MODULE 1 - RATIOS AND LINEARITY

Scientific Notation

100

Write the following numbers in standard form:

8.3 x 10⁴

8.3 x 10^-4

83,000

0.00083

200

Write the following numbers in scientific notation:

320,000,000

0.0000905

89.201

3.2 x 10⁸

9.05 x 10^-5

8.9201 x 10¹

300

Earth's orbit is approximately 1.5 x 10⁸ and Neptune's orbit is approximately 4.5 x 10⁹. How many times greater is Neptune's orbit than Earth's orbit?

Neptune's orbit is 3 x 10¹ times greater than Earth's.

400

Solve both problems below:

1. (3.65 x 10²) - (9.2 x 10¹)

2. (9.99 x 10^-1) + (7.39 x 10^-3)

Make sure you answer is in scientific notation.

1. 2.73 x 10²

2. 1.0639 x 10^-1

500

Solve both problems below:

Write 3 digits behind the decimal if the answer is long.

1. (2.5 x 10⁶)(7 x 10⁴)

2. (7.3 x 10^-5) / (8.8 x 10^-2)

1. 1.75 x 10¹¹

2. 8.295 x 10^-4

Exponent Rules

100

Simplify.

10⁷ * 10^-10

10^-3

200

Simplify.

3^-2 / 3^-8

3⁶

300

Simplify.

(x^-1y⁵z¹³)(x⁷y^-5z^-2)

x⁶y⁰z¹¹

400

Simplify.

(2x)⁵ / x²y⁹

2⁵x³ / y⁹

500

Simplify.

x⁵y⁰z^-4 / x^-7y³z^-10

x¹²y^-3z⁶

Squares and Cubes

100

Find the values below:

1. square root(64)

2. square root(129)

3. square root(-25)

1. 8

2. 11.357...

3. NO SOLUTION

200

Find the values below:

1. cube root(-3,375) 

2. cube root(745)

3. cube root(1000)

1. -15

2. 9.065...

3. 10

300

Find x and y.

x² = 361

y² = -36

x = 19

y = no solution

400

Find a and b.

a³ = 1,728

b³ = -88

a = 12

b = -4.447...

500

Solve the following equations:

t³ - 10 = 115

e² + 2 = 227

z² + 23 = 12

t = 5

e = 15

z = no solution

Irrational Numbers

100

What is an irrational decimal?

A decimal that does not end and does not repeat.

200

Write whether the answer is rational or irrational.

1. square root(49)

2. cube root(49)

1. rational 

2. irrational 

300

Round the following irrational numbers to the nearest thousandth:

1. square root(65)

2. square root(2,456)

1. 8.062

2. 49.558

400

Find the values.

1. cube root(3)

2. cube root(pi)

1. 1.442...

2. 1.464...

500

If we find the square root of pi and the square root of 3.14, why would we get two different answers?

We would get two different answers because pi and 3.14 are two different numbers.

Pythagorean Theorem

100

What is the formula for Pythagorean Theorem?

a² + b² = c²

200

How do I know which of the sides are c (hypotenuse)? 

The hypotenuse is always across from the right angle, and is the longest side.

300

Find c when a=5 and b=12.

c=13

400

Find c when a=7 and b=8.

c=square root(113) = 10.63...

500

Find c when a=39 and b=20. If your answer is irrational, write what two numbers it is in between.

c = square root(1,921) = 43.829...

This is in between 43 and 44.