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9TH Grade Math Final Review

Total questions: 50

Worksheet time: 2hrs 42mins

Name
Class
Date
1.

In laws of exponents, (am) (an)\left(a^m\right)\ \left(a^n\right)  =

a)

a(m−n)a^{\left(m-n\right)}  

b)

amna^{mn}  

c)

a(mn)a^{\left(\frac{m}{n}\right)}  

d)

a(m+n)a^{\left(m+n\right)}  

2.

Simplify the expression: (ab7)(a2b5)\left(ab^7\right)\left(a^2b^5\right)  

a)

b2a\frac{b^2}{a}  

b)

a2b12a^2b^{12}  

c)

a3b12a^3b^{12}  

d)

a2b35a^2b^{35}  

3.
Write the linear inequality in standard form for this situation: In order to raise money to attend upcoming competitions, the Math Pentathalon team is selling apple cider and hot chocolate. They hope to make at least $240 by selling hot chocolate for $1 a glass and hot apple cider for $2 a glass.
a)
x + 2y < 240
b)
x + 2y > 240
c)
x + 2y ≤ 240
d)
x + 2y ≥ 240
4.
Which of the following equations match the given graph?
a)
x ≥ -1
b)
x ≤ -1
c)
x > -1
d)
x < -1
5.

2x - 6 = 12

a)

x = 10

b)

x = 9

c)

x = 1

d)

x = 4

6.
Write the linear inequality in standard form for this situation: Ms. Savva is ordering pizzas and breadsticks for a school party and has a budget of no more than $81. An order of breadsticks costs $7 and a pizza costs $13. 
a)
7x + 13y < 81
b)
7x + 13y ≥ 81
c)
7x + 13y ≤ 81
d)
7x + 13y > 81
7.
At a community swimming pool there are 2 managers, 8 lifeguards, 3 concession stand clerks, and 2 maintenance people.  If a person is selected at random, find the probability that the person is either a lifeguard or a manager.
a)
2/3
b)
8/15
c)
2/15
d)
not enough information
8.
Given the graph below, what are the x and y intercepts? 
a)
x = -2 and y = 1
b)
x = 1 and y = -2
9.
Find the slope of the line.
a)
-2
b)
2
c)
-1
d)
1
10.
If m=3 and b=6, what is the correct slope intercept equation?
a)
y=3-6
b)
y=3x-6
c)
y=3x+6
d)
y=6x+3
11.
Which of the following has a y-intercept of 3?
a)
y = 3x +2
b)
x=3
c)
y=2x+3
d)
y=x
12.

Solve the following equation by factorizing: 5x2 − 125 = 0

a)

x=±5x=±5

b)

x=±25x=±25

c)

x=±125x=±125

13.

Use the quadratic formula to solve the equation:

x2 + 3x + 2 = 0

a)

1, 2

b)

1, -2

c)

-1, -2

14.

Use the quadratic formula to solve the equation, your answers correct to (3 s.f.):

2x2 − 4x + 1 = 0

a)

x = 1.71 or x = 0.293

b)

x = -0.293 or x = -1.71

c)

x = -0.293 or x = 0.293

15.

Solve the following equation.

7n+2[3(1−n)−2(1+n)]=147n+2\left[3\left(1-n\right)-2\left(1+n\right)\right]=14  

a)

- 4

b)

4

c)

-36

d)

15

16.
What decimal is equivalent to 7/20?
a)
0.35
b)
1.34
c)
2.85
d)
7.20
17.
Dallas got a raise.  His hourly wage was increased from $9 to $10.25.  What was the percent increase in Dallas' wage to the nearest whole percent?
a)
10%
b)
12%
c)
14%
d)
125%
18.
The circumference of a circle is 28
π meters.  What is its radius?
a)
7 m
b)
14 m
c)
21 m
d)
28 m
19.
To the nearest square inch, what is the surface area of the square pyramid below?
a)
175 in2
b)
200 in2
c)
400 in2
d)
700 in2
20.
Solve the proportion below
a)
21
b)
7
c)
8
d)
24
21.
Which fraction is equivalent to -0.06?
a)
-1/6
b)
-3/5
c)
-7/10
d)
-3/50
22.
On a map, the distance between two cities in 7.3 centimeters.  The map scale is 1 cm : 50 km.  What is the actual distance between the two cities?
a)
365 cm
b)
365 km
c)
400 km
d)
500 km
23.

What was Brian's unit rate?

a)

3/2 word per minute

b)

30 minutes per word

c)

60 minutes per word

d)

30 words per minute

24.

Elena deposits $1,500 in a savings account that earns 3.0% simple interest per year. If no deposits or withdrawals are made during the year, how much money will be in her account after one year?

a)

$1,530

b)

$1,545

c)

$1,800

d)

$1,950

25.

Kristen bought a game for $24.95. She paid 7.75% sales tax. How much did she pay?

a)

$17.20

b)

$19.34

c)

$26.88

d)

$32.70

26.

There are 240 students at Madison Middle School. The ratio of boys to girls is 2:3. How many girls go to Madison Middle School?

a)

160

b)

144

c)

96

d)

80

27.

At best buy they have a 42” TV that sells for $1250 and is on sale for 15% and sales tax is 6.5%. What is the final cost?

a)

$187.50

b)

$11,130

c)

$1,131.56

d)

$1,250

28.

The ratio of rabbits to chickens at the state fair was 7:9. If there were 693 chickens, how many rabbits were there?

a)

539

b)

567

c)

772

d)

891

29.

Robert is paid $12.00 per hour to chop firewood. He chops 40% of the pile of firewood in 3/4 of an hour. At this rate, how much will Robert be paid to chop the entire pile of firewood?

a)

$18.00

b)

$22.50

c)

$30.00

d)

$40.00

30.

Glenn drives 1/3 of the way to a grocery store and uses 1/11 gallon of gas. What fraction of the distance can he drive to the store with one gallon of gas?

a)

1/14

b)

1/33

c)

3/11

d)

11/3

31.

Which expression below is equivalent to the expression 18a + 12b + 9a + 24b?

a)

63ab

b)

30ab + 33ab

c)

27a + 36b

d)

21a + 42b

32.

On Mondays, a coffee shop offers its customers a 25% discount on all coffee purchases. The coffee shop usually charges c dollars for a flavored coffee. The expression below can be used to determine the cost of a flavored coffee on Mondays.

𝑐 − 0.25𝑐

Which expression could also be used to determine the cost of a flavored coffee on Mondays?

a)

0.25c

b)

0.75c

c)

1.25c

d)

1.75c

33.

What is (– 4.8y + 20.1) – (12.7y + 9.3)?

a)

–17.5y + 10.8

b)

–7.9y + 29.4

c)

7.9y – 29.4

d)

17.5y – 10.8

34.

A scale drawing of a triangular field is shown below.

Which statement explains how to find the actual lengths of the sides of the field, in feet?

a)

Multiply the length of each side in the scale drawing by 1.

b)

Multiply the length of each side in the scale drawing by 175.

c)

Add 175 to the length of each side in the scale drawing.

d)

Add 175 to the sum of the lengths of the sides in the scale drawing.

35.
Solve for x 
a)
x = 98/5
b)
x = 5/98
c)
x = 101/5
36.
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.
37.
Does the mapping of these points represent a function?
a)
Function
b)
Not a Function
38.
Is this a function? Explain.
a)
Yes; it passes the horizontal line test.
b)
No; it is not a straight line.
c)
Yes; it passes the vertical line test.
d)
No; there is a line connecting the dots.
39.
What is the equation for this line?
a)
y = x - 2
b)
y = x + 2
c)
y = 2x
d)
y = -x + 2
40.
Express the following in scientific notation:
.000457
a)
457 x 106
b)
457 x 10-6
c)
4.57 x104
d)
4.57 x 10-4
41.
Write 7.8 x 10-3  in standard form.
a)
0.0078
b)
7,800
c)
78
d)
0.078
42.
Find the slope:
a)
2
b)
-2
c)
1/2
d)
-1/2
43.
Find the volume of the cylinder.
a)
282.6
b)
516.2
c)
133
d)
214
44.
Find the volume of the cone. Round your answers to the nearest tenth. Use 3.14 for π.
a)
320.4 in3
b)
314 in3
c)
205.5 in3
d)
267.4 in3
45.
What is the surface area of this figure?
a)
3000 cm 2
b)
164 cm 2
c)
236 cm 2
d)
328 cm 2
46.
What is the total surface area of the triangular prism shown? 
a)
468 in2
b)
540 in2
c)
576 in2
d)
700 in2
47.
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.
48.
Is this mapping a function or not a function? 
a)
Function
b)
Not a Function
49.
Is this graph a function or not a function? 
a)
Function 
b)
Not a Function 
50.
Is this graph a function or not a function? 
a)
Function 
b)
Not a Function

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