Math Worksheets

Archive for April, 2009

Subtarction of Numbers

Question: What is the period, asymptotes and x-intercepts of tan(3x)?

Can someone help me find the answers with some explanation. My math worksheet doesn’t explain it very well. How would I derive the answers from just the equation and then how would use all those information to start to graphing that equation?

Answer: tan (3x) has a period of 180°. That means that every 180°, the tan curve will be repeated. (Take at look at what a tan curve looks like. You will see that every time you add 180° on any degrees, you will get the same answer. Sorry, I couldn’t find any decent ones on the internet.)

To find asymptotes, let tan (3x) = tan (90°) [Every period of 90° on a tan curve, there is an asymptote.] Have you done general solutions yet? If so, apply them. (The general solution for tan a = tan b is a = 180°n + b, where n is an integer.)

tan (3x) = tan (90°)
3x = 180°n + 90°
x = 60°n + 30°

n = 0, x = 30°
n = 1, x = 90°
n = -1, x = -30°
n = 2, x = 150°
etc.

How many numbers you substitute into n will depend on your domain.

To find the x-intercepts of tan (3x), let tan (3x) = 0. Again, use general solutions.

tan (3x) = 0 = tan 0.
3x = 180°n + 0
x = 60°n
n = 0, x = 60°
n = 1, x = 180°
n = -1, x = -180°
etc.

Solving Multi-Step Equations with Variables on Both Sides

Answer the following math questions about The Average. 

1. When do you need to calculate The Average?

How to find an average?

What is The Average of all the numbers between 1 and 10 (including 1 and 10)?

Two math classes each with 5 students.

• Class I scores 8, 6, 8, 7, and 10.
• Class II scores 6, 10, 4, 10, 10.
• Which class scores better on average?

This week the temperatures were:

• 80^o, 78^o, 79^o, 81^o, 82^o, 79^o, and 77^o.
• What is The Average temperature this week?

Anna has three bags. The bags weigh:

• 10 lb, 10.5 lb, and 9 lb.
• What is The Average weight of Anna’s bags?

Mike has three TVs of:

• 25 “, 27″, and 32″.
• What is The Average size of Mike’s TVs?

Isaac has 3 sisters of height:

• 5′ 0″, 4′ 9″, and 3′ 6″.
• What is The Average height of Isaac’s sisters?

James played video games 6 times. He scored:

• 423, 475, 522, 638, 758, 715
• What is The Average video games score?

Linda baked 10 cookies. The diameters of the cookies are:

• 4 cm, 4.3 cm, 3.9 cm, 5 cm, 4.3 cm, 4.15 cm, 4.21 cm, 3.99 cm, 4.17 cm, 4.9 cm
• What is The Average diameter of Linda’s cookies?

Click here for answers to the above Math Worksheets problems on The Average 

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