Sample Final Exam MATH 3032


1. Find x in each of the following cases. (6 points each)

    a)

    b)

    c)

2. Find the area of the shaded region a semicircle taken from a rectangle. (8 points)

3. Consider the three dimensional figure below.

    a) Find the volume (6 points)

    b) Find the total surface area. (6 points)

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

'

6. Consider the following figure and calculate the measures of the requested angles. The two horizontal lines are parallel. (2 points each)

          a. Angle 1           d. Angle 4

          b. Angle 2           e. Angle 5

          c. Angle 3

7. Consider the convex polygon shown:

a. The measures of the two missing interior angles are? (6 points)

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

8. If 24 of 28 students passed the test what percentage passed? (4 points)

9. 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) The slope of a line perpendicular to a line with slope 3 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? ___________

10. 102 is 5% of what? (4 points)

11. Using a compass and straight edge only construct the following.

    a) A line segment equal in length to (y - x)/3. (6 pts. )

                                      

    b)The bisector of angle M. (4 pts. )

                                      

12. What fraction problem is represented by the following model? Write the problem and the correct solution. (5 pts.)

            

13. Shade a portion of the grid below to represent 3/5. (4 pts.)

            

14. Display, using unit squares, that 2/3 = 6/9. (4 pts.)

15. Given the following values:

    M = 53 x 74 x 112 x 132

    N  = 56 x 72 x 115

what are each of the following numbers? You do not need to multiply them out. (4 points each)

    a) The G C F of M and N.

    b) The L C M of M and N.

16. What are the two numbers before and after the following? (3 points)

    _____, _____, 400twelve, _____, _____

17. Convert 13421five to base ten. (6 points)

18. Convert 1987 to base eleven. (6 points)

19. Compute the following multiplication problem by the lattice method in base five. (6 points)

3 2 4 x 4 2five

20. What is the digit in the ones place of 350? (5 points)

21. Compute the following subtraction problem in base eight. (6 points)

       4  1  6  2eight

    - 1  2  4  6eight

22. For each of the below figures show the result of applying the given transformation. (5 pts. each)

    a)   Shift right 2 & up 3

    b)   Shrink about O by 3/4

    c)   Rotation of 90° about O.

    d)   Reflection in the indicated line.

23. 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 pts. 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

24. Using the spinner below, find the following probabilities. (3 points each)

The probability of getting in one spin:

    a) Black

    b) Red or Green

    c) White

25. 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)

26. There are eight parents willing to help with the soccer team. In how many ways can you pick 2 coaches and a scorekeeper? ( 6 pts.)

27. Below there are 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 (3 pts.)

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

        A     16, 4, 5, 14, 8, 4, 5

        B     3, 4, 9, 8, 1

        C     2, 3, 8, 2, 5

28. Find a set of data whare the mean and the mode are the same and the median is greater than the mode. (6 pts.)

29. When 100 students took a test the mean score was 92.3. Two students took a makeup. The mean of their two scores was 77. What is the combined mean of the two sets of 102 scores? (6 pts.)

30. Evaluate each of the following. (3 pts. each)

    a) 10C3

    b) 7P4

31. Below is a picture of the standard normal distribution. If the results of a test have such a distribution with a mean of 100 and a standard deviation of 10, use this picture to answer the following questions. (3 pts. each)

    a) What portion of the test takers scored above 130?

    b) What portion of the test takers scored between 90 and 120?

32. Which of the following arrow diagrams are functions?

Explain each answer. (4 points each)

    a)

    b)

    c)

33. In each case below, determine the pattern and continue for the next three terms. (3 points each)

    a) 1, 8, 27, 64, ...

    b) 2, 2, 4, 6, 10, 16, ,,,

34. Find the slope of the line perpendicular to 3y -x = 9

35. Graph the line 6y -3x = 8. Label 3 points on the line. (6 points)

36. Given A=(3, 4) and B=(-2, -1)

    a) Find the length of AB. (4 points)

    b) Find the equation of the line through A & B. (6 points)


This page updated by Frank Matthews Nov. 24, 2003