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Port Moresby International School P.O. Box 276, Boroko, Papua New Guinea Phone +675 325 3166, Fax +675 325 4439 Owned and operated by the International Education Agency. Unit & Assessment Semester Outline for Students & Parents Grades 11 – 12. 2015 Year Curriculum Subject Title/s Course Name Unit Name Course Code 12 Semester 1 Grade ACT/IB Mathematics Mathematical Methods/ Mathematics SL Further Calculus and Statistics 1297 Unit Code Assessment Tasks Week Due Topic(s) 7 Statistics 15 Statistics Investigation 16 Calculus 18 Summative Assessment Unit Value 1.0 12979 Type of Task Test Portfolio Test Examination Weighting 15% 25% 25% 35% Learning outcomes against which the students will be reported Can calculate the probability of independent and dependent events and describe the features of a probability distribution Can apply the binomial distribution to find probabilities and use the normal distribution to model data sets of continuous random variables Can differentiate exponential, logarithmic and trigonometric functions and apply differential calculus to solve problems Can find indefinite and definite integrals, use integral calculus to find areas and volumes Can use integration to solve problems. Assessment Criteria This course should enable students to: describe a data set in terms of its summary statistics calculate the probability of independent and dependent events describe the features of a probability distribution apply the binomial distribution to find probabilities use the normal distribution to model data sets of continuous random variables investigate models of growth and decay differentiate exponential, logarithmic and trigonometric functions apply dfferential calculus to solve problems find indefinite and definite integrals use integral calculus to find areas and volumes use integration to solve problems. Regulations governing Late Submission of Work, Non-Submission of Work, Attendance, Cheating/Plagiarism, Grade Descriptors, Moderation Procedures, Method of unit score calculation, meshing procedures, Course information, Procedures for calculating course scores & Rights of Appeal may be found in the Grade 11-12 Curriculum Handbooks, or from the POMIS website; www.pmis.iea.ac.pg Summary of Content Weeks Content Outline Statistics.Concepts of population, sample, random sample and 1-2 frequency distribution of discret and continuous data. Presentation of data: frequency tables and diagrams, box and whisker plots. Grouped data mid-interval values, interval width, upper and lower interval boundaries, frequency histograms. Mean, median, mode, quartiles, percentiles. Range, interquartile 3-4 range, variance, standard deviation (both of population and sample). Measures of both spread and central tendency Linear correlation of bi-variate data, including Pearson's PMCC. Curriculum Links IB 5.1 ACT This is a NARC accredited course 5-6 IB 5.3, 5.5 ACT All references are on NARC document 7-8 Cumulative frequency and CF graphs. Use these to find median, quartiles and percentiles. Probability. Concepts of trial, outcome, equally likely outcomes, sample space and event. Complementary events A and A', P(A) + P(A') = 1. Combined events P(A or B) = P(A) + P(B) - P(A and B). Mutually exclusive and independent events. Conditional probability P(A|B).Use of Venn diagrams. Concept of discrete random variables (drv), expected value, mode, median, variance and sd of these. IB 5.2, 5.4 ACT It forms 2 0.5 combined units IB 5.6, 5.7 9-10 Binomial distribution. IB 5.8 Expected value and standard deviation. Application of the binomial distribution to find the probability of events (both pdf and cdf). 11-12 Normal distribution. Properties, standard normal distribution, normal distribution as an approximation to the binomial distribution. Standardisation of normal variables. IB 5.9 13-14 Calculus. Derivative of sin x, cos x, tan x, e^x and ln x. Use of chain, product and quotient rules. Local maximum and minimum problems, using first and second derivatives. Indefinite integration as anti-differentiation. IB 6.2, 6.4 15-16 Anti differentiation with boundary condition. Definite integrals. Areas between curves. Volumes of revolution (about x axis only.) IB 6.4, 6.5 17-18 Kinematic problems involving s, v, a. IB 6.6 19-20 Review of semester material Port Moresby International School P.O. Box 276, Boroko, Papua New Guinea Phone +675 325 3166, Fax +675 325 4439 Owned and operated by the International Education Agency.