Topic 1

Rational or Irrational

100

Is 0.777777... a rational or irrational number?

Rational because it is a repeating decimal and can be written as a fraction (7/9)

200

Is the square root of 23 rational or irrational?

Irrational because it is not the square of an integer

300

Classify PI as a rational or irrational number and explain

Irrational number because it does not terminate or repeat

400

These types of numbers can not be written as a fraction.

Irrational numbers

500

Is the square root of 36 rational or irrational? Explain

It is rational because the square root of 36 is 6.

Properties of exponents

100

simplify 6⁴x6³

6⁷

200

simplify (3⁶)^-2

3^-12

300

Simplify: 1,025,000⁰

1

400

Write with a positive exponent:

4^-9

1/4⁹

500

Evaluate when x=2 and y=5

-4x^-2+3y⁰

2

Scientific Notation

100

write the number 803,000,000 in scientific notation

8.03 x 10⁸

200

Write the number 0.0000000068 in scientific notation

6.8x10^-9

300

Write 1.359 x 10⁵ in standard form

135,900

400

The area of Connecticut is about 12,549,000,000 square meters. The area of Rhode Island is about 2,707,000,000. How many times greater is the land area of Connecticut than the area of Rhode Island.

about 3 times greater

500

Is this number written in scientific notation? Explain.

14 x 7⁴

No it is not because the first factor is greater than 10 and the second factor needs to be a power of 10.

Square and Cube Roots

100

Is 27 a perfect square, perfect cube, or neither

perfect cube

200

A gift box is a cube with the volume of 512 cubic inches. What is the length of each edge of the box?

8 in

300

A container is a cube shape with a volume of 216 cubic inches. What are the dimensions of one face of the container?

6in x 6 in 

400

Mattie wants to build a square deck to make a play are of 144 square feet. What is the length of each side of the deck?

12 feet

500

Why is the square root of 125 both a positive and negative value?

Because a positive x a positive is positive and a negative x a negative is a positive value. So, the square root of 125 is about 11.1 and -11.1

Random

100

Would you rather have 5 x 10⁴⁵ dollars or 3 x 10⁹⁵ dollars? 

3 x 10⁹⁵ because it is greater than 5 x 10⁴⁵

200

What sport does Mr. Tocci coach?

Soccer

300

What high school did Ms. Mammone and Mrs. Forgues graduate from?

Leominster high school

400

Ms. Mammone says that (2³)¹ equal to 16. Why is that incorrect? 

No it is equal to 8. She added the exponents when you should have multiplied

500

The population of town a is 1.26 x 10⁵ and the population of town b is 2.8 x 10⁴. How many times greater is the population of town A than town B?

about 4.5 times greater