8th grade math test

Print your 8th grade math test before you start and then try to answer all the questions.

Name _____________________                                        Date:_____________________

Solve the following problems


1.

a. 5⁷ × 5^-10 =

A. 1/3      B. 5^-2      C. 1/125      D. 5^-17     


2.

If 2x³ = 54, what is x?

A. 1      B. 5      C. 2      D. 3     


3.

a. The answer for 20000000 × 3.5 × 1000000 in scientific notation is

(Hint: put 20000000 and 1000000 in scientific notation first)

A. 7 × 10¹³      B. 3.5 × 10¹³      C. 2 × 10¹³      D. 7 × 10¹²     


b. 0.0004 × 4000 as a decimal is ___________ and as a fraction is ____________

4.

a. Which set contains only rational numbers?

A. { √(49), √(7), 1/2, 9/5}     
B. { √(121), 12/5, √(169), 0.333333333333}     
C. { 4 × √(5), 2 , √(100), 0}     

b. Pull out all the irrational numbers from each set above and write them down here.

_______________________________________________________

5.

To go to school, you have to walk 6 miles east and then 8 miles north ?

a. Draw a figure representing your path from home to school

b. Draw a line representing the shortest distance you could have taken. Then, calculate this distance _________________

6.

The formula for the area of a circle is shown below

A = pi × r²

a. Which of the following is the correct expression for r or the radius in terms of A and pi?

A. r = √(A / 2pi)      B. r = √(2A / pi)      C. r = √( pi / A)      D. r = √(A / pi)     

b.Use the correct formula you found in part a and pi = 3 to find r when A = 48 square feet.

r = __________________


7.

A company charges a flat fee of 1500 dollars to rent a yacht. In addition, renters must pay 100 dollars per hour.

a. Which equation shows the cost C to rent a yacht for h hours?

A. C = 100 + 1500 × h     B. C = 1500 × h      C. C = 100 × h + 1500     D. C = 100 × h + 1500 × h     

b. How much would it cost you to rent a yacht for 5 hours?

c. What is the slope of the cost? what is the y-intercept?

d. Using the answers for c, graph the cost on the coordinate system.

8.

Escalator 1 has a rise of 6 and a run of 4. Escalator 2 has a rise of 12 and a run of 6. Do the escalators have the same slope? Explain with math computation.

9.

Celita has a garden shaped like a square. How does the area changes if she triples the length of each side?

A. The area of the garden is tripled      B. The area of the garden is nonupled C. halved      D. sextupled     


10.

Find the volume of a cone with a radius of 8 inches and a height of 3 inches.

(Hint: Use v = 1/3 (pi × r² × h)

11.

a. Look at the figure above and then tell which graph(s) show the following correlation.

Positive correlation. ____________ 
Negative correlation_____________
No correlation___________



b. What kind of correlation is the following situation? 

Number of gallons of gas in your car and the distance you can travel ___________________

Number of oranges you can eat and your height ___________________

Number of students going to a concert and the revenue generated.____________________

c. If a scatter plot shows a negative correlation, which line of best fit could represent the scatter plot?

A. y = x - 5      B. y = -1000x + 5000      C. y = 100x - 7      D. y = 5     

  
12.

What is the equation of a line that has a slope of 3/5 and a y-intercept of 2?

A. 5y + 3x = 10        B. 5x - 3y = 10      C. 5y - 3x = 10      D. 5x + 3y = 10

13. 

Triangle ABC has vertices (1,1), (3,5), and (5, 3). This triangle is dilated by a factor of 3. What are the images of the 3 vertices. Graph ABC and the image A'B'C'




14.

The diagonal of a square computer screen is 50 inches. What is the perimeter of this TV? ______________

15.

100 students take a survey to see what kind of ice cream people in America like to eat.

Which of the following will most likely flaw the survey?

A. Some students were not born in the United States

B. The students were not young enough

C. The survey may not include people who travel 50 miles to get ice cream

D. Choose students from a variety of schools. 


16.

Which statement shows the similarity between the following 2 graphs?


4y = 2x + 0.5 and 4y = 5x + 1/2

A. The y-intercepts are the same 

B. The graphs are identical

C. The x-intercepts are the same 

D. The slopes are the same

17. 

Below are 3 equations

1) 4x -2x + 1 = -1 + 2 + 2x

2) 2x - 2 = 6 - 4 + 4x 

3) 5 + 3x = 2 + 3x + 5 

Solve all equations and then say

Which equation has 1 solution _______________, no solutions _______________, infinitely many solutions ______________

18.

A tree is 8 feet tall and cast a shadow that is 6 feet. a. If your child's height is 4 feet, which equation can you use to find the length of his shadow?

a. Which proportion can you use to solve this problem?

A. 8/5 = 6/x      B. 4/6 = x/8      C. 8/4 = 6/x      D. x/4 = 8/6      


b. What is the length of the shadow?_______________

19. 

Solve the following silmultaneous equations.

2x + 4y = 8

4x - 4y = 6

a. by graphing

b. algebraically 

20.


The cup below is 2/3 full. How much water can the cup hold? _____________

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