Algebra 1 review

Name: __________________________________________
Algebra Keystone Exam Review
1)

Simplify the expression:
√

√

√
√

A)

√

B)

√

C)

√

D)

A right triangle has one leg that is twice the length of the other leg. If the hypotenuse is √ , find the length of the longer leg.

2)

A)

8

B)

16

C)

4

D)

32

3)

Which statement has the largest value of x?

A)

√

B)

√

C)

√

√

D)

√

√

4)

Simplify:

( √ )
A)
B)
C)

27

D)

54

√
√

5)

What is

subtracted from

?

A)
B)
C)
D)
What is the value of ( )

6)
A)
B)
C)
D)

7)

What is a factor of the trinomial
A) (x - 24)
B) (x – 8)
C) (x + 8)
D) (x – 5)

8)

What is a factor of the trinomial
A) (x + 10)
B) (x – 90)
C) (x + 90)
D) (x – 10)

9)

Simplify:
A)
B)

C)
D)

(
(

)(
)(

)
)

when

?

10)

Simplify:
A)
B)

C)

(

)(

)

D) Cannot be Simplified
11)

A park charges rental fees of $5 per x adult and $3 per y child. The Smith family had a family reunion there and was charged $134 for their 32 family members that attended. The system of equations shown below represents this situation.

Which statement is true?
A) More adults attended the reunion than children.
B) Six more children attended than adults.
C) Nineteen children attended the reunion.
D) Three more adults attended than children.
12)

A)

B)

C)

D)

Timmy has collected plain and colored marbles. He has a total of 180 marbles, and there are
32 more plain marbles than colored marbles. Knowing that x represent the number of plain marbles and y represent the number of colored marbles, which of the following systems of equation represents the number of marbles Timmy has?

13)

Which is a graph of the solution of the inequality |

|

C)
A)

B)

D)

14)

Which is a graph of the solution of the inequality

A)

|

?

C)

B)

|

D)

15)

You can work at most 25 hours next week. You need to earn at least $200 to cover your expenses. Your cat-walking job pays $8.00 per hour and your job as a pizza delivery person pays $9.50 per hour. Which system of linear inequalities models this problem situation?

x  y  25
A) 8.00 x  9.50 y  200

B)

16)

x  y  25
8.00 x  9.50 y  200

C)

x  y  25
8.00 x  9.50 y  200

D)

x  y  25
8.00 x  9.50 y  200

A gym offers two options for membership plans. Option A includes an initial fee of $121 and costs $1 per day. Option B has no initial fee but costs $12 per day. After how many days will the total cost of the gym membership plans be equal?
A) 11 days
B) 12 days
C) 13 days
D) 14 days

17)

The scatterplot below shows the resting heart rates, y, of the people, based on their age x.

Which equation best describes the line of best fit?
A)
B)
C)
D)

y = -.43x + 40 y = -.43x + 76 y = -.86x + 10 y = -.86x + 80

18)

The scatterplot below shows the number of active dentists, y, based on the year, x.

160

Number of Dentists Active in the US

155
Dentists

150
145
140
135
130
125
120
0

5

10
Year (after 1980)

A)
B)
C)
D)

y=x+5 y = 2x + 160 y = 2.5x + 200 y = 2.5x + 120

15

19)
5

The average monthly rainfall is recorded in inches over the past year. Which statement correctly describes the data?
7
8
3
1
4
12
0
2
3
3
1

A)
B)
C)
D)

The median value is 3.5
The interquartile range is 4.5
The lower quartile value is 2.
The upper quartile value is 12

20)

The average weekly miles run by a marathon runner are listed below:
62
45
60
57
61
53
55
A) The mean is 56.
B) The mode is 56.
C) The median is 56.
D) The range is 7.

21)

Mike asked 24 people their hair color and recorded the results below.

Number of People

Hair Colors
12
10
8
6
4
2
0

Mike will ask another 16 people their hair color. Based on the information in the bar graph, how many of the 16 people would you expect to have red hair.
A)
B)
C)
D)

1
2
3
4

22)

Kevin asked 200 students to select their favorite food and then recorded the results in the bar graph above.

Favorite Foods
70
60

Students

50
40
30
20
10
0
Pizza

Hamburgers

Ice Cream

Steak

Popcorn

Salad

Food

Kevin will ask another 80 students to select their favorite food. Based on the information in the bar graph, how many more students of the next 80 asked will select hamburgers rather than pizza?
A)
B)
C)
D)
23)

10
4
5
7
A number cube with sides labeled 1-6 is rolled two times, and the sum of the numbers that end face up is calculated. What is the probability that the sum of the numbers is 4.

A)
B)
C)
D)
24)

A number cube with sides labeled 1-6 is rolled two times, and the sum of the numbers that end face up is calculated. What is the probability that the sum of the numbers is 7.
A)
B)
C)
D)

25)

Which of the following is not a function?

A. x y

C.
2
1

3
1

4
1

x y B. x y

7
7

5
5

3
3

6
1

5
2

4
3

1
4

2
0

4
3

D.
0
4

2
1

2
3

x y E. x y
If f(x) = x2 + 3x – 5, what is f( –2) ?

26)
A. –7

27) x y

28)

D. –3

E. 0

Which linear equation best describes the relationship between x and y?

-3
-7.5

A.
B.
C.
D.

C. –12

B. 5

0
6

1
4.5

2
0

y = 2.5x2 – 3x – 3 y = 2x2 + 5x + 7 y = –1.5x2 + 6 y = 0.5x2 + 1
The table below shows values of y as a function of x.

x y
1 4
3 9
9 24
15 39
23 59

Which linear equation best describes the relationship between x and y?
A)
B)
C)
D)

29) x 8
12
16
20
24

The table below shows values of y as a function of x.

y
12
19
26
33
40

Which linear equation best describes the relationship between x and y?
A)
B)
C)
D)

30)

John is selling hot dogs at the entrance to the beach. He charges each customer the cost of a plain hot dog plus an additional cost for each toping. This is shown in the equation below.

What does the number 3.50 represent in the equation?
A)

the cost for one topping

B)

the cost of a hot dog with one topping

C)

the cost of one plain hot dog

D)

the number of toppings

31)

Jess owns a restaurant. She charges a set price for an entrée plus an additional charge for each side item. This is modeled by the equation below.

What does “y” represent in the equation?
A)

The cost for one entrée

B)

the number of sides a costumer can order

C)

the cost for a meal with one side

D)

the cost of a meal given a certain number of sides

32)

A graph of a linear equation is shown below.

Which equation describes the graph?
A)
B)
C)

y

D)

33)

y

y

A graph of a linear equation is shown below.
Which equation describes the graph?
A)

y

B)
C)
D)

34)

Which value is not in the range of the function graphed to the right? A) 0

B) 3

35) Which graph shows y as a function of x?

C. 4

D. 5

Answer Key
1) D
2) B
3) D
4) A
5) D
6) B
7) B
8) D
9) C
10) B
11) A
12) C
13) D
14) B
15) A
16) A
17) B
18) D
19) B
20) A
21) B
22) B
23) C
24) B
25) B
26) A
27) C
28) D
29) C
30) C
31) D
32) A
33) D
34) B
35) B