Sample Final Exam MATH 3032


Bring the following to the final exam.

*      Calculator (check batteries)

*      Tracing paper

*      Straight edge (or ruler)

*      Protractor

*      Three 3x5 cards (both sides)


1. Find x in each of the following cases. ( 8 points each )

    a)

    b)

    c)

2. Consider the three dimensional figure below.

    a) Find the volume ( 6 points )

    b) Find the total surface area. ( 8 points )

3. Evaluate the following: ( 4 points each )

          a. 9! - 5!

          b.     22!    

               19! 3!

4. Consider this figure.

                                      

    a) This is a ______________. ( 2 points )

    b) Find the height. ( 5 points )

    c) Find the volume. ( 5 points )

5. Tell the number of faces, edges, and verticies for the pictured 3-D shape. ( 4 points )

                             

                             F                              V                              E

This is a __________________

6. Measure each of the following angles. ( 3 points each )

7. Consider the following figure and calculate the measures of the requested angles. The two horizontal lines are parallel. ( 3 points each )

The drawing is not to scale.

          a. Angle 1           d. Angle 4

          b. Angle 2           e. Angle 5

          c. Angle 3

8. Consider the convex polygon shown:

a. The measures of the two missing interior angles are? ( 8 points )

b. The measure of Q, the exterior angle at point E? ( 2 points )

9. All of the students in a grade take a test and their mean score is 82.4 overall. If the total points for the class is 8652 then how many students are there in the grade? ( 8 points )

10. Fill in each blank below: ( 4 points each )

    a) The standard deviation is _________ of the variance.

    b) If point A=(-2, 7) is moved down 5 and right 1 its new coordinates are________.

    c) If 3/5 of the sample is red what is the proportion of red to non red? _________

    d) If the odds are 8 to 5 then the probability is ________ .

    e) If the side of a square is 3x then the diagonal is _________ .

    f) The most common value of a set of data is? __________

    g) If a ball is contained in a cube of side 4 then the largest volume it can have is _________ .

    h) If the total surface area of a cube is 12 then what is its volume? ___________

    i) The volume of a cylinder is _______ times the volume of the enclosed cone .

    j) In the metric system the basic unit of length is the ___________.

11. Fill in each blank below to show a correct conversion: ( 4 points each )

    a) 4524 m are _________ km.

    b) 3 pecks are________pints.

    c) 432 sq. in. _________ sq. ft.

    d) 1/2 m3 is ________ cm3.

12. Jeff scored 72 on his math test. The averages were: median = 68, mode = 70, mean = 60. The variance was 36 and the standard deviation was 6. What was his z-score? ( 8 points )

13. In each of the following cases determine if the information is sufficient to prove that triangle ABC is congruent to triangle XYZ and, if they are congruent, what congruence property applies. ( 4 points each )

    a) These angles are congruent: A & X, B & Y, C & Z

    b) These angles and lines are congruent: A & X; C & Z; AB & XY

    c) These angles and lines are congruent: A & X; AB & XY; BC & YZ

14. Using the spinner below, find the following probabilities. ( 4 points each )

The probability of getting in one spin:

    a) Black

    b) Red or Green

    c) White

15. For each of the below figures relocate the figure according to the transformation indicated. (6 pts. each)

    a)   Shift right 2 & up 3.

    b)   Shrink about the point O by 3/4.

    c)   Rotation clockwise of 90° about the point O.

    d)   Reflection in the indicated line.

16. Consider a tournament with the best 2 out of 3 winning where the probability that Chicago wins a given game is 2/3.

    a) Draw the probability tree diagram for this tournament, and label the probabilities for each branch. ( 6 points )

    b) Determine the probability of Chicago winning at least two games. ( 3 points )

    c) Determine the probability that the tournament ends after two games. ( 3 points )

17. Below there are three problems. Each has three sets of data and a description which fits one or more of those sets of data. Choose the set(s) that fit each description ( 5 points each )

  I.    The data has a mean of 8 and a median of 5.

        i       16, 4, 5, 14, 8, 4, 5

        ii      3, 4, 9, 8, 1

        iii     2, 3, 8, 2, 5

  II.   The data has a mode of 8 and a median of 5.

        i       1 , 8 , 6 , 3 , 8 , 3 , 9 , 2 , 5 , 8 , 6

        ii      2 , 3 , 8 , 5 , 8 , 4 , 1 , 3 , 9 , 6 , 8

        iii     3 , 6 , 9 , 4 , 3 , 8 , 8 , 5 , 3

  III.  The data has a mean of 8 and a mode of 5.

        i       2 , 9 , 17 , 5 , 12 , 4 , 8 , 19 , 6 , 5 , 13

        ii      3 , 8 , 19 , 4 , 5 , 20 , 2 , 4 , 7

        iii     8 , 18 , 4 , 5 , 15 , 9 , 5 , 3 , 5

18. For a regular six sided die the results of a number of rolls are in the rable below. ( 4 points each )

    a) According to the table, how many times were the dice rolled?

    b) According to the table, what is the probability of rolling a 2 on the die in this experiment?

    c) What is the probability of rolling a 2 on a fair die (or the theoretical probability)?

    d) Do you think that the die is a fair die? Explain ______

19. Find the perimiter and area of the below figure. ( 6 points each )

    a) Perimiter _________

    b) Area __________

20. Sketch the following six shapes on the isodot paper. ( 5 points each )

    a) A kite that is not a parallelogram.

             

    b) An isosceles trapezoid.

             

    c) A rhombus that is not a rectangle.

             

    d) An obtuse scalene triangle.

             

    e) A non-convex hexagon.

             

    f) A parallelogram that is not a rectangle.

             


This page updated by Frank Matthews April 30, 2009