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Math233 Final Exam Review

Due 5/19/09 before the final. The following questions are similar to some of those you will
encounter on the final. Complete and show your work on a seperate sheet of paper.

REMARK 1. This review sheet is a guideline and a starting point, it is expected that you also
review all past exams and exam reviews.

1. Chapter 1 - Order of operations , rules of exponents, simplifying exponents, scientific notation.
See also review for exam 1.

(a) Evaluate the following:

when x = 9, y = -3.

(b) Simplify and write the answer without a negative exponent :

2. Chapter 2 - Solve linear equations , problem solving (word problems), linear inequalities, abso-
lute values.

(a) Solve the linear equations or inequalities:

3. Chapter 3 - Understand functions and graphing, graphing lines, slope, slope-intercept form,
point- slope form , graphing linear inequalities.

(a) Know how to use the vertical line test. (See problem 1 from exam 2 review).
(b) For the functions , evaluate
(c) Equations of lines :
i. Find the x- and y-intercept of 2x - 3y = 12, graph the line.
ii. Find the slope and y-intercept of 5x + 15y = 30, graph the line.
iii. Find an equation of the line that passes through the points (1, 3) and (2, -1).
(d) Linear Inequalities : Graph 3x - 4y≤ 12

4. Chapter 4 - Solving systems of linear equations in two variables, matrix notation, Cramer's

(a) Solve systems of equations:

(b) Solve the system of equations using Cramer' s rule :

5. Chapter 5 - Polynomials : addition, subtraction, multiplication, division, factoring.
(a) Multiply and simplify completely:

(b) Divide using long division:

(c) Factor :

6. Chapter 6 - Domains of rational functions, multiplication, division, addition and subtraction
of rational functions, finding LCD, solving rational equations.

(a) Multiply or divide, simplify completely:

(b) Find the LCD and add or subtract, simplify completely:

(c) Solve, remember to check your solutions:

7. Chapter 7 - Rational exponents, simplifying radicals, add, subtract, multiply, and divide rad-
icals, solve radical equations.

(a) Simplify:

(b) Solve:

8. Chapter 8 - Completing the square , quadratic formula, quadratic form (substitution), graph
quadratic functions.

(a) Solve by completing the square: x2 + 10x = 11
(b) Solve using the quadratic formula : (2a + 3)(3a - 1) = 2
(c) Graph, label the vertex , y-intercept, and x-intercepts if any: f(x) = -x2 - 2x + 24

9. Chapter 9 - Composition and inverse of functions, graph exponential functions , definition and
properties of logarithm , common logarithms, solving exponential equations.

(a) If f(x) = 3x + 3 and g(x) = 2x + 5, find (f o g)(x)
(b) If find
(c) Graph
(d) Write in logarithmic form
(e) Write in exponential form.
(f) Solve the equation for x.
(g) Expand using the properties of logarithms:
(h) Write as a single logarithm:
(i) Solve

10. Word Problems - Know how to set up and solve the following application problems: Section
2.3 # 29; Section 2.4 # 1, 11; Section 4.3 # 5; Section 8.5 # 73, 99

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