Ninth grade math test







Name _____________________                                        Date:_____________________

Solve the following problems

1.

If
3y + 1 / 2
= 5,
4x / 3
= 8
  and  
z / 3
+ 
z / 4
= 2


A. y > x      B. x = y      C. y > z      D. x > z     


2.

A man selling hotdogs, french fries, and a soda as a combo meal at a fairground has to pay the country 250 dollars each day plus 2 dollars per combo meal sold.The price of a combo is 7 dollars.How many combo meals must he sell each day to break even?

A. 25      B. 50      C. 35      D. 70     


3.

Simplify (41/3)3 × (61/6)6 × (31/2)4

A. 416 B. 116      C. 316      D. 216     


4.

A and B are independent events.

If P(A) =
5 / 8
 and P(A and B) =    
1 / 4
,what is P(B)?


5.

a. Choose the correct information about the the graphs of the two lines below

5x - y - 2 = 0
y - 3x = 9

a. A. Intersect at (5.5, 25.5) B. Parallel     C. Identical      D. Perpendicular     


b. What are the slopes of the graphs? b. _____________ and _____________

6.

A rectangle has a perimeter of 18 inches. The long side is 1 inch more than three times the small side. How big is the small side

The small side is ____________

7.

The seventh term of the sequence 16, 9 , 2, -5,... is A. -37     B. 37      C. 26     D. -26     

8.

Find the degree of 2x3 + -6x4 + 4x2 - 1

a. A. 3      B. 2     C. 4      D. 3 + 4 + 2     


9.

Find the greatest common factor of the terms of 16x6 + 8x4 + 2x12

A. 8x12      B. 2x4     C. x6     D. 4x6     


10.

What is the maximum or minimum value of y = x2 + 3x - 10 ?

The value is y = ____________

11.

Table 1
x 1 2 3 4
y 3 7 11 15


Table 2
x 1 1 2 4
y 3 7 11 15




a. Which relations are functions? Put a check mark next to the table that is a function

Table 1 ___________

Table 2 ___________

b. If a table is a function, model the table with a function.






12.

Evaluate | y - x | + -y2 + 2z + x2y3z-2   for x = 3, y = 2, and z = -2

13.

There are 6 red balls and 4 blue balls in a bag.

Find each probability
P(red and red ) with replacing
P(red and blue) with replacing
P(red and red) without replacing
P(red and blue) without replacing

14.

Solve 3(2x - 1) = 4x + 5

15.

Simplify (4x3 - 5x3 + x + 8 ) - (3x3 - 4x + 9 + 6x2 )

16.

What is the standard form of the product (3x - 1) (5x + 3)

A. 15x2 + 2x + 3      B. 15x2 + 4x - 3     C. 15x2 + 4x + 3      D. 15x2 + 2x - 3     


17.

Triangle ABC is a right triangle with a right angle at A. Which of the following is false?

sin(C) =
AB / BC
 cos(B) =
AB / BC


sin(C) =
AB / AC
 cos(C) =
AC / BC


18.

Find the median and mode of this set of data

5 , 1, 3, 5, 8 , 10, 8, 14

19.

Find the equations that are parallel and perpendicular to x + 5y = 50 and passing through the points (5, 10)

20.

Simplify (1.5 × 108)(6 × 10-8)

21.

Simplify each radical expression

a.

5 √32
-  3 √2


b.

√8x8 / 2x2


22.

Solve the inequality 2y - 4x < 6   for y. Then, give 2 points that are solutions

23.

a. Factor x2 - 8x - 20

b. Solve x2 - 8x - 20

24.

Solve 12x2 + 7x - 10

25.

Solve the following proportion by setting up a proportion

The hours of operation of a park is 8:00 am - 10:00 pm Wednesday through Sunday. A Ferris wheel can make a 360 degrees turn 5 times every 10 minutes. How many 360 degrees turn can the Ferris wheel make in a week?

26.

How can you find out how many solutions a quadratic equation has without solving the quadratic equation?

27.


The solution of the system ax - 4y = 8 and 6x + by = -30 is (-2, -3)

1. Find a and b

2. Replace a and b into the system. Then solve the system to verify that the solution is indeed (-2, -3)

28.

Find the value of 6P4

29.


Simplify  
30x4y8z / 50x10y7z


30.

What is the value of the f(x) = 
-8 / x - -2
for x = -2


a. A. 0      B. undefined     C. 2      D. -2     


31.

Solve the equation -2 + √y - 5 = 10


32.

Write a function rule for the following table

x y
0 -4
6 -5
12 -6
24 -7


33.

Suppose x - 25 = -75, what is x + 25? What is x + 50?

34.


What is the length of the diagonal of a rectangle with sides equal to 9 and 12?

35.


What are extraneous solutions and what type of equations give extraneous solutions?

36.

Solve and graph 4|2x - 5| ≥ 20

37.

Graph the following functions using what you know about the graph of y = |x|

a. y = |x - 4|

b. y = |x| + 2

c. y = 2|x|

d. y = 2|x - 4| + 2

38.

The product of two positive integers is 45. The second is 4 more than the first. Find the integers by setting up an equation

39.

What is the percent of decrease from 12 to 4?

40.

A company enrolls computer programmers and secretaries at a ratio of 5 to 3. There are a total of 24 secretaries and computer programmers. How many people are secretaries? How many are computer programmers?

41.

The price p of an item is sold with a discount of 20%. The expression that represents the sale price of the item is ___________

A.p - 20p      B. 0.20p      C. p + 0.20p      D. p - 0.20p     

42.

Graph y > 
-2 / 3
x + 1


43.

The sides of a rectangle are -5x + 10 and x - 4

a. Write an expression for the perimeter.

b. Write an expression for the area.

c. For what value of x is the area the biggest?

44.

Simplify  
4x - 20 / x2 - 10x + 25


45.

Find the horizontal and vertical asymptotes of the function below

f(x) = 
-10 / x - 3
 + 5


46.

Simplify  
x - 6 / x2 - x
÷  
x2 - 4x - 12 / 3x2 - 3x


47.

Graph the following system of inequalities?

2y > x + 4
3y + 3x > 13

48.

Find the LCD of x5y and x2y4

49.

a. How many different ways can you choose 3 books from the 8 books on your shelf?

b. A 20 member club needs 2 members to lead. How many different pairs are possible?

50.

John has a 15 feet ladder. When he leaned the ladder against a building, the ladder makes an angle of 60 degrees with the ground. What is the distance from the side of the building to the base of the ladder?



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