Unit Test 0/1 – Review Packet



Unit Test 0/1 – Review Packet

There are four major review topics for this Unit Test. By the end of class on Friday, you should feel confident about the following types of problems:

Problem Set

I. Writing equation for problem situations

II. Writing equations in equivalent forms (i.e. express x in terms of z and y)

III. Solving equations and checking solutions

IV. Creating and interpreting graphs

You can complete these Problem Sets in any order. Our recommendation is for you to begin with the problem set that looks most challenging. Once you feel confident with a Problem Set, check your answers against the posted answer key. If you are getting all of the problems correct, move to a new Problem Set.

A few reminders:

• Show all of your thinking.

• Check your solutions wherever possible. If your solutions don’t work, PROBLEM SOLVE!

• Don’t leave fractions in denominators

• When taking a square root to “undo” a squared term, don’t forget [pic]

• Help each other. No one becomes a strong mathematician working alone. Don't forget your notes.

• Graphing calculators will not be permitted for this test. You will be provided with a small scientific calculator.

[pic]

Problem Set I - Writing equations for problem situations

1. Recall that the perimeter of any rectangle can be expressed as a function of the length L and width W of that rectangle in two equivalent ways: [pic] or [pic].

[pic]

a. Find the perimeter of a rectangle that is 5 meters long and 3 meters wide.

b. Find the length of a rectangle that is to have a perimeter of 45 meters and width 5 meters.

c. Write an equation expressing length L as a function of perimeter and width of any rectangle.

d. Write an equation expressing width W as a function of perimeter and length of any rectangle.

e. Suppose you wished to determine the maximum area of a rectangle garden that could be enclosed with 50 meters of flexible fencing.

• Which of the equations in this task would be most useful in this regard?

• How would you use the equation to find the maximum area?

• What is your best estimate of the maximum area and of the dimensions of the enclosing rectangle?

2. Earlier this week, you wrote an equation expressing the relationship among the following five variables:

[pic]

S1 = average speed to work or school (in miles/hour)

S2 = average speed from work or school (in miles/hour)

[pic]

[pic]

Equation [pic]

Use this expression to answer each of the questions below.

a. A commuter’s round-trip was 45 miles. The trip to work took ½ hour at an average speed of 40 miles per hour, and the trip home took 2/3 hour. What was the average speed on the trip home?

b. If a school bus takes 0.75 hour to cover its morning route at an average speed of 20 miles per hour and 0.5 hour in the afternoon at an average speed of 25 miles per hour, what total distance does the bus travel?

c. If an airplane makes a 5,200-mile trip from New York to Los Angeles and back, averaging 450 miles per hour on the 6-hour outbound leg and 550 miles per hour on the return, how long does the return trip take?

d. Rewrite the original equation to express time going to work or school, [pic] as a function of the time returning home [pic], the total distance traveled, [pic], and the average speeds of the two parts of the trip [pic]and [pic].

e. Express average speed returning home [pic] as a function of the four other variables.

3. A cup of coffee contains 130 milligrams of caffeine. If caffeine is eliminated from the body at a rate of 11% per hour, how long will it take for half of this caffeine to be eliminated from a person’s body? Write an equation to model the situation and answer the question.

4. A tool & die business purchased a piece of equipment for $250,000. The value of the equipment depreciates at a rate of 12% each year.

a. Write an equation to model this situation.

b. What is the value of the equipment after 5 years?

5. Write an equation relating the following variables:

[pic]

[pic]

[pic]

Equation ______________________________

Use the equation to answer the problems below.

a. John left home and drove at the rate of 45 mph for 2 hours. He stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination. How many miles did John drive?

b. Linda left home and drove for 2 hours. She stopped for lunch then drove for another 3 hours at a rate that is 10 mph higher than the rate before she had lunch. If the total distance Linda traveled is 230 miles, what was the rate before lunch?

Problem Set II - Writing equations in equivalent forms

1. Express the following standard form equation in slope-intercept form. Identify the slope and y-intercept.

[pic]

2. Solve each function for the indicated variable.

a. [pic], Solve for x c. [pic], Solve for y

b. [pic] , Solve for l d. M=[pic]Solve for v

Problem Set III –Solve each equation AND check your solutions.

1. [pic] 6. [pic]

2. [pic] 7. [pic]

3. [pic] 8. [pic]

4. [pic] 9. [pic]

5. [pic] 10. [pic]

Problem Set IV - Creating and interpreting graphs

1. Without using a graphing calculator, identify the function family for each equation. Create a table of values and then graph each function.

a. [pic] b. [pic]

Function family: Function family:

______________________ ______________________

c. [pic] d. [pic]

Function family: Function family:

______________________ ______________________

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