Math Preparedness Assessment: Matter and Motion 2016-17
PLEASE READ THE FOLLOWING CAREFULLY
The following Math Preparedness Assessment is not intended as a placement or entrance test for
Matter and Motion. In fact, we do not expect all students to be able to answer all the questions.
Rather, we hope that by taking this Assessment, you will be able to determine how prepared you
are mathematically for MM. Experience has shown us that adequate math preparation is crucial
for success in calculus and physics.
These questions represent some of the mathematical background and preparation we think students
should have. The algebra diagnostic from the calculus textbook serves a complementary role. (See
the Algebra Review link here: http://www.stewartcalculus.com/media/9_home.php)
If you are able to work through many (but not necessarily all) of these problems well, it is likely
that you are adequately prepared mathematically for MM. If you are unfamiliar with or rusty on
some of the topics, you have a good idea of what you should review; we have an excellent math
center on campus the Quantitative and Symbolic Reasoning (QuaSR) Center in the library. If you
struggled with many questions, you might want to seriously consider spending some time improving
your mathematics preparation and taking this kind of program in the future. We will be happy to
work with you in making this judgment call.
INSTRUCTIONS:
• You MUST complete this worksheet by yourself.
• You are allowed and encouraged to use a calculator as you work on this worksheet.
• You are allowed to use notes/homework from previous math classes, math textbooks, and
the internet to look up formulas or relationships. As noted above, you must complete this
worksheet by yourself, so please dont consult with anyone or look up answers.
• Please pay attention to the amount of time that you spend working on the worksheet. Well
ask you to report a rough estimate of that time.
• Also, note whether you use a calculator, notes/homework from previous math classes, math
textbooks, or the internet; youll report that as well.
• To aid us and you in understanding your worksheet, youll be asked to judge the level of
difficulty of the worksheet.
The answer key is provided for you at the end of this worksheet. Do not use the key until you
have completed the worksheet. Assess your grade by assigning one point for every correct answer,
and then convert it to a percentage. Please bring your completed, self-graded worksheet
to the first day of class.
Sincerely,
your MMM16-17 faculty team
Maija Benitz, Dharshi Bopegedera
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1. Calculate and report the following in decimal form:
a) 53 + 72
b)
4
5
∗
5
8
c)
4
5
÷
5
8
d) 5.6 − 2(7.3 + 8.2)
e)
|25−4|
|3−10|
2. Simplify the following:
2 +x−2
a) x x−1
b)
x−7
7−x
3. Simplify the following:
a) x4 x3 + x2 x5
b) x5 x−4
c)
x3 y 4
x2 y 6
4. Solve for x:
a) 5x − 10 = 25x
b)
6x+9
x−5
=3
c) x2 − 2x − 15 = 0
5. Solve for x: a) 272x−4 = 33
b) log3 x = 5
2
6. Light visible to the human eye has a wavelength that generally is less than 0.000082 millimeter (mm). Express this number in scientific notation.
7. Express the following number in scientific notation: 1456789.034
8. Divide and express the final answer in scientific notation:
5.37×10−15
1.79×10−4
9. A teacher wants to schedule individual mid-quarter conferences with 24 students. If each
conference is to last 15 minutes, how many total hours will the teacher be in conferences?
10. 1 inch is equal to 2.54 centimeters. How many inches are equal to 1 centimeter?
11. If 90 feet of wire weighs 18 pounds, what will be the weight of 100 feet of the same wire?
12. Given D = VT
a) Find D when V = 35 miles per hour and T = 2.5 hours. Include proper units in answer.
b) Find T when V = 55 miles per hour and D = 385 miles. Include proper units in answer.
13. Two commonly used temperature scales are the Fahrenheit scale and the Celsius scale. To
convert between them, you can use the following relationship: F = 95 C + 32. In this relationship C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit.
a) What is the temperature in degrees Celsius when it is 95 degrees Fahrenheit?
b) If you make a plot of degrees Fahrenheit vs. degrees Celsius, youll obtain a straight line.
What is the slope of this straight line?
c) What is the y-intercept of this straight line?
14. What are the slopes and intercepts of the line represented by the given equations?
Equation
a) −2y + 8x − 3 = 0
b) 6y − x − 24 = 0
c) −3y + 6x + 27 = −3x
15. Convert 45 degrees to radians
16. Convert π/3 radians to degrees
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Slope
Intercept
17. Find the length of sides x and y in the triangle below:
18. Find the angle θ, in degrees, of the triangle below:
19. Consider the trapezoid shown in the figure below.
a) What is the area of the trapezoid, in square meters?
b) What is the perimeter of the trapezoid, in meters?
20. Evaluate: limx→0
3(x−2)2 −12
x
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Complete this Survey
1. How much time did you spend completing this worksheet?
2. Did you use any resources (textbook or notes) to complete this worksheet? If so please indicate
what you used.
3. Which of the following statements best describes the level of difficulty of the worksheet? Please
circle one only.
• I found this to be a very challenging exercise.
• There were several challenging problems but I was able to complete the worksheet.
• I struggled with a few problems (1 to 4 problems) but the rest of the worksheet was not
difficult.
• This was not a difficult worksheet to get through
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Answer Key
Problem
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Answer
a) 5.16, b) 0.5, c) 1.28, d) -25.4, e) 3
a) (x+2), b) -1
a) 2x7 , b) x, c) x/y 2
a) -1/2, b) -8, c) -3, 5 (two roots)
a) 5/2, b) 35 = 243
8.2 × 10−5 mm
1.456789034 × 106
2.944 × 10−11
6 hours 8 hours
0.393 inches
20 lbs
a) 87.5 miles, b) 7 hours
a) 35C, b) 9/5 slope, c) 32 y-intercept
a) 4 slope, -3/2 intercept, b) 1/6 slope, 4 intercept, c) 3 slope, 9 intercept
π/4 radians = 0.785 radians
60 degrees
x = 9.829, y = 6.882
θ = 33.68 degrees
a) 136 m2 , b) 52 m
-12
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