Variables and Patterns

Unit Test Review

Write an equation for each situation:

1) Carl drives 43 miles in one hour. (Use d for distance and t for time.)

2) Sara has $400 and saves $40 every month. (Use s for total savings and t for time.)

3) Craig has $500 and spends $100 a month. (Use t for money left and t for time.)

4) Sandra earns $7 each hour. (Use t for time and e for total earnings.)

1) d = 43t

2) s = 400 + 40t

3) t = 500 – 100t

4) e = 7t

Jack buys fifty baseball cards every month.

• What is the IV and the DV?• What is the pattern of change?• How would you see the pattern of change in– A table?– A graph?– An equation?

• IV = time in months; DV = total number of cards

• As time increases by one month, baseball cards increase by fifty.

• Table- differences would be the same (50)• Graph- you’d see a straight line because every

time you move right one on the x-axis, you move up 50 on the y-axis.

• Equation- the coefficient is 50

• What is a coefficient?

• The coefficient is the number that you are multiplying by a variable. It is usually in front of it, but without a multiplication sign.

• In an equation, the coefficient tells you the “thing” that gets repeated. Often key words are every, each, or per.

• For example, Kevin has 50 stamps. He adds 3 to his collection every year. s = 50 + 3t

• In the Rocky and Adrian problem in our text, what was the pattern of change for Rocky’s shop?

• As number of bikes increases, the total cost increases but not at a steady pace.

• In the Rocky and Adrian problem in our text, what was the pattern of change for Adrian’s shop?

As number of bikes increase by 5, the total cost increases by $150.

OR

As number of bikes increase by 1, the total cost increases by $30.

• In the Rocky and Adrian problem, why does Adrian’s data turn into a straight line?

• It’s a straight line because it’s a steady increase. That is, every time you move right one on the x-axis, you move up 30 on the y-axis.

• If you have a graph with the following labels:

IV = number of carsDV = total weight (pounds)

would it make sense to connect the points?

• No, because cars are discrete data. You can’t break a car into smaller parts and still have it make sense.

• Consider the following table:

– What is the first ordered pair?– What does the ordered pair represent?– What is the fourth ordered pair?– What does the ordered pair represent?

Time (weeks)

0 1 2 3 4

Weight(pounds)

0 12 24 36 48

• The first ordered pair is (0,0). The numbers mean that at 0 weeks, the weight is 0 pounds.

• The fourth ordered pair is (3,36). The numbers mean that at 3 weeks, the weight is 36 pounds.

Hopefully you found this to be a helpful review for Thursday’s unit test. To help you even more:

• Review the unit test study guide that is on my website• Review homework, classwork, notes and old

quizzes/miniquizzes• Look at any ACE problems you have worked on already• Check out any answer keys or that are on my website

you might have• Maybe form a study group with a friend/friends?