NAME:______DATE:______CORE:______

Math 8 Benchmark Review Practice Problems

I. SQUARE/SQUARE ROOTS & CUBE/CUBE ROOTS

A. Estimate each of the following square roots to the nearest tenth. Show your work.

1.  15 2. 29

3.  45 4. 37

5. Write each square root from above in order on the number line below

______

B. Simplify each expression
6. / 81 + 196 -8 / 10. / 364+169
7. / 300-75 − 81 / 11. / 25 + 225 -8
8. / 38+64 / 12. / 16 - 289 - 62
9. / 16 - 169 / 13. / 9 - 169

C. Simplify

14. 95 15. 74

16. 124 17 230

II. REAL NUMBER SYSTEM

A. Identify the group(s) that each number belongs to

1. π 2. 0.9758231…. 3. -8.6 4. 45

B. Convert each decimal to a fraction. Reduce to simplest form

5. 0.76 6. 3.75 7. 0.5 8. .125

C. Convert each fraction to a decimal

9. 34 10. 1620 11. 78

D. Order the numbers below from least to greatest.

4.123 8 215 π

III. EXPONENTS

A. Simplify the following

B. 9) Evaluate for x = 2 and y = -3

IV. Scientific Notation

1. Place the following numbers in order from least to greatest:

7.8 x 106, 5.1 x 104, 1.25 x 105, 4.09 x 104

2. Which one of these numbers is the least?

A. 3.5 x 107 B. 3 x 107 C. 5 x 107 D. 5.5 x 107

Write each number in scientific notation.

3. 0.00647 = ______4. 45,200,000 = ______

Write each number in standard notation.

5. 3.49 x 10 5 = ______6. 8.62 x 10 –4 = ______

Find the product or quotient (multiply or divide) the following.

7. (2.2 x 10 4) x (3 x 10 -6) 8. (36.5 x 10 7)÷(4.3 x 10 5)

Find the sum or difference (add or subtract) of the following. Answers must be in scientific notation!

9. 5.88 x 1012 + 7. 21 x 1014 10. 6.1 x 109 - 9.5 x 105

11. A house spider weighs 4.22 x 10-3 ounces. How many house spiders are there in a pound? Note: there are 16 oz. in one pound. Show your work, including what you make the calculator do. **Hint- use division*

V. Solving Equations

Solve the following Equations:

1. 5x + 17 = 47 2. 4y + 1 = -15 3. 16 – z =12

4. 5. 6.

7. 4c + 2c + 6 = 24 8. 9. 8 – 6g + 15 = 19

10. 5k + 9.3 = 21.8 11. 3x + 13 = x + 1 12. 9w – 2w + 8 = 4w + 38

13. A car rental company charges $39.99 per day plus $0.20 per mile. Jill rented a car for one day and the charges were $47.39, before tax. Use m for number of miles. Write an equation. Find how many miles Jill drove.

14. On his last three math tests, Mark scored 85, 95, and 80. What grade must he get on his next test to have an average of 90 for all four tests? (Write an equation; then solve to find the answer.)

VI. Geometric Properties

1. Use the diagram to answer the questions that follow.

a.  m2 is 70°. Find the m6.

b.  m3 = 5x and m 6 is 3x + 8. Find the value of x and the measure of

4 and 5.

c.  Given the m8 = 110°. Find the measure of as many of the other angles as possible.

d.  m 4 = 20x + 20 and m6 is 10x + 10. Find the value of x.

Find each missing angle measure.

2. In triangle DEF the measure of angle D is 36 and the measure of angle E is 92. Find the measure of angle F. / 3.
4.



5. The measure of one angle of a triangle is twice the measure of a second angle. The measure of the third angle is 12 less than the sum of the other two. Find the measure of the angles of the triangle.


a.



/ b.


6. Are the following figures similar? Explain.

7. Each figure shows a pair of similar triangles. Find each unknown length.

30 30

VI. Pythagorean Theorem

1. Justin wanted to figure out how far above the ground a bird nest in a tree was. He leaned his 25 foot ladder against the tree so the top of the ladder just reached the nest, as shown in the figure. He then measured the distance from the bottom of his ladder to the base of the tree directly underneath the nest. This distance was 7 feet. How high above the ground is the bird nest?

A 24 feet B 20 feet C 18 feet D 13 feet

2. Tereika leaves home and bikes 2 miles south, 3 miles west, 1 mile south, and 1 mile west. Which triangle could be used to find the distance Tereika is from home?

3. Using the answer from number 8, how far is Terieka from her home?

A 3 miles B 4 miles C 5 miles D 6 miles

4. The height of a stage being built for a bluegrass festival in Rocky Mountis 10 feet. The base of a ramp must be 9 yards from the base of the stage. How long will the ramp be, to the nearest tenth of a yard?

A 13.5 feet B 13.5 yards C 9.6 yards D 29 feet