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CURRICULUM SUMMARY – September to December 2016 SUBJECT: Mathematical Studies YEAR GROUP: IB2 TEACHER: Agata Piskorz Week Date Learning objectives Activities (in brief) 1 FINANCIAL MATHEMATICS Students will understand and use: currency conversion Reading currency – conversion tables. Using different ‘buy’ and ‘sale’ rates. Perform currency transactions involving commission. Using the Graphical Display Calculator (TVM Solver ) to find the future value of the investment; the present value; interest rate or number of compounding periods. Revision – solving problems at class and at home. Writing a test. Discussing results of the test. 2 3 5-9 Sep 12 -16 Sep 19-23 Sep compound interest – different compounding periods depreciation DESCRIPTIVE STATISTICS – revision discrete and continuous data, frequency tables and histograms for grouped data; mean, median mode from different type of data. quartiles, interquartile range; boxplots; outliers. cumulative frequency graphs. Percentiles. variance and standard deviation. Revision – solving problems at class and at home. IA- Submit focus of the Project (not necessarily the title yet) with a general outline/plan supported by some sources e.g. websites, textbooks (at least one A4 page) – deadline September 19 26-30 Sep LINEAR MODELS gradient of a line from its equation; gradient of a line from its graph. Gradient formula; equation of a straight line through two given points; 5 3-7 Oct scatter plot; correlation; Pearson’s correlation coefficient; line of best fit; the least square regression line; interpolation and extrapolation. 6 10-14 SETS AND PROBABILITY – revision 4 Calculating gradient of a line. Finding equation of a line. Using the gradient of a line in practical situations. Applications of linear models. Describing correlation. Using of the equation for prediction purposes. Mathematical and contextual interpretation of the regression line. Revision – solving problems at class and at home. Writing a test. Discussing results of the test. Solving numerical problems on two or three sets. Oct 7 17-21 Oct Venn diagrams to illustrate set operations; regions on a Venn diagram; the universal set; complement of a set; set operations with three sets; theoretical probability of an event; compound events; independent events; conditional probability PROBABILTY DISTRIBUTIONS Students will understand and use: discrete random variables and their probability distributions; expected value (mean), E(X ) for discrete data; applications of expectation, for example, games of chance. Shading regions in Venn diagrams – two or three sets. Solving real word problems – numbers in regions of Venn diagrams. Using tables of outcomes, grids, tree diagrams to represent a sample space and calculate probability. Calculating conditional probability with Venn diagrams and tree diagrams. Students’ homework. Revision – solving problems at class and at home. Writing a test. Discussing results of the test. Using tables of probability distributions Using the formula: E( X ) xP( X x) IA -Submit organized data (frequency tables, graphs , diagrams) with a short analysis - deadline October 17 8 9 24-28 Oct 31 Oct – 4 Nov 7 -11 Nov 10 14 – 18 Nov 11 21 – 25 Nov the normal curve; significance of the standard deviation. normal distribution. Using normal distribution to calculate probabilities in practical situations. Use of calculator to find normal probabilities; the reverse process. Revision – solving problems at class and at home. Writing a test. Discussing results of the test. Mid-Term Break STATISTICAL TESTS - the 2 test of independence Students will understand and use: independent variables; the null hypothesis; degrees of freedom, critical value; formal test for independence NUMBERS Students will understand and use: the exponential expression: a b , b Q; rules of indices; Analyzing contingency tables, finding the expected contingency table, finding the number of degrees of freedom. calculating 2 , reading the critical value, performing the formal test for independence.; revision – solving problems at class and at home; writing a test; discussing results of the test; Revising rules of indices and scientific notation. Using GDC (Graphic Display Calculator) for conversion between scientific 12 28 Nov – 2 Dec the index notation (scientific notation): a 10n , where 1 a 10 and a Z; very large and very small numbers in scientific, economic and other applications; awareness and use of scientific mode on the GDC; operations with numbers expressed in the form: a 10n , where 1 a 10 and a Z; decimals; decimal places; approximations; rounding off to a given number of decimal places or significant figures; the absolute errors; percentage errors; System International (SI); other basic units of measurements; conversion between different units. the relationship between the set of natural numbers; the set of integers; the set of rational numbers and the set of real numbers; sets of prime numbers, multiples and factors; and standard notation. Rounding and estimating numbers. Calculating errors. Estimating and accuracy –homework investigation. Converting between different units . Revision – solving problems at class and at home. Writing a test. Discussing results of the test. IA Submit the first draft, printed or in electronic format for teacher’s comments - deadline November 28 13 5 Dec – 9 Dec 14 12 Dec – 16 Dec GEOMETRY AND TRIGONOMETRY - revision Students will understand and use: trigonometric ratios in a right angled triangle; the area of a triangle; relationship between trigonometric ratios of the same angle. the sine rule; the cosine rule; Applications of trigonometric ratios - solving different types of geometrical and practical problems. Calculating areas of triangles – using different formulae. Using the Pythagorean identity and other relationships between trigonometric ratios. Solving problems with triangles that do not contain a right angle applications of sine and the cosine rules. Solving practical problems in navigation, surveying, engineering and geography that involve solving a triangle. Solving problems in 3D space Revision – solving problems at class and at home. Writing a test. Discussing results of the test.