PRE-CALCULUS
FINAL EXAM REVIEW 2015
EXAM DATE:
BRING: Textbook
Pencils
Scientific Calculator
TEST FORMAT: Part I: 4 Graphs [32 pts total]
Part II: 25 Open-Ended [98 pts]
FORMULAS to Remember:
This Review Packet is due on: Per. 6: Friday 6/5 and Per. 8: Thursday 6/4
It is worth 87 POINTS towards your second semester grade. All work must be shown to receive credit.
As a member of the Northern Highlands school community, I abide by the Academic Integrity Policy as outlines in the Student Handbook. By signing below I pledge that I understand the penalties as described in the handbook, and that I in no way shared knowledge with any of my classmates during this assignment.
Signature______Date______
PRE-CALCULUS
EXAM REVIEW
This practice exam is designed to give you a sense of what to expect on the open ended portion of the final. Study the questions carefully, and make sure that you know how to do each of them!
PART I: GRAPHING [3 points each for take home grade, 12 points total]
1. Sketch the graph of the following: f(x) = x3 – 3x2 + 2x. Be sure that your graph shows the
end behavior and includes all real zeros.
X / Y2. Sketch the graph of y = - 2 sin x + 3 on the axes below and show two full periods.
State the amplitude, period, horizontal and vertical shift, etc.
3. Sketch the graph of the following rational function.
a) State any vertical asymptotes
b) State any horizontal asymptotes
c) Identify the x and y intercepts
d) Complete table of values
x / ye) Sketch graph.
4. Sketch the graph of the exponential and logarithmic functions following the format below.
i) Provide a table of values for the base function and sketch its graph with a dashed line
ii) State the transformation that occur to the base function to get the given function
iii) Include the final sketch of the transformed function on the same set of axes
a)
b)
Part II: OPEN-ENDED [75 points]
1. Solve the following using a number line & sign test: [2]
Simplify the following. [2 each]
2. 3.
4.
5. Given the polynomial with roots and ,
find the remaining roots using synthetic division. [2]
6. Solve the inequality 4 + 2. Write the final solution set using inequality
Notation [2]
7. Evaluate the function for . [2]
8. Let and
Calculate the following and state the domains for each. [2 each]
a. b. c.
9. Find the inverse of h(x) = 4x + 7. [2]
10. Based on the original function y = f(x), identify the transformations that should occur so that
y = - f (x – 2) + 5 [2]
11.
Find each of the following for the piecewise-defined function above: [1 each]
f(-5) f(8)
12. Solve log3(x – 2) + log3(x) = 1. [2]
13. Solve 32x = 70. [2]
14. Solve: Round to the nearest hundredth. [2]
15. Write as a single logarithm: log M – 3 log N [2]
16. The current population of Little Pond, New York, is 20,000. The population is decreasing, as represented by the formula , where P = population, t = time, in years, and A = initial population. What will the population be 3 years from now? Round your answer to the nearest hundred people. To the nearest tenth of a year, how many years will it take for the population to reach half the present population? [2]
17. If tan x = and sinx >0, find the values of the other five trigonometric
functions. [2]
18. State the exact value for the following: [1 each]
a) sec b) sin 135° c) cot(-120◦)
19. Solve the triangle ABC, if a = 8, b = 5, and angle C is 60 degrees. [2]
20. Solve for q, such that .
Round your answer to the nearest tenth, if necessary. [2 each]
a) b)
21. Solve for x, such that .
Round to the nearest hundredth, when necessary.
Otherwise, express answers in terms of . [2 each]
a) b)
c) -2 cos x = d) tan2x = tan x
22. Simplify the following to a single trig term: [2]
a) b)
23. Prove the following identities: [2]
a) b)
24. Write a sine and cosine equation for the given function below: [2]
THIS PAGE DOES NOT COUNT FOR TAKE HOME ASSESSMENT!!!!
25. In an arithmetic sequence, t2 = 10 and t4 = 36, find t25.
26. Give an explicit formula for the arithmetic sequence: 7, 19, 31, 43, 55 . . .
27. Using the sequence in #29, find the value of n if tn = 367
28. Find t9 for the geometric sequence in which t2 = 15 and t5 = 405. Give an exact answer, not a decimal approximation.
29. Give the first six terms of the sequence described by the recursive formula
t1 = 6
t2 = 8
tn = -2tn-1 + 3tn-2