IB Precalculus
Welcome to the IB Precalculus page!
IB Precalculus is designed to provide the first year of a two-year program of a realistic mathematics course for students who already possess knowledge of basic mathematical concepts. Through the development of mathematical techniques, students will focus on important mathematical concepts including, but not limited to, the study of algebra, functions and graphing, trigonometry and circular functions, matrices, and vectors.
IB Statistics and Calculus is designed to provide the second year of a program for students pursuing further mathematical, scientific, and technical studies. The curriculum includes a study of probability and statistics and a comprehensive study of calculus. The skills needed to cope with the mathematical demands of a college or university program are sharpened and emphasis is placed on the application of real life situations.
During the course of this study, students are encouraged to appreciate the cultural and historical perspective of mathematics and its global impact. Students are encouraged not only to utilize their mathematical skills to provide reasonable solutions to given situations, but to appreciate the methods used to formulate the solution and the mathematics responsible for the development of the concept. Students should expand logical, critical, and creative thinking skills while demonstrating their patience and persistence in problem solving whether manually or through use of technological tools. Solutions should be presented clearly and concisely using appropriate notation and terminology.
The international dimension and the universality as a means of communication make it appropriate to encourage students to discuss and learn the difference in notation, the cultural context of mathematical discoveries, and the attitudes of different societies toward mathematics.
Expected assessment will cover topics presented in each course, a portfolio assignment in each of the two courses, as well as the IB externel assessment at the conclusion of the second year.
Topic 1: Algebra
Students will solve problems including those that are application based involving sequences with recurrence relations, determine characteristics and sums of arithmetic and geometric sequences and series both finite and infinite where applicable including the use of sigma notation, apply the laws of exponents and logarithms to simplify expressions and to solve equations, expand binomials raised to a whole number power using the Binomial Theorem, and analyze the graphs of logarithmic and exponential functions.
Topic 2: Functions and Equations
Students will produce and analyze graphs of rational, quadratic, logarithmic, exponential, trigonometric, composite, inverse, reciprocal, and piecewise defined functions by determining the domain and range, identify vertical, horizontal, or oblique asymptotes, and classify the function as increasing or decreasing, continuous or discontinuous, and noting the type of discontinuity if one exists. They will also study variations of functions through translations, stretches, and reflections, and incorporate the use of a graphing display calculator to graph a variety of functions and to analyze solutions of functions.
Topic 3: Circular Functions and Trigonometry
Students will define the six trigonometric functions using ratios of the sides of a right triangle, coordinates on the unit circle, and the reciprocal of other functions; verify simple trigonometric identities using Pythagorean, reciprocal, and double-angle identities; solve trigonometric equations and inequalities with degree or radian measure using sum, difference, and half- and double-angle identities; solve mathematical problems involving real-world applications using Law of Sines, Law of Cosines, and area of triangles, circles, and sectors; and analyze the graphs of trigonometric functions determining the amplitude, period, phase shift, domain, and range.
Topic 4: Matrices
Students will solve matrices and systems of linear equations or inequalities in two or three variables using matrix operations both manually and with a graphic display calculator.
Topic 5: Vectors
Students will define the vocabulary and correct notation of vectors and vector components including, but not limited to, magnitude, scalar, position, and unit vectors; perform the vector operations of addition, scalar multiplication, and absolute value; determine coincidence, parallelism, collinearity, or perpendicularity of vectors as well as the angles between vectors or lines; and use vectors to model real-life problems and mathematical situations.
Topic 6: Statistics and Probability
Students will calculate and compare descriptions and summary statistics for sets of data represented on a graph, stem or leaf chart, box and whiskers graph, histogram, linear or quadratic equation of best fit for a scatterplot, and a frequency distribution; study the characteristics of the measures of central tendency, measures of dispersion, and measures of position; using a data set, create a normal distribution curve noting the standard deviation from the mean and the properties of the distribution; calculate probabilities of mutually exclusive, independent, dependent, and combined events using permutations, combinations, and laws of probability, including situations involving conditional probabilities; and study the concept of discrete random variables, their probability distributions, the expected value (mean) of discrete data, and its application.
Topic 7: Calculus
Students will study the basic concepts of limit and convergence finding limits of functions at specific values and at infinity numerically, algebraically, and graphically; apply limits in problems involving convergence; define and interpret the derivative of a function as a limit, as a gradient function, and as a rate of change; apply the rules of derivatives to analyze a variety of types of functions, to determine maximum and minimum values, points of inflection and concavity, and to identify increasing and decreasing intervals of the curve. Students will distinguish antidifferentiation as the indefinite integral with a general solution and for a particular solution; further define the indefinite integral as the definite integral with the Fundamnental Theorem of Calculus; apply the definite integral to problems of area under or between curves and volumes of revolution; apply the methods of differentiation and antidifferentiation to solve problems dealing with optimization, kinematics, and rates of change.
Homework Assignments :September 7- September 11, 2009
Monday- LABOR DAY
Tuesday-pg. 200-201 #1-8 (odd letters beginning with a)
Wednesday-pg. 203 #1,2
Thursday-pg. 204 #1-3
Friday-pg. 206 #1,2
THIS IS THE FIFTH WEEK OF THE FIRST SIX WEEKS!!
IB Junior CAS Project: Honduran Christmas Boxes- bring in items by September 23rd.
WEB CHALLENGE PROBLEM - You are on your way to visit your Grandma, who lives at the end of the valley. It's her birthday, and you want to give her the cakes you've made. Between your house and her house, you have to cross 7 bridges, and as it goes in the land of make believe, there is a troll under every bridge! Each troll, quite rightly, insists that you pay a troll toll. Before you can cross their bridge, you have to give them half of the cakes you are carrying, but as they are kind trolls, they each give you back a single cake.
How many cakes do you have to leave home with to make sure that you arrive at Grandma's with exactly 2 cakes?
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