Download Name:_______________________________________________ Date:________ Period:_______ Practice Final #4

Name:_______________________________________________
Practice Final #4
Date:________ Period:_______
Practice Final #4
Part I: Multiple Choice. On the final all of these questions will be multiple choice questions. You will have
to answer 25 out of 30 questions (omit 5).
1. Which of the following functions is NOT one-to-one?
(1) {(1,2), (2,1), (8,7)} (2) {(0,0), (1,1), (2,2)} (3) {(1,4), (2,3), (8,8)}
(4) {(9,1), (6,1), (0,3)}
2. Express (tan x)(csc x) as a single trigonometric function.
3. What are the values of
in the interval
that satisfy the equation:
4. If f(x) = x2 + 3 and g(x) = 2x + 5, evaluate (f ○ g)(-1)?
5. Draw a graph (using a number line) that represents the solution set of |3x + 6| < 24.
6. The expression (2 – 5i)2 is equivalent to:
7. In ΔQRS, m<R = 39○, s = 16, and q = 18. What is the area of ΔQRS to the nearest square inch?
8. Which graph does not represent a function?
(1)
(2)
9. What is the third term in the expansion (x – 4)4?
10. Factor completely: x4 – 625.
(3)
(4)
?
11. Simplify the expression, there should be no negative exponents:
12. Write an equation with integer coefficients where the sum of the roots equals
and the product
of the roots equals -8.
13. Write the equation of the graph of the graph that’s given:
14. Evaluate:
15. Nine students in Ms. Anderle’s class were asked how many hours a week they spend doing their
homework. Below is the data collect
6, 2, 6, 8, 5, 2, 3, 5, 6
Determine the standard deviation for this data to the nearest tenth.
16. Simplify:
17. If
, what is
?
18. Simplify:
19. Evaluate: log264
20. Sketch the graph of the inverse of the function y = log6x.
21. What is the solution of the equation log6(2x) = 2?
22. What is the axis of symmetry of the equation y = 3x2 – 24x + 10?
23. What is the domain of the function
?
24. A circle has a radius of 12 inches. In inches, what is the length of the arc intercepted by a central
angle of 6 radians?
25. Write a formula to determine the total number of different 11 letter arrangements that can be
formed using the letters in the word MISSISSIPPI?
26. The solution set of |3x – 18| = 33 is:
27. Express x3 – 10x2 + 21x in factored form
28. If side a = 18 and angle A = 62o, find side b to two decimal places when angle B = 36o.
29. Given the equation sin(2x + 8) = cos (3x – 23) solve for the value of x.
30. The solution set of
is:
Part II: Answer all 5 questions from this section. Show all work, including formulas.
31. What change will be made to the graph of y = x2, if the equation is change to y = (x+6)2 – 10?
32. Using the formula V = Pert find the value of V for an investment of $3900 at an annual rate of 7.4%,
compounded continuously after 8 years.
33. Express
with a rational denominator, in simplest radical form.
34. Find the center and radius of the circle with the equation: (x – 12)2 + (y + 8)2 = 49.
35. Solve the fractional equation for x:
Part III: Answer 3 out of the 4 questions in this section. All work necessary to the solution must be written
in the space provided and on the graph when necessary.
36. Answer both parts a & b.
a. Solve x2 + 6x + 15 = 0 expressing the result in simplest a + bi form.
b. Solve x3 + 3x2 – 5x – 15 = 0 by factoring by grouping.
37. The table below shows the amount of time someone spends studying and their grades on the math
test.
Time (hrs)
Test
Grade
0
50
1
60
2
68
3
75
4
89
5
85
6
92
7
92
8
100
a. Find the linear equation of best fit for the given data. Round decimals to three places.
b. Find the correlation coefficient “r” correct to 4 decimal places for part a.
c. Find the quadratic equation of best fit for the given data. Round to 3 decimals.
d.
Find the correlation coefficient “r” correct to 4 decimal places for part c.
e. Use the values of “r” to determine which equation, linear from part a or quadratic from
part c, is a better fit for the given data.
f.
Use the equation of best fit found in part e to estimate the grade on a test a student will
receive to the nearest tenth after 10 hours of studying.
38. Answer both parts a and b.
a. Two forces have magnitudes of 100 pounds and 160 pounds respectively, and act upon a body at an
angle of
between them. Find, to the nearest pound, the resultant force of these two forces.
b. In ∆XYZ, side x = 9.2, side y = 6.3, and the measure of angle X = 54°. Find, to the nearest degree, the
measure of angle Y.
39. Answer both parts a and b.
a) On the same set of axes, sketch and label the graphs of the equations
in the interval
b) Using the graphs drawn in part a, determine the number of values in the interval
that satisfy the equation
.
39. Continued: