24

c)

44

d)

4

20.

b² + 4
when b = 3

a)

10

b)

12

c)

13

d)

11

21.

Evaluate the expression when
x =5 and z = 4
z²- 2x

a)

6

b)

2

c)

17

d)

26

22.

(4 + 3)²+5 x 3

a)

57

b)

64

c)

29

d)

44

23.

91 + 27 ÷ (72 ÷ 24)

a)

100

b)

96

c)

90

d)

127

24.

8² +(7-4)²

a)

74

b)

72

c)

70

d)

73

25.

$13\ =s-21$

What is s?

a)

s = 34

b)

s = -8

c)

$s=\frac{13}{21}$

d)

s = 0

26.

$5+w=17$

What is w?

a)

w = 17

b)

w = 22

c)

w = 5-17

d)

w = 12

27.

$\frac{x-7}{4}=-2$

What steps would solve this equation?

a)

Multiply both sides by 4, then add 7 to both sides.

b)

Divide both sides by -2, then add 7 to both sides.

c)

Add 7 to both sides then multiply both sides by 4.

d)

Divide both sides by 4 then subtract 7 from both sides.

28.

$9-2x=35$

What is x?

a)

x=22

b)

x=-13

c)

$x=\frac{35}{9}$

d)

x=-4

29.

Solve for x:
8x - 10 = -34

a)

4

b)

3

c)

-3

d)

-24

30.

What inequality does the number line graph represent?

a)

x > 5

b)

x < −5

c)

x ≥ 5

d)

x ≥ −5

31.

When you graph an inequality, you use a closed dot when you use which symbols?

a)

≤, ≥

b)

<, >

c)

≤, <

d)

≥, >

32.

When graphing an inequality, you use an open dot when you use which symbol?

a)

<, >

b)

≤, ≥

c)

≤, <

d)

≥, >

33.

Match the graph with its inequality.

a)

b > –2

b)

b < –2

c)

b ≥ –2

d)

b ≤ –2

34.

Would you use a closed or open circle to graph x < 3?

a)

Closed

b)

Open

35.

Which graph matches the inequality

k < 3?

a)

A

b)

B

c)

C

d)

D

36.

a)

x > 4

b)

x > 9

c)

x < 3

d)

x < 4

37.

a)

x ≥ 19

b)

x ≤ 11

c)

x < 11

d)

x > 19

38.

a)

x > 3

b)

x ≤ ⅕

c)

x ≥ 3

d)

x ≤ ⅕

39.

a)

x > ⅓

b)

x > 1

c)

1 > x

d)

x = 1

40.

a)

x < 16

b)

x > 16

c)

x < 32

d)

x < 10

41.

Translate this phrase into an algebraic expression.
8 less than the product of 4 and a number
Use the variable m to represent the unknown number.

a)

8 - 4m

b)

8m - 4

c)

8m + 4

d)

4m - 8

42.

The difference of four times a number and six.

a)

4x − 6

b)

4x + 6

c)

6x − 4

d)

43.

the difference between forty-six and a number

a)

46 x n

b)

46/n

c)

n-46

d)

46 − n

44.

46 less than a number

a)

46 - n

b)

n - 46

c)

46 + n

d)

n + 46

45.

The quotient of a 15 and a number plus 1

a)

15 / g - 1

b)

15 / g + 1

c)

g / 15 + 1

d)

g + 1 / 15

46.

"Subtracted from" and "less than" are terms that mean you need to "turn" or "flip" the terms around.

a)

True

b)

False

47.

5 times a number, minus 8

a)

5m - 8

b)

5(m + 8)

c)

8m + 5

d)

8(m + 5)

48.

A number h increased by 12

a)

12h =

b)

12 + h =

c)

h - 12 =

d)

h + 12 =

49.

4a-2=3a-7

a)

a=-9

b)

a=-2

c)

a=7

d)

a=-5

50.

$21=3+4n+5n$

a)

9

b)

$-7$

c)

6

d)

2

51.

4 = 2(x + 3)

a)

1/2

b)

7/2

c)

-1

d)

5

52.

2x - 3 + 4x = 27

a)

12

b)

4

c)

5

d)

15

53.

9y+8=9y-8

a)

No Solution

b)

One Solution

c)

Infinite Solution

54.

3(x-8)=3x-24

a)

No Solution

b)

One Solution

c)

Infinite Solutions

55.

6(m+3)=2(m+5)

a)

No solution

b)

One Solution

c)

Infinite Solutions

56.

What is the solution to this equation?

a)

one solution

b)

no solution

c)

infinite solutions

d)

none of these

Algebra 1st Semester Study Guide 2023

Total questions: 56

Worksheet time: 2hrs 18mins

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