**Print out your 8th grade math test before you begin, then try to answer all of the questions.
**

Name Date: _____________________

**Solve the following problems**

**1.**

a. 5^{7th} × 5^{-10} =

**A.** 1/3 **BB** 5^{-2}**C. ** 1/125 **DD ** 5^{-17}

**2.**

If 2x^{3rd} = 54, what is x?

**A.** 1 **BB** 5 **C. ** 2 **DD ** 3rd

**3.**

a. The answer for 20,000,000 × 3.5 × 1,000,000 in scientific notation is

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

**A.** 7 × 10^{13th}**BB** 3.5 × 10^{13th}**C. ** 2 × 10^{13th}**DD ** 7 × 10^{12th}

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

**4th**

a. Which set contains only rational numbers?

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

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

_______________________________________________________

**5.**

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

a. Draw a figure that represents your journey from home to school

b. Draw a line that represents the shortest distance you could travel. Then calculate this distance _________________

**6th**

The formula for the area of a circle is shown below

A = pi × r^{2}

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

**A.** r = √ (A / 2pi) **BB** r = √ (2A / pi) **C. ** r = √ (pi / A) **DD **
r = √ (A / pi)

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

r = __________________

**7th**

A company charges a flat fee of $ 1,500 to rent a yacht. In addition, tenants must pay $ 100 an hour.

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

**A.** C = 100 + 1500 × h **BB** C = 1500 × h **C. ** C = 100 x h + 1500 **DD **
C = 100 × h + 1500 × h

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

c. How high are the costs? What is the y-intercept?

d. Using the answers for c, plot the cost in the coordinate system.

**8th.**

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 incline? Explain with math calculations.

**9.**

Celita has a garden in the shape of a square. How does the area change when it triples the length of each side?

**A.** The area of the garden is tripled **BB** The area of the garden is not duplicated **C. ** halved **DD ** sextupled

**10.**

Find the volume of a cone that is 8 inches in radius and 3 inches in height.

(Hint: use v = 1/3 (pi × r^{2} × h)

**11.**

a. Look at the figure above, then say 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 gasoline in your car and the distance you can travel ___________________

Number of oranges you can eat and size ___________________

Number of students attending a concert and the income generated .____________________

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

**A.** y = x – 5 **BB** y = -1000x + 5000 **C.** y = 100x – 7 **DD **y = 5

**12th**

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

**A.** 5y + 3x = 10 **BB** 5x – 3y = 10 C. 5y – 3x = 10 **DD **5x + 3y = 10

**13th**

The triangle ABC has corner points (1,1), (3,5) and (5, 3). This triangle is expanded by a factor of 3. What are the pictures of the 3 corner points? Graphic ABC and the image A’B’C ‘

**14th**

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

**fifteen.**

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

Which of the following will be the most __ probably__ Error in the survey?

**A.** Some students were not born in the United States

**BB** The students weren’t young enough

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

**DD **Choose students from different schools.

**16.**

Which statement shows the similarity between the following 2 graphics?

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

**A.** The y-sections are the same

**BB** The graphics are identical

**C. **The x sections are the same

**DD **The slopes are the same

**17th **

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, then say

Which equation has 1 solution _______________, no solutions _______________, infinite number of solutions ______________

**18th**

A tree is 8 feet tall and casts a shadow that is 6 feet. a. If your child is 4 feet tall, what equation can you use to find the length of their shadow?

a. What is the ratio with which you can solve this problem?

**A.** 8/5 = 6 / x **BB** 4/6 = x / 8 **C.** 8/4 = 6 / x **DD **x / 4 = 8/6

b. How long is the shadow _______________

**19th**

Solve the following equations.

2x + 4y = 8

4x – 4y = 6

a. through graphical representation

b. algebraic

**20th**

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

## Things To Look For On This 8th Grade Math Test.

**Note**: A score of 16 or more on this 8th grade math test is a good indication that most of the skills taught in 8th grade have been mastered

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