Topic 1 Review

Rational and Irrational Numbers

100

Is the following rational or irrational?

-3/2196

Rational

200

Is the following rational or irrational?

cube root 81

Irrational

300

Rational numbers consist of what three things

Integers

Whole

Natural

400

Order the rational and irrational numbers from least to greatest

3.14159..... , square root 16 , cube root 9 , 7

cube root 9 (3) , 3.14159... , square root 16, 7

500

Determine which numbers are rational and irrational. Order them from least to greatest.

cube root 64 , square root 63 , 8 , 3.14159....

Rational - cube root 64 , 8

Irrational - square root 63 , 3.14159...

3.14159... , Cube root 64 , square root 63 , 8

Squares and Cubes

100

Cube root 27

3

200

Solve for x:

x² = 196

x = + 14 and x = - 14

300

How would you classify 100 

(Square, cube, both, neither)

Perfect square

400

Solve for x:

x³ = 2744

x = 14

500

Estimate the cube root of 210

Lower end - cube root 125

Higher end - cube root 216

It would be between 5 and 6

Estimate 5.9

Exponents

100

x⁵ * x¹²

x¹⁷

200

217⁰

1

300

( x ⁴ )²

x⁸

400

2⁸ / 2¹⁰

1/2² or 1/4

500

x⁶ y² z⁵ / x⁴ y⁴ z⁴

x² z / y²

Scientific Notation

100

Write 0.0000000567 in scientific notation

5.67 x 10^-8

200

Write the following in standard form

6.45 x 10⁶

6,450,000

300

Evaluate: Write in scientific notation

(3.4 * 10⁵) + (9.7 * 10⁶)

1.004 * 10⁷

400

Evaluate: Write in scientific notation

(3.2 *10²) * (1.8 * 10⁴)

5.6 * 10⁶

500

Evaluate: Write in scientific Notation

(5 * 10^-2) / (2 * 10⁶)

2.5 * 10^-8

Word Problems

100

The area of a square is 121m². What is the length of one side of the square? Show your work.

11m

200

A cube-shaped box has a volume of 729 cubic inches. What is the area of one face of the box?

Side length = 9 in

A = l * w or A = S² 

A = 9 * 9 = 81in²

300

A corporation has 4.8 * 10³ employees. The average annual salary for each of its employees is $4.5 * 10⁴. Approximately how much does a corporation pay its employees each year?

(4.8 * 10³) (4.5 * 10⁴)

2.16 * 10⁸

400

A light year is the distance light travels in a year. One light year is about 5.88 * 10¹² miles. The sun is about 1.6 * 10^-5 light years from earth. About how many miles is the sun from the earth?

(1.6 * 10^-5) (5.88 * 10¹²)

= 9.41 * 10⁷

500

If 446 billion telephone calls were placed by 135 million United States telephone subscribers, what was the average number of calls per subscriber? (Write your answer in scientific notation)

Note: Put 446 billion and 135 million in scientific notation

4.46 * 10¹¹ / 1.35 * 10⁸

= 3.3 * 10³