### MATH 113: Final Exam Review

The questions below are intended to give an idea of the sorts of questions you might find on the final exam. Often these questions are more difficult than true final exam questions.

• Understand and apply concepts of measurement:
• Estimate and calculate measurements using customary, metric and nonstandard units of measurement.
1. Estimate the areas of the four quadrilaterals on the web page http://www.mathsisfun.com/quadrilaterals.html using appropriate standard and metric units.
2. About how many pencil-lengths long is a piece of paper? How many pencil-lengths wide? What's the area of a sheet of paper in square pencil-lengths? If you measured your paper using a shorter pencil, would your paper be more or fewer pencil lengths long?
3. Estimate the volume of our classroom using appropriate standard and metric units.
• Use unit conversions and dimensional analysis to solve problems.
1. Estimate the volume of our classroom in gallons.
2. A cheetah can sprint at a speed of 100 feet per second. How fast is this in miles per hour?
3. An tanker is leaking oil at a rate of 30 liters per minute. What is the rate of oil loss in gallons per hour?
• Derive and use formulas for calculating lengths, perimeters, areas, volumes and surface areas of geometric objects.
1. What is the surface area of an ice cream cone?
2. What is the volume of an equilateral triangular pyramid? (There will not be a problem this difficult on the exam.)
• Understand how the characteristics (area, volume, etc.) of an object is affected by changes in its dimensions.
1. Suppose you double the height of a right circular cone. How does the volume of the cone change?
2. An equilateral triangular prism whose sides all have length 1 has volume equal to one fourth the square root of 3. An equilateral triangular prism with sides of length 2 has volume two times the square root of 3. What is the volume of an equilateral triangular prism with sides of length 4?
• Solve a variety of measurement problems (e.g. time, temperature, rates) in real world situations.
(See above.)
• Understand and apply concepts of geometry:
• Classify and anlayze polygons using attributes of sides and angles.
1. You're told that the side lengths of a triangle are 5, 6 and 9. Does this triangle exist? If not, why not? If so, is it a right, acute or obtuse triangle?
2. Use the equivalences indicated on the workshseet at http://secondary.rcsdk12.org/20172021895525977/lib/20172021895525977/Triangle_Congruence_Worksheet.pdf to decide whether the triangles show must be congruent, similar, or neither.
• Classify and analyze three-dimensional objects using attributes of faces, edges and vertices.
1. A polyhedron is constructed which has four equilateral triangles meeting at each vertex. Describe the polyhedron or draw a net for it.
2. How many edges does a square prism have?
3. How many faces does a pentagonal pyramid have?
4. How many vertices does a hexagonal prism have?
• Recognize and use geometric transformations -- translations, rotations, reflections, and dilations.
1. Draw two lines at an angle of 60 degrees to each other. Draw the letter J between them. Reflect the letter J over the line to the right of it, then reflect the mirror image you just created over the other line. Describe the transformation that takes the original J to the one you just drew.
2. Given a figure and a point, draw the result of rotating the figure 45 degrees about the point.
• Use the language of geometric transformations to describe symmetry, similarity and congruence.
1. List all the symmetries of the letter H.
2. Choose two congruent triangles shown on the worksheet at http://secondary.rcsdk12.org/20172021895525977/lib/20172021895525977/Triangle_Congruence_Worksheet.pdf. Describe the transformation that transforms one into the other.
3. The geometric operation dilation expands a figure about a point, as discussed at http://www.regentsprep.org/regents/math/geometry/GT3/Ldilate2.htm. Why were dilations not included in the list of transformations we discussed in class?
• Match three-dimensional figures and their two-dimensional representations -- e.g. nets, projections and perspective drawings.
1. Given a net of a cube with labels on its faces, identify which of several isometric drawings of the cube can be assembled from that net. There may be more than one correct answer to this question.
2. Given an isometric drawing of an object, identify which of several nets it might be assembled from.
• Recognize and apply connections between algebra and geometry (e.g. coordinate systems, area formulas, the Pythagorean theorem).
1. Compute the volume of a square pyramid whose triangular sides are equilateral.
2. If a park is 3 blocks wide and 4 blocks long, how many blocks long is a path that runs diagonally through the park?
• Understand and use descriptive statistics:
• Use measures of central tendency (mean, median, mode) and range to describe and interpret real world data.
1. The students in Mr. Davis' class have the following heights, in inches: 43, 52, 39, 50, 45, 44, 40, 51, 44, 39, 44, 52.
a) What is the average height of Mr. Davis' students?
b) What is the median height of Mr. Davis' students?
c) What is the mode of the heights of Mr. Davis' students?
d) Which of these three measures of central tendency best represent the heights in Mr. Davis' class? Why?
e) Draw a box and whisker plot illustrating the range of heights in Mr. Davis' class.
f) Are any of the heights in Mr. Davis' class outliers?
g) Find the standard deviation of the heights of the students in Mr. Davis' class.
• Select appropriate ways to present data in communicating statistical information (e.g. tables, graphs, line plots, Venn diagrams).
1. Marsha wants to draw a graph comparing the heights of students in Ms. White's class to the heights of students in Mr. Davis' class.
a) Marsha starts to draw a pie chart with each slice of pie labeled with a different height. Explain why this might not be the best way to compare student heights between classes.
b) How would you recommend Marsha present the data from the two classes? Give reasons for your answer.
• Analyze and interpret graphic and non-graphic data representations (e.g. frequency distributions, percentiles).
1. Consider the frequency distribution shown at http://mathworld.wolfram.com/FrequencyDistribution.html.
a) What percentage of the population falls in the interval from 90 to 100?
b) What percentage of the population falls in the interval from 0 to 50?
c) If this histogram reports data on tax rates for 973 individuals, out of those 973 people how many have a tax rate below 30%?
• Compare different data sets.
1. In Mrs. White's class, the students' heights (in inches) are: 35, 42, 44, 32, 43, 44, 38, 39, 40, 37.
a) Use an appropriate measure of central tendency to compare the heights of students in Mrs. White's and Mr. Davis' class.
b) Which class has a greater standard deviation in heights? How would that greater standard deviation affect staging for a group picture of each class?
c) What conclusions might you draw from comparing the student height data of the two classes?
• Understand and apply basic concepts of probability:
• Calculate probabilities of simple and compound events and of independent and dependent events.
1. Give an example of two independent events.
2. Give an example of two mutually exclusive events.
3. Calculate the probability of drawing an ace or a heart from a deck of 52 cards.
4. Calculate the probability of drawing an ace and then a heart from a deck of 52 cards if the ace is not replaced in the deck. (If this is too hard, calculate the probability of drawing an ace of spades and then a heart.)
5. Calculate the probability of drawing an ace and then a heart from a deck of 52 cards if the ace is replaced and the deck is reshuffled after drawing.
6. A hand of five cards contains only hearts. There are 13 hearts in a deck of cards. Calculate the probability that the hand contains the ace, king, queen, jack and ten of hearts.
7. Susan deals cards face up from a standard deck of cards. What is the probability that the first five cards she deals out are an ace, two, three, four and five, in that order?
• Recognize and apply the concept of conditional probability.
1. In Mrs. Schmidt's classroom, 7 female students prefer pizza and 5 female students prefer grilled cheese. 8 male students prefer pizza and 2 male students prefer grilled cheese.
a) What is the probability that a male student prefers grilled cheese to pizza?
b) What is the probability that a student who prefers grilled cheese is female?
c) What is the probability that a student selected at random prefers pizza?
• Recognize the difference between experimentally and theoretically determined probabilities in real-world situations.
1. In the example of Mrs. Schmidt's class above, were the probabilities you calculated thoretical or experimental?
2. The weather report declares that there is a 40% chance of rain. Is this more likely to be an experimental probability or a theoretical probability? Justify your answer.
3. Give an example of when you would calculate a theoretical probability.
4. Give an example of when you would calculate an experimental probability.
• Apply knowledge of combinations and permutations to the computation of probabilities.
(see above.)