MTH 214 Week 5 Final Exam

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MTH 214 Week 5 Final Exam
MTH 214 Week 5 Final Exam
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 MTH 214

Mathematics for Elementary Educators II

The Latest Version A+ Study Guide 

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MTH 214 Week 5 Final Exam

Prerequisite Assignment: MyMathLab® Study Plan for Final Examination

Complete the MyMathLab® Final Exam.

  1. Click the Final Exam tab.
  2. Click External Content Launch to access MyMathLab®.
  3. Complete the Final Exam in MyMathLab® after earning at least 80% of the Mastery Points in the MyMathLab® Study Plan for Final Examination.

 

MTH 214 Week 5 Final Exam

Classify each of the following as true or false.

a. A trapezoid is a parallelogram.

b. No trapezoid is a square.

a. Is the statement “Upper A trapezoid is a parallelogram” true or false? Choose the correct answer below.

True

False

b. Is the statement “No trapezoid is a square” true or false? Choose the correct answer below.

True

False

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On dot paper, use the pentomino shown on the right, to make a tessellation of the plane. There may be more than one correct tessellation.

Using what you learned by creating your own tesselation, determine which tessellations below correctly use only the given pentomino.

Choose the true statement below.

A.

Upper A is the only correct tessellation of the plane.

B.

Upper C is the only correct tessellation of the plane.

C.

Upper B and Upper C are both correct tessellations of the plane.

D.

Upper A and Upper B are both correct tessellations of the plane.

One student says, “My sister’s high school geometry book talked about equal angles. Why don’t we use the term “equal angles” instead of “congruent angles?” How do you reply?

Choose the correct answer below.

A.

Since an angle is a set of points determined by two rays with the same endpoint, to say that two angles are equal implies that the two sets of points determining the angles are equal. The only way this can happen is if the two angles are actually the same angle.

B.

There is no difference between “equal angles” and “congruent angles.” Either wording can be used.

C.

“Equal angles” require the addition of two angles while “congruent angles” do not.

D.

Congruent angles only make sense when talking about a polygon. Open angles cannot be congruent.

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A student observes the spinner to the right and claims that the color red has the highest probability of appearing, since there are two red areas on the spinner. What is your reply?

Choose the correct answer below.

A.

The student is right since the number of regions in one color determines the probability of that color appearing.

B.

The student is wrong since the area of the red regions is equal to the area of the green region, both of the probabilities of appearing red and green are the highest.

C.

The student is wrong since the area of the red regions is smaller than the area of the green region, so the color red does not have the highest probability of appearing.

D.

The student is wrong since the area of the blue region is the largest, the color blue has the highest probability of appearing.

How does this sixth grade geometry common core type question meet the goals behind the common core standards?

Choose the correct answer below.

A.

It assesses students’ ability to classify three-dimensional shapes.

B.

It assesses students’ ability to transform shapes.

C.

It assesses students’ ability to find relationships between different three-dimensional shapes.

D.

It assesses students’ understanding of the properties of cubes, as well as their ability to find multiple ways to create a cube.

Two dice are tossed 60 times and the sums of the numbers are recorded in the table. Draw a bar graph for the data.

Frequency of Sums on Dice

Sums on Dice

2

3

4

5

6

7

8

9

10

11

12

Frequency

1

3

5

7

10

11

8

6

6

2

1

Select the correct graph below.

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75 men and 55 women are enrolled in calculus. There are 20 business majors, 50 biology majors, 50 computer science majors, and 10 mathematics majors. No person has a double major. If a single calculus student is chosen, find the following probabilities.

Find the probability that the student is female.

P(female)equals

(Simplify your answer. Type a fraction.)

Find the probability that the student is a biology major.

P(biology)equals

(Simplify your answer. Type a fraction.)

Find the probability that the student is not a business major.

P(not business)equals

(Simplify your answer. Type a fraction.)

Find the probability that the student is a biology major or a business major.

P(biology union business)equals

(Simplify your answer. Type a fraction.)

Draw a reflecting line to show that the name AYA can be its own image under a reflection.

Choose the correct answer below.

Find the volume of the each of the following. Complete parts (a) through (e) below.

a. Find the volume of the right rectangular prism to the right.

The volume is

cm.

cm squared .

cm cubed .

(Simplify your answer.)

A right rectangular prism has a length of 4 centimeters, a width of 2 centimeters, and a height of 6 centimeters.

2 cm

4 cm

6 cm

b. Find the volume of the right square pyramid to the right.

The volume is

cm cubed .

cm squared .

cm.

(Type an integer or a fraction.)

A right square pyramid has side lengths of 7 centimeters, and a height of 7 centimeters.

7 cm

7 cm

7 cm

c. Find the volume of the right circular cylinder to the right.

The volume is

cm squared .

cm cubed .

cm.

(Type an exact answer in terms of pi.)

A right circular cylinder has a radius of 9 centimeters, and a height of 7 centimeters.

9 cm

7 cm

d. Find the volume of the shape to the right.

The volume is

ft cubed .

ft.

ft squared .

(Simplify your answer.)

A right triangular prism is on top of a right rectangular prism such that they share a rectagular base. The rectangular prism has a length of 35 feet, a width of 30 feet, and a height of 13 feet. The triangular prism has a height of 9 feet and a slant height of 18 feet.

18 ft

9 ft

30 ft

35 ft

13 ft

e. Find the volume of the shape to the right.

The volume is

ft.

ft squared .

ft cubed .

(Simplify your answer.)

A right rectangular prism has a length of 59 feet, a width of 46 feet, and a height of 24 feet. A right trapezoidal prism is constructed on top of the rectangular prism such that they share a rectangular base. The height of the trapezoid is 6 feet and the top horizontal base of the trapezoid is labeled 10 feet. The length of the trapezoidal prism is 59 feet. A triangular prism is constructed on top of the trapezoidal prism such that they share a rectangular base. The height of the triangular prism is 5 feet. The length of the triangular prism is 59 feet.

46 ft

24 ft

59 ft

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The figure below is a rectangular box in which EFGH and ABCD are rectangles and BF overbar is perpendicular to planes EFGH and ABCD.

Use the figure to complete parts a through d.

A rectangular box has rectangular bases A B C D and E F G H. The following edges are perpendicular to the bases: A E; B F; C G; D H. Rectangle B D H F is inside the rectangular box.

a. What is the intersection of ModifyingAbove BF with left right arrow and plane ABC?

b. Which pair of planes are perpendicular?

c. Which lines are perpendicular to plane EFH?

d. What is the measure of the dihedral angle Upper B dash EF dash Upper H?

a. What is the intersection of ModifyingAbove BF with left right arrow and plane ABC?

A.

{Upper G}

B.

empty set

C.

{Upper B}

D.

{Upper D}

b. Which pair of planes are perpendicular?

A.

ABE and CDG

B.

ADE and BCF

C.

ABE and ADE

D.

ABC and EFG

c. Which lines are perpendicular to plane EFH? Select all that apply.

A.

ModifyingAbove AE with left right arrow

B.

ModifyingAbove GH with left right arrow

C.

ModifyingAbove AB with left right arrow

D.

ModifyingAbove CG with left right arrow

d. What is the measure of the dihedral angle Upper B dash EF dash Upper H?

A triangle has two sides of length 10 cm and 14 cm. What can you say about the length of the third side?

Choose the correct answer below.

A.

The third side must be greater than 24 cm and less than 140 cm.

B.

The third side must be less than 24 cm and greater than 4 cm.

C.

The third side must be less than 140 cm.

D.

The third side must be greater than 4 cm.

Gloria drew two examples of figures in which one is the image of the other under reflection in the y-axis as well as under a half-turn with center A. In the second example, the image of the two upper circles under reflection in line j are the two lower circles. However, the lower circles are also the image of the upper circles under a half-turn about N. Therefore, Gloria claims that the image of every figure under reflection can also be obtained by rotation. How do you respond?

Choose the correct answer below.

A.

Gloria is incorrect. The figures drawn have additional reflection symmetries. Figures that don’t have such lines of symmetry will not have a half-turn symmetry.

B.

Gloria is incorrect. In the first figure, the trapezoid on the right cannot be transformed into the trapezoid on the left by a rotation.

C.

These figures show that Gloria is correct.

D.

If the circles are changed to squares, the resulting figure would refute Gloria’s claim.

Explore the Transformations eManipulative and then solve the problem.

A green crescent opens to the right.

A red crescent opens upward.

Describe the transformation from the green picture to the red picture.

Reflection

Glide-Reflection

Identity

Rotation

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A family plans to have 4 children. Assume that the probability of a child being a girl is one half

, and births are independent events.

a. What is the probability of the event of the third child being a boy?

b. What are the odds in favor of the family having all girls?

a. The probability of the third child being a boy is

.

(Simplify your answer.)

b. The odds in favor of the family having all girls are

:

.

(Simplify your answer.)

Merle says that there is no reason to practice drawing graphs because spreadsheets can be used to draw any images desired. How do you respond?

Choose the correct answer below.

A.

Spreadsheets cannot create every graph we want, so we need to understand graph creation for cases where the software fails.

B.

It is true that spreadsheets can create any graph we want, but we need to understand graph creation to utilize the software correctly.

C.

It is true that spreadsheets can create any graph we want, so there is no need to learn how to create graphs.

Find the area of the following figures.

a.

b.

A quadrilateral is made up of a smaller quadrilateral and an adjacent right triangle. The base of the quadrilateral is made up of one leg of the triangle and one side of the smaller quadrilateral. The length of the base is 20 centimeters. The remaining sides of the smaller quadrilateral are as follows starting clockwise from the side along the base of the main quadrilateral: 2 centimeters, 18 centimeters, 10 centimeters. The sides measuring 18 centimeters and 10 centimeters meet at a right angle. The side measuring 2 centimeters is the second leg of the triangle.

18 cm

20 cm

10 cm

2 cm

A triangle has a base of length 24 meters. The base of the triangle forms an obtuse angle with a side of length 39 meters. The triangle has a height of 36 meters.

36 m

39 m

24 m

a. The area is

cmsquared. (Simplify your answer.)

b. The area is

msquared. (Simplify your answer.)

How does this seventh grade common core type question challenge a student’s understanding of triangles more so than a traditional triangle question?

Choose the correct answer below.

A.

Students must know the definition of the different types of triangles.

B.

Students must be able to classify triangles.

C.

Students must be able to use mathematical tools to measure angles of multiple triangles.

D.

Students must find all of the different ways to create a triangle based on the criteria.

A student claims that all squares are congruent to each other. How do you respond?

Choose the correct answer below.

A.

The student is correct. A square has four sides of the same length and four angles of the same measure, so all squares are congruent.

B.

The student is correct. All squares have four 90degrees angles, so their angles are congruent, meaning that all squares must be congruent.

C.

The student is incorrect because not all squares have congruent angles.

D.

The student is incorrect. Although all squares have four congruent 90degrees angles, any congruent squares must also have the same side lengths, which is not true for all squares.

This fourth grade common core type question requires students to have knowledge in multiple mathematics areas. What mathematical areas do student need to understand in order to correctly answer this question?

Choose the correct answer below.

A.

Perimeter, properties of squares, and rectangles

B.

Perimeter, quadrilaterals and their properties, difference

C.

Area

D.

How to find the perimeter and area of quadrilaterals

The spinner shown on the right is spun. (Assume that the size of each sector is the same.) Find each probability.

a) P(factor of 56) b) P(multiple of 8)

a) P(factor of 56)equals

(Type an integer or a simplified fraction.)

b) P(multiple of 8)equals

(Type an integer or a simplified fraction.)

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Explain why only three types of regular polygons tessellate the plane.

Choose the correct answer below.

A.

In order for a regular polygon to tessellate the plane, its interior angle measure must be a divisor of 360degrees. Only three regular polygons have interior angle measures that divide 360degrees . Those polygons are the equilateral triangle, square, and regular hexagon.

B.

In order for a regular polygon to tessellate the plane, its angle bisectors must intersect at 90degrees angles.

C.

In order for a regular polygon to tessellate the plane, its exterior angle measure must be a divisor of 360degrees. Only three regular polygons have exterior angles that divide 360degrees. Those polygons are the equilateral triangle, regular hexagon, and regular nonagon.

D.

In order for a regular polygon to tessellate the plane, its number of sides must divide 9. Therefore only the equilateral triangle, regular hexagon and regular nonagon can tessellate the plane.

To determine students’ preferred mode of transportation, which sample is more likely to be random?

a. Ask students all over the country.

b. Ask students that live in your city.

Choose the correct answer below.

A.

Sample b is more likely to be random because the chosen sampling location is random as well as the people being sampled.

B.

Sample a is more likely to be random because fewer people are being sampled, so the data will appear more random.

C.

Sample b is more likely to be random because more people are being sampled, so the data will appear more random.

D.

Sample a is more likely to be random because the chosen sampling location is random as well as the people being sampled.

How many gallons of paint are needed to paint the walls of a rectangular prism-shaped room that is 17 ft by 10 ft and 8 ft high if 1 gallon of paint covers 40 sq ft? Assume there are no doors or windows.

The amount of paint needed is

gallons.

(Type a whole number.)

Consider the translation left parenthesis x comma y right parenthesis right arrow left parenthesis x plus 3 comma y minus 1 right parenthesis. For each figure, find the coordinates of the images of the labeled points.

a. For the circle with center at B, type the images of the 3 labeled points.

A(minus2,2)right arrowUpper A prime

(Type an ordered pair.)

B(minus2,1)right arrowUpper B prime

(Type an ordered pair.)

C(minus2,0)right arrowUpper C prime

(Type an ordered pair.)

b. For quadrilateral DEFG, type the image of each vertex.

D(negative 4,minus1)right arrowUpper D prime

(Type an ordered pair.)

E(negative 4,3)right arrowUpper E prime

(Type an ordered pair.)

F(2,2)right arrowUpper F prime

(Type an ordered pair.)

G(1,minus1)right arrowUpper G prime

(Type an ordered pair.)

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Find the measure of the angle marked x in each of the following triangles.

(a)                             (b)                   (c)                                    (d)

In triangle a, two of the interior angles measure 63 degrees and x. The exterior angle at the third vertex measures 136 degrees. In triangle b, one of the interior angles is marked with a small square. The remaining angles measure x and 61 degrees. In triangle c, two of the interior angles measure 58 degrees and x. The exterior angle at the third vertex measures 2 x. In triangle d, the top angle is marked with a small square and the angle at the bottom left measures x. A line segment extends from the top vertex to the bottom side and is perpendicular to the bottom side, dividing the triangle into two smaller triangles. In the triangle on the right, the angle at the top left measures 67 degrees.

63 degrees

136 degrees

x

61 degrees

x

58 degrees

2 x

x

x

67 degrees

(a) Find the measure of x in figure a.

xequals

degrees

(b) Find the measure of x in figure b.

xequals

degrees

(c) Find the measure of x in figure c.

xequals

degrees

(d) Find the measure of x in figure d.

xequals

degrees

A spotlight is mounted on the eaves of a house 12 feet above the ground. A flower bed runs between the house and the sidewalk, so the closest the ladder can be placed to the house is 5 feet. How long a ladder is needed so that an electrician can reach the place where the light is mounted?

The length of the ladder needs to be

ft.

Assuming that the segment ____ is 1 cm in length, estimate the length of the following segment.

________________

Express the answer in each of the following units.

a. Centimeters

b. Millimeters

a. Estimate the length and express the answer in centimeters. Choose the correct answer below.

A.

40 cm

B.

0.3 cm

C.

4 cm

D.

12 cm

b. Now express the answer in millimeters. Choose the correct answer below.

A.

1.2 mm

B.

120 mm

C.

40 mm

D.

400 mm

E.

0.4 mm

F.

300 mm

G.

3 mm

H.

4 mm

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A class of eighth graders undertook an ambitious project to compile the most dominant color of uniforms for all 491 middle school sports teams in their state this year. The circle graph to the right shows the results. Approximately how many teams are represented in each sector?

There are approximately

teams represented by the sector labelled black, approximately

teams represented by the sector labelled navy blue, approximately

teams represented by the sector labelled white, approximately

teams represented by the sector labelled gray, approximately

teams represented by the sector labelled maroon, and approximately

teams represented by the sector labelled other.

(Simplify your answers. Round to the nearest whole number.)