Math 1303 Final Exam Review Chapters 0 – 5
1. Factor each of the following completely:
a. Page 893 (43 – 46)
b. Page 900 (83 – 88)
2. Rationalize the numerator or the denominator as indicated.
a. Rationalize the numerator: Page 899 (61 – 66) b. Rationalize the denominator: Page 899 (55 – 60)
3. Write the equation of the line indicated: (See your notes, quiz, and test for this section).
a. Write the equation of the perpendicular bisector of the segment whose endpoints are (3, -10) and
(5, 11).
b. Write the equation of the line tangent to circle with center (6, -1) at the point
(-2, 4).
4. Find the domain for each function shown below. Write the domain in interval notation.
Page 55 (55 – 60)
5. Suppose f(x) is given. Describe each of the indicated transformations. Page 66 (21 – 28)
a. y = f(x) + 8 b. y = f(x – 2) – 2 c. y = f(-x) d. y = d. y = -f(x + 3)
6. Piecewise Functions: Page 67 (43 – 48) Sketch the graph of x + 2 if x < -1
f(x) = x3 if -1 < x < 1
-x + 3 if x > 1
7. Maximize/Minimize: Page 82 (61 B,C; 62 B,C)
A cable television firm presently serves 5000 households and charges $20 per month. A marketing
survey indicates that each decrease of $1 in the monthly charge will result in 500 new customers. Let
R(x) denote the total monthly revenue when the monthly charge is x dollars. Find the value of x that
results in the maximum monthly revenue.
8. Break-Even Analysis: Page 82 (63 B; 64 B)
The marketing research department for a company that manufactures and sells “notebook” computers
established the following Revenue and Cost Functions where x is thousands of computers and both
C(x) and R(x) are in thousands of dollars. Both functions have domain 1 < x < 25. Find the break-even
points.
R(x) = 1625x – 45x2 C(x) = 4500 + 500x
9. Cost, Revenue, Profit functions: (See notes)
A manufacturer has monthly fixed costs of $40,000 and a production cost of $8 for each item produced.
The product sells for $12 each. Find a function for each of the following:
a. Total Cost function b. Total Revenue function
c. Profit function d. Number of units needed to break-even.
10. Difference Quotient: Page 55 (77 – 82 part c only).
Given f(x) = x – 1 and g(x) = x2 + 3x
a. Find b. Find
11. Use a sign chart to help you determine the solution for each inequality: See notes.
a. 3x2 + 2x – 8 < 0 b.
12. Page 93 (43-46)
a. Find all asymptotes, holes, intercepts, and graph: y =
For exercises 13, 14, and 15, solve each indicated equation. If you get a decimal answer, round to 3 decimal places.
13. Exponential equations: Page 143 (29 - 38)
a. 101-x = 6x b. e3-2x = 4
14. Properties of Logarithms: Page 115 (43 – 48)
a. 2 log x = log 2 + log (3x – 4) b. log5 x + log5 (x + 1) = log5 20
15. Change from log form to exponent form and solve: Page 115 (49, 50)
a. ln (x – 4) = 3 b. log x + log (x – 3) = 1
16. Using exponential functions.
The temperature of a cup of coffee t minutes after it is poured is given by T = 70 + 100e-0.0446t
where T is measured in degrees Fahrenheit.
a. What was the temperature of the coffee when it was poured?
b. when will the coffee be cool enough to drink (120° F)?
17. Compound Interest and Continuous Compound Interest: Know the formulas! Page 143 (43 – 46)
How long will it take an investment of $1,000 to double if the interest is 8.5% per year,
a. compounded quarterly b. compounded continuously
Blakely Investment Company owns and office building in the commercial district of a city. As a
result of continued success of an urban renewal program, local business is enjoying a mushroom
growth. The current market value of the property is $300,000. If the expected rate of inflation for the
present market price is 10% per year, find how long it will take for the property to be worth $500,000.
18. Solve the system. You may use whatever method you prefer. Page 179 (5 – 26)
4x – 3y = 10
9x + 4y = 1
19. Set up a system of equations and use whichever method you prefer to solve the problem.
Page 180 57, 58, 61A, 62A, 69, 70)
a. Find the equilibrium price and quantity, if the weekly demand and supply functions for
Sportsman 5 x 7 tents are given by:
Demand: p = −0.1x2 – x + 40 where p is the price measured in dollars, and
Supply: p = 0.1x2 + 2x + 20 x is the quantity measured in hundreds of tents.
b. Michael has $25,00 invested in two accounts. The interest earned on the accounts is 8% and 9%
per year. He receives a total of $2,110 per year from these accounts. How much is invested in each?
20. Systems of Inequalities: Page 263 (13 – 22)
Solve the system graphically. Indicate whether the solution region is bounded or unbounded. Then
Find the coordinates of all corner points.
2x + y < 10
x + y < 7
x + 2y < 12
x > 0
y > 0
21. Linear Programming: Page 275 (31A, 32A, 33A)
A company makes 2 models of machines, model X and model Y. Each model X costs $100 to make
and each model Y costs $150. The profits are: $30 for each X and $40 for each Y. The total number
of machines must be less than 2500 per month. The company can spend no more than $330,000 on
costs. How many of each should be produced to maximize the profit?
22. Find the indicated term of the sequence:
a. Arithmetic: Page 920 (9 - 14) b. Geometric: Page 920 (15 - 28)
Find the 30th term of the sequence Find the 12th term of the sequence
1, 5, 9, 13, . . . -3, 6, -12, 24, . . .
23. Write each series in sigma notation. Page 913 (51 – 54 (part A only); 55 – 58)
a. Write in sigma notation: 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100
24. Find the common difference or the common ratio. Page 920 (1, 2)
a. Find the common difference: b. Find the common ratio:
The first term of an arithmetic sequence is -9 The first term of a geometric sequence is 2
and the tenth term is 15. Find the common and the fourth term is . Find the
difference. common ratio.
25. Sum of an Infinite Geometric Sequence: Page 920 (31, 32)
a. Find the sum, if it exists: b. Find the sum, if it exists:
+ . . . . . .