Math 115: Precalculus Algebra Section 4 Time: TR 14:30 16:0 Place: L305 Instructor: J. Jang Office: B019g Phone: 33 5786 Email: jjang@langara.bc.ca Office hours: TBA Prerequisite: C- in Principles of Math 1 (within the last 3 years), permission of the Department (based on performance on the Diagnostic Test), or Math 1150 with a C- or better. Transfer Credits: Check www.bctransferguide.ca Text: 1. College Algebra (5 th edition) by Stewart, Watson, and Redlin. Student Solutions Manual by Banks Grading Scheme: 1. Quizzes: 10%. Two term tests: 5% each (October 1, and November 18) 3. Final: 40% Important notes: 1. No make-up quizzes or exams will be given. In case you miss a quiz or test due to illness and such, the average of your scores on the rest of the quizzes or the tests (including the final exam) will replace the missing one.. You must write at least one term test and the final exam in order to pass the course. If you do not write the final exam as scheduled by the registrar s office, you will not be able to finish the course. In case of a schedule conflict, contact the registrar s office. 3. By the end of the course, you are expected not only to have mastered all mechanical aspects of precalculus material but also to have acquired a certain level of mathematical maturity for successful completion of the first year calculus. First of all, you should feel absolutely comfortable about basic algebraic skills such as factoring, and solving equations and inequalities. But more importantly, after thorough treatment of the concept of function and properties of various functions including polynomials, rational functions, and exponential and logarithmic functions, you should be ready for more abstract ideas such as instantaneous rate of change of a function.
e Math 115 Text: College Algebra by Stewart, Redlin, and Watson, 5 th edition Section Topics Exercises Hours P. The real line 1-39 0.5 P.3 Sets and intervals, Absolute value 1-61 0.5 P.4 Integer exponents, Laws of exponents 1-71, 97 P.5 Radicals, Rational exponents, Rationalizing the 1-87 denominator P.6 Special formulas 1-89 0 P.7 Factoring 1-97 0 P.8 Simplifying rational expressions and compound 1-107 0 fractions, Rationalizing the denominator or the numerator 1.1 Solving equations 1-95 0 1. Applications 1-65 0 1.3 Solving quadratic equations, Zero product property, 1-101 Completing the square, The discriminant, Applications 1.4 Geometric interpretation, Definition, Arithmetic 1-79 operations on complex numbers 1.5 Polynomial equations, Radical equations, Equations of 1-73 0 quadratic type, Applications 1.6 Linear and non linear inequalities 1-79 1 1.7 Absolute value equations and inequalities 1-55 1.1 The distance formula, The midpoint formula 1-59. Graphing by plotting points, Intercepts, Equation of a 1-91 0.5 circle, Symmetries.4 The slope of a line, Equations of lines, Vertical and 1-75 horizontal lines, Parallel and perpendicular lines, Rate of change.5 Direct, Inverse, and Joint variations 1-47 0.5 3.1 Definition, Evaluating functions, The domain of a function 3. Graphing functions, Piecewise defined functions, The vertical line test 1-83 1-7, 33-45, 53-67, 75-77 3.3 Increasing and decreasing functions, Local maximum 1-7, 19-1 and minimum 1, 31-33 3.4 Average rate of change and its applications 1-9 3.5 Vertical and horizontal shifting, Reflections on the axes, 1-57, 65-1 Even and odd functions 77 3.6 Algebra of functions, Composition of functions 1-15, 1-65
3.7 One to one functions, The horizontal line test, The 1-57, 69- inverse of a function, Graphing the inverse of a function 73 Focus on Optimization 1-9 1 Modelling 4.1 Graphing quadratic functions, Max and Min of quadratic 1-47, 49- functions 53, 63-77 4. Definition of polynomial, Graphs of polynomials, End 1-39, 47- behaviour and the leading term, Using zeros to graph polynomials, Intermediate value theorem, Shape of a graph near zeros 49 4.3 Long division, Synthetic division, The remainder and 1-67 factor theorems 4.4 Rational zeros theorem 1-61 4.5 Fundamental theorem of algebra, Complete factorization 1-67 0.5 theorem 4.6 Horizontal and vertical asymptotes, Graphing rational 1-63 3 functions 5.1 Definition, Graphs of exponential functions, The natural 1-43 1 exponential function, Continuously compounded interest 5. Definition, Properties, Graphs of logarithmic functions, 1-67 1 Common and natural logarithms and their properties 5.3 Laws of logarithms 1-61 1 5.4 Solving exponential and logarithmic equations 1-57 1 5.5 Exponential growth, Radioactive decay 1-1 1 8.1 Equations and graphs of parabolas 1-1 1 8. Equations and graphs of ellipses 1-1 1 8.3 Equations and graphs of hyperbolas 1-19 1 8.4 Equations and graphs of shifted conics 1-15, 3-1 33 Trigono -metry Similarity, Triangular trigonometry, Applications Handout 3 * The topics should have been covered prior to 115; do not spend any time on them unless you can and must.
e Math 115 Definitions to know from Stewart (5 th edition): Section Definitions Page P.3 x 16 P.4 & P.5 n 0, 7 n 0 n m a, a, a, a, n-th root, principal n-th root & 8 1.3 Discriminant of a quadratic equation 91. Intercepts 148. Circle 149. Symmetry about the x-axis, y-axis, and origin 15.4 Slope of a line 167 3.1 Function, domain, range 05 3.3 Increasing/ decreasing function 8 3.3 Local maximum and minimum 30 3.4 Average rate of change 37 3.5 Even/ odd function 49 3.6 f g 57 3.7 One to one function 65 3.7 Inverse function 67 4. Polynomial 300 4.6 Rational function 343 4.6 Vertical and horizontal asymptotes 345 5.1 The value e 375 5. log x 384 a 8.1 Parabola 55 8. Ellipse 563 8.3 Hyperbola 57 Trigonometry Radian, the six trigonometric ratios of an acute angle Handout
Theorems and Proofs to know from Stewart (5 th edition): Section Proofs Page P.4 Laws of exponents 1 P.5 Properties of n th roots 7 1.3 Quadratic formula 89.1 Distance formula, midpoint formula 139,141. Equation of a circle 149.4 Equation of line: point-slope formula 169 3.4 Applications of average rate of change 38 &39 4.3 Remainder and factor theorems 318 &319 4.5 Fundamental theorem of algebra (no proof required), complete factorization theorem 335 5.1 nt r 378 rt P 1 Pe as n n 5.3 Laws of logarithms, change of base formula 394, 397 8.1 Equation of a parabola with focus ( 0, p ) and directrix y p 553 Trigonometry 1 Handout s r, A r, sin cos 1, 1 tan sec