Download Sketch a pair of lines whose system of equations has infinitely many

Review for the Written Portion of Math 108 Test #1
Read all directions carefully. Directions:
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Write legibly, with correct mathematical notation, label all units when applicable, and clearly
indicate final answers.
When applicable and undirected, round to the nearest thousandth.
Show all work for full credit. You will not receive full credit for writing an answer, even if it is
correct. Make sure you attempt all problems and explain your thinking.
You may use a calculator (not a phone/ipod/computer/laptop/ipad) and a pen or pencil, but no
other resources.
Objective 1
Students will be able to recognize when to apply rounding rules for rounding up to the next whole
number, rounding down to the previous whole number and rounding for transactions in dollars and
cents.
Sample problem type 1
Round 1.86325213 appropriately for each of the following scenarios:
How many busses are needed for a field trip?
How much should we charge for a dozen eggs?
How many new computers can we afford?
Sample problem type 2
Describe a situation when it would be appropriate to round 5.13845434 to 5.
Describe a situation when it would be appropriate to round 5.13845434 to 6.
Describe a situation when it would be appropriate to round 5.13845434 to 5.14.
Objective 2
Students will be able to identify how many solutions there are to a system of two linear equations
graphically and algebraically.
Sample problem type 1
Sketch a pair of lines whose system of equations has exactly one solution.
Sketch a pair of lines whose system of equations has no solutions.
Sketch a pair of lines whose system of equations has infinitely many solutions.
Sample problem type 2
How can you tell algebraically that a system of equations has exactly one solution? Give an example and
explain.
How can you tell algebraically that a system of equations has no solutions? Give an example and explain.
How can you tell algebraically that a system of equations has infinitely many solutions? Give an example
and explain.
Sample problem type 3
You solve a system of linear equations and get: 3y-2=3y-2. How many solutions does the system of linear
equations have?
You solve a system of linear equations and get: x=8. How many solutions does the system of linear
equations have?
You solve a system of linear equations and get: 5=3. How many solutions does the system of linear
equations have?
Sample problem type 4
How many solutions are there to the following system of linear equations?
x+2y=7 and y=-3x+1 (one)
y=-1/4x-1 and -x-4y=-4 (none)
y=-x-1 and -2x-2y=2 (infinite)
Objective 3
Students will be able to interpret the components of an applied linear equation.
Sample problem type 1
Given an equation in slope intercept form, identify the slope, y-intercept, dependent variable and
independent variable.
V=-2250t+13500
C=C0+bYd
V=v0+at
E=1/2kA2
W=P∆V+wext