MATH 115 Administrative Overview Chapter 1 Review

Transcription

1 MATH 115 Administrative Overview Chapter 1 Review Dr. Pete Goetz Lecture 0 Typeset by FoilTEX

2 Outline Professor s Contact Information Syllabus and Course Expectations Course Website WebAssign - online homework system

3 Professor s Contact Information Dr. Pete Goetz BSS 358 Office Hours: MWF 11:30am - 1:00 pm and by appointment pdg11@humboldt.edu (707)

4 Syllabus - Logistics Lectures on MWF 8AM in FH 118 Class size 140 people Lectures will be content dense! Come to class prepared! Discussions on Th (times and locations vary) Discussion size is 28 people Discussions will consist of supplements to the lecture as well as offer a chance to answer questions and clarify issues from homework and lecture. Weekly quizzes. Come to the discussions prepared!

5 Syllabus - Logistics continued Required Text: Precalculus: Functions and Graphs (11 ed.) by Swokowski and Cole Available HSU bookstore now E-book is OK WebAssign registration is also required Calculators Not required but strongly recommended Calculator usage will be limited on exams

6 Syllabus - Logistics continued Your course grade will be based on your scores on... Assignments Daily homework problems submitted with WebAssign Weekly quizzes Exams 3 midterm exams and 1 (cumulative) final exam See syllabus and/or timeline for exam dates

7 My expectations are high! Syllabus - Conduct Namely, I expect all students to... treat one another and myself with courtesy and respect take an active interest in this course stay informed about all assignments and deadlines seek outside assistance (if necessary) before it is too late assume the ultimate responsibility for learning this material and passing this class

8 Course Website Course Website: Syllabus Timeline Daily lectures Solutions to Quizzes and Exams Exam Review sheets

9 WebAssign WebAssign - on line homework system Class Key: humboldt

10 Questions? The wind and the waves are always on the side of the ablest navigators. Edward Gibbon in The History of the Decline and Fall of the Roman Empire.

11 Chapter 1 Review Intermediate algebra (HSU MATH 44) is the pre-requisite course for MATH 115 so that you have worked with most of the material contained in Chapter 1. For review and diagnosis purposes, we will begin by looking at some problems from Chapter 1. Again, I assume you are familiar and confident with the material in Chapter 1. Section 1.1: The Real Numbers Section 1.2: Exponents and Radicals Section 1.3: Algebraic Expressions Section 1.4: Equations Section 1.6: Inequalities

12 Section 1.1: The Real Numbers Suppose that a and b are real numbers with a > 0 and b < 0. What is the sign (positive or negative) of ab? a 2 b? ab 2? a(a b)? (negative) (negative) (positive) (positive) Simplify the expression 3 ( 2 4 ) (answer: 6)

13 Properties of Real Numbers Terminology Notation Comment + is commutative a + b = b + a order doesn t matter + is associative (a + b) + c = a + (b + c) grouping doesn t matter 0 is the identity a + 0 = a = 0 + a a is the inverse ( a) + a = 0 = a + ( a) Analogous properties hold for multiplication. See p. 4

14 Section 1.2: Exponents and Radicals Rules of Exponents a 0 = 1 a n = 1/a n a n a m = a n+m an a m = a n m (a n ) m = a nm a n b n = (ab) n a n/m = m a n (a/b) n = a n /b n Simplify 12a 4 b 2 3a 2 b 2 = 12a2 b 2 b 2 3a 4 = 4b4 a 2 Simplify (.008) 2/3 = ( ) 2/3 8 = 1000 ( ) 2 2 =

15 Section 1.3: Algebraic Expressions Factor completely: x 3 25x = x(x 2 25) = x(x 5)(x + 5) Factor completely: 7x x 8 = (7x 4)(x + 2) Simplify the expression r 2 r 12 r 3 + 3r 2 = (r 4)(r + 3) r 2 (r + 3) = r 4 r 2

16 Section 1.3: Algebraic Expressions Simplify the expressions: t t t t 3 18 t 2 9 (x + h) 2 3(x + h) (x 2 3x) h

17 Section 1.4: Equations Solve 2x 7 = 5 for x. (answer: x = 6) Solve r 2 r 12 = 0 for r. (answer: r = 4 or r = 3) What about quadratics that aren t so easy to factor? Solve 2x 2 6x + 3 = 0 for x.

18 The Quadratic Formula If a 0 and ax 2 + bx + c = 0, then x = b ± b 2 4ac. 2a Solve 2x 2 6x + 3 = 0 for x. x = 6 ± 36 4(2)(3) 4 = 6 ± 12 4 = 6 ± = 3 ± 3. 2

19 Section 1.4: Equations Solve the equation 2x(3 x) = 3. Solve the equation 3x = 7.

20 Section 1.4: Equations Solve the following equation by factoring. 2x x x 4 = 18 x 2 + 3x

21 Section 1.6: Inequalities Interval Notation a x b [a, b] closed interval a < x < b (a, b) open interval a x < b [a, b) half open interval a < x b (a, b] half open interval < x b (, b] half infinite closed interval a x < [a, ) half infinite closed interval < x < b (, b) half infinite open interval a < x < (a, ) half infinite open interval

22 Section 1.6: Inequalities Express the inequality x > 4 as an interval and sketch its graph. Express the inequality 3 x < 7 as an interval and sketch its graph.

23 Section 1.6: Inequalities Express the interval (, 3] as an inequality in the variable x. Express the interval ( 4, 7) as an inequality in the variable x.

24 Section 1.6: Inequalities Solve the inequality 4x 3 > 2x 11 and give your answer as an interval. Answer (, 4).

25 Section 1.6: Inequalities Solve the inequality 4 3x and give your answer as an interval. Answer ( 2/3, ).