MAT 116 Course Prep
This collection of problems is meant to provide practice for a range of skills needed for MAT 116. Read and attempt each problem first; if you aren’t sure how to start a problem, explore the resources on the right to refresh your memory and try again. A dropdown button is found beneath each problem for you to compare both your logic and final answers. Keep track of the skills you aren’t comfortable with, and reacquaint yourself with them so you’re fully prepared for the topics you’ll grapple with soon. Get help in the Math Lab. Return to the Course Prep page.
Problem 1: Identify whether the given statement is an expression or an equation. If it is an equation, determine if it is also an identity. Determine whether each term in the statement is constant or variable.
Part a 
Click here to show solution.Solution: This first statement is an equation since there is an equal sign, but it is not an identity since we can choose a value of that breaks the equality. For example, if , then the statement claims that , which is obviously not true. The term is variable, while the terms 3 and 5 are constant. 
Video: Variables, Expressions, and Equations 
Part b 
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Part c 
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Part d 
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Part e 
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Part f 
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Part g 
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Part h 
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Problem 2: Rewrite the following expressions in the form , where and are real numbers.
Part a 
Click here to show solution.Solution: 
Video: Intro to Rational Exponents 
Part b 
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Video: Rewriting Roots as Rational Exponents 
Part c 
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Part d 
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Video: Exponents in denominators 
Part e 
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Part f 
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Part g 
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Video: Intro to Rational Expression Simplification 
Part h 
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Problem 3: Given that , , , simplify the following expressions. If possible, find exact values.
Part a 
Click here to show solution.Solution: 
Video: Worked Example: Evaluating Functions from Equation 
Part b 
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Part c 
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Part d 
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Part e 
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Part f 
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Part g 
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Part h 
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Problem 4: Solve the following equations for x, and verify your solution.
Part a 
Click here to show solution.Solution: To give you an idea of what it would look like if we somehow got the incorrect answer, pretend we solved the original equation and got . Then, in the verification step, we would have . This is obviously false, and so is not a valid solution to the equation. 
Video: Solving Linear Equations I 
Part b 
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Part c 
Click here to show solution.Solution: 
Video: Solving Linear Equations II 
Part d 
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Part e 
Click here to show solution.Solution: 
Video: Solving Equations with Rational Exponents 
Part f 
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Part g 
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Part h 
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Problem 5: Given , either find the value of the given expression or solve the given equation for x.
Part a 
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Part b 
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Writeup: Simplifying Fractions 
Part c 
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Part d 
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Video: Worked Example: Using the Quadratic Formula 
Problem 6: Expand the following expressions.
Part a 
Click here to show solution.Solution: 
Video: Multiplying Binomials 
Part b 
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Problem 7: Find the slope of the line passing through the following points.
Part a  (0,5) and (4,19)
Click here to show solution.Solution: 
Worked Example: Slope from Two Points 
Part b  (2,11) and (3,3)
Click here to show solution.Solution: 

Part c  and
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Problem 8: Find the equation of the line passing through the following points.
Part a  (0,5) and (4,19)
Click here to show solution.Solution: In slopeintercept form, the slope and yintercept of the line need to be known (unsurprisingly). We calculated the slope between these points above: . Separately, when , we know that since is given as a point on this line. Therefore, the yintercept, commonly denoted with the symbol , is 5. The equation of the line is therefore . In pointslope form, the slope and any one point on the line must be known (unsurprisingly). Choose , for example: then which reduces to . Adding 5 to both sides gives the same answer as before: . Pointslope form is generally more helpful, as needing any point on the line is a less strict requirement than knowing the yintercept. The slope is needed in either case. 
Video: PointSlope and SlopeIntercept Equations 
Part b  (2,11) and (3,3)
Click here to show solution.Solution: 

Part c  and
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Problem 9: From the table below, identify the points and write them in the form (x,y).
Part a 
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Problem 10: Identify the points on the following xy plane and write them in the form (x,y).
Part a 
Click here to show solution.Solution: 
Video: Introduction to the Coordinate Plane 
Problem 11: Find the area of the following figures (including units).
Part a  A rectangle with a length of 5 meters and width of 9 meters.
Click here to show solution.Solution: 

Part b  A square with side length 7 inches.
Click here to show solution.Solution: 

Part c  A triangle whose base is 20 cm and whose height is 11 cm.
Click here to show solution.Solution: 

Part d  A circle of radius 4 feet.
Click here to show solution.Solution: 
Problem 12: Your annual salary is $40,000 for the year 2018. Use the information below to calculate your salary in 2019, 2020, and 2021.
Part a  Assume your salary increases by $1500 per year.
Click here to show solution.Solution:


Part b  Assume your salary increases by 3% per year.
Click here to show solution.Solution: Let’s start with the calculation for 2019. An increase of 3% over the salary in 2018 means that is earned in 2019. Factor 40,000 out of the left hand side to find . This logic can be applied recursively for the other future years:

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