Math 322 Final Exam

12. Tracy has two blue disks plus one green disk that equals 45. He has one blue disk and two green disks that
equals 38,

[2pts] Draw a picture using circles as disks to represent the problem.

Solution :

[2pts] Write algebraic equations to represent the statements in the problem.

Solution:

[2pts] What does one blue disk equal?

Solution:

[2pts] What does one green disk equal?

Solution:

Check:

13. [10pts] Solve the Quadratic Equation 6x² −11x − 8 = 0 by using the Quadratic Formula.
Write the Quadratic Formula in the box .

Solution:

14. [8pts] Write the six trig ratios of x in the right triangle below.

Solutions:

15. [6pts] Solve for x in the following triangle. State an equation using trig function that would be used to
solve for the variable in each of the following right triangle.

16.[10pts] The scores for the first exam in Mrs. Mandrell’s algebra class of ten students were 98, 67, 72, 88, 71,
65, 99, 77, 83, and 80. The mean for this class is 80. Calculate the variance and standard deviation for this
exam. Make a table and show your work.

Find the z-score for the student with 88 and how is this student’s performance?

This student is average and is doing okay.

17. Consider the circle sketched below.

a) [1pt] What point is the center of the
circle?

Solution: (−1, 2)

b) [1pt] Find the radius of the circle.

Solution: r = 3

c) [5pts] Write the equation of the
circle in standard form.

Solution: (x + 1)² + (y − 2)² = 9

18. [8pts] State the properties of the following examples. Write the entire name of the
property with no abbreviations.

19. [12pts] Sketch a graph for the following equations. Label the vertex and the y -intercept for a parabola, and
five points for a circle. Show work. Do not use a table when graphing a parabola or circle. Use the
transformation properties to find the vertex of the parabola and the center of the circle.

20. [5pts] Graph the line that passes through the point (-2, 1) and has a slope of . Label at least two points .

21. [5pts] Find the slope of the line in the following graph, using the stairstep method .

22. [5pts] Construct the first 5 rows of the Pascal’s Triangle.

a) [4pts] Find one sequence (pattern) found in the Triangle. State the type of sequence you found.

Various Answers

b) [3pts] Expand (x + y)⁶ using Pascal’s Triangle.

Solution:

c) [3pts] What is the sum of the 100^th row of the Pascal’s Triangle?

Solution: