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Year 12 2 CD 2015 Semester 1 Week Unit Topic/syllabus entry Resources A.J.Sadler Term 1 1-2 2CMAT 3.1 3.1.1 3.1.4 Quantify chance use Venn diagrams to represent sample spaces for two events and to illustrate set concepts (subset, intersection, union, complement) use two-way tables to represent sample spaces for two events use Venn diagrams and two-way tables to calculate simple probabilities for compound events (event A or B, event A and B, event A given event B, complement of A) use fractions, decimals and percentages to describe probability and move freely between them 3.1.5 use set and probability notation n(U), n(A), n(A') or n( A ), n(A B), n(A B), n(A|B) and P(A), P(A) , P(A B), … 3.1.2 3.1.3 3 2CMAT 3.2 3.2.1 3.2.2 4-5 5 2CMAT 2CMAT 6-7 2CMAT 8-9 2CMAT 2.2 2.2.1 2.2.2 2.2.3 2.2.4 Interpret chance use probabilities to predict proportions and number of outcomes that are likely to satisfy provided criteria in n trials use chance terminology when describing events (‘probability of’, ‘complement of’). Networks interpret information represented in network diagrams (basic networks only, project networks not included) develop systematic methods to determine the shortest path between two vertices of a network determine minimal spanning trees for networks using network diagrams and Prim’s algorithm determine the maximal flow for networks with one source and one sink. 1.1 Estimation and calculation 1.1.1 use calculators and written methods efficiently 1.1.2 round numbers to a given number of significant figures 1.1.3 round, truncate and decide on appropriate accuracy as part of calculation and estimation 1.1.4 recognise the effects of errors due to truncating and rounding 1.1.5 convert numbers to and from scientific notation. 2.1 2.1.1 2.1.2 1.2.1 Coordinate geometry determine the gradient and equations of parallel and perpendicular lines apply distance and gradient relations to solve problems in the Cartesian plane. sketch quadratic functions in the following forms: y a( x b )( x c ) y a( x b )2 c Chapter 1 Preliminary Chapter 2 EPW 1 Preliminary Chapter 3 TEST 1 (chapter 1-3) Preliminary Chapter 4 Chapter 5 Chapter 6 TEST 2 Chapter (4-6) y ax 2 bx c , where, a, b and c are integers 1.2.2 1.2.3 1.2.4 1.2.6 Week Unit identify families of quadratic functions from their equations identify features of parabolas: – intercepts– lines of symmetry – – turning points – – concavity. interpret parabolas: – relationships between variables – turning points and optimisation. use function notation. Topic/syllabus entry Resources A.J.Sadler Term 2 1 2CMAT 1.3 Equivalence, equations and inequalities 1.3.1 without a calculator, factorise differences of two squares such as a 2 b2 , a 2 x 2 b 2 and readily-factorised quadratic expressions of the form x2 bx c 1.3.2 solve quadratic equations: – algebraically, if in factored form – graphically. 2 3 2CMAT 2CMAT 1.4 1.4.1 1.4.2 1.4.3 1.4.4 1.4.5 1.4.6 3.4 3.4.1 3.4.2 3.4.3 3.4.4 Finance calculate compound interest recursively with technology calculate repayments and amount owing for loans interpret and compare loans with simple and compound interest make decisions about loans calculate inflation and depreciation. interpret financial information including tax tables, commercial advertisements, and credit card rates, charges and credit limits. Represent data construct frequency histograms for ungrouped and grouped data fx x calculate mean using x and x notation, and median and mode for ungrouped frequency f n data calculate weighted mean, mean for grouped data, and modal and median classes describe spread between data displayed in frequency tables and graphs using terms such as gaps, clusters, Preliminary Chapter 7 Chapter 8 EPW 2 Chapter 9 more dense/less dense regions, outliers calculate range for ungrouped and grouped data calculate relative frequency and proportions of data in fractional, decimal and percentage forms and use them to describe spread 3.4.7 plot time-series and bivariate data, fit trend lines by eye and calculate their equations. 3.5.1 identify independent and dependent variables for experimental and time-series data 3.5.2 predict using interpolation and extrapolation and trend line graphs and equations, recognising the risks of extrapolation 3.5.3 explain why predicted and actual results are likely to differ. 3.4.5 3.4.6 4 2CMAT Revision and Exams 5-6 Chapter 10 TEST 3 (Chapter 7-9) EXAM Semester 2 7 2DMAT 8 2DMAT 1.1 1.1.1 3.2 3.2.1 3.2.2 3.2.3 3.2.4 1. 9-10 2DMAT Estimation and calculation use index laws to multiply and divide numbers with integer powers. Quantify chance use long-run relative frequency to estimate probabilities use lists, tables and tree diagrams to determine sample spaces for one-, two- and three-stage events use sample spaces to calculate simple probabilities and probabilities for compound events use the relationship P(A) + P(A΄) = 1 to calculate probabilities for complementary events use the facts that probabilities sum to 1 and range from 0 to 1 to check probabilities. Functions and graphs 1.2.1 sketch graphs of: y bx , b 0 1.2 Chapter 1 Chapter 2 Preliminary EPW3 y x n , for n = 2, 3, -1 1.2.2 recognise functions of the forms y b x , b 0 and y x n for n = 2, 3, -1 from tables and graphs 1.2.3 describe the effects of varying a, b and c on the graph of y af ( x b ) c where f ( x ) x2 , Chapter 3 f ( x ) x3 or f ( x ) k x (Vary up to two parameters in any one example.) 11 2DMAT 1.2.4 1.2.5 distinguish linear, quadratic, cubic, exponential and reciprocal functions from equations and graphs sketch the cubic functions: y a( x b )( x c )( x d ) y a( x b )( x c )2 Preliminary Chapter 3 TEST 4 (chapter 1-3) y a( x b )3 1.2.6 use technology to graph y ax3 bx2 cx d Term 3 1 2DMAT 1.4 Patterns 1.4.1 link arithmetic sequences to linear functions, and geometric sequences to exponential functions 1.4.2 determine recursive rules for terms of arithmetic, geometric and Fibonacci sequences and Tn1 Tn 3 , T1 4 test generalisations by systematically checking cases and searching for counter-examples investigate real-world applications of arithmetic, geometric and Fibonacci sequences. write the rules with recursive 1.4.3 1.4.4 2 2DMAT 1.3 1.3.1 1.3.2 1.3.3 1.3.4 3 2DMAT 4 2DMAT 3.5 3.5.1 3.5.2 3.6 3.6.1 3.6.2 3.6.3 3.6.4 3.6.5 3.6.6 5 2DMAT 6 2DMAT Chapter 4 notation such as Equivalence, equations and inequalities rearrange and simplify algebraic expressions into forms useful for computation estimate the solutions for ab x c using substitution, where a, b and c are constants solve quadratic, cubic and exponential equations graphically solve simultaneous equations graphically. Represent data produce tables and graphs and summary statistics to support analysis determine the standard deviation, n, for grouped and ungrouped data using the inbuilt facility on a calculator. Interpret data discern viability of range and standard deviation for ranking datasets in order of spread interpret spread summaries in terms of their mathematical definitions compare datasets using mean and standard deviation, and noting features of tabulated or graphed data use words that acknowledge uncertainty when comparing data sets such as ‘scores for … tend to be more spread than scores for …’ infer results for populations from samples, recognising possible chance variation between them report on collected data to include commenting on external factors i.e. hidden variables that might have affected data and recognising possible chance variation in sample. 3.1 Conduct chance experiments 3.1.1 plan and conduct simulations using technology-based random number generators. 3.3 Interpret chance 3.3.1 predict the results for repetition of simulations with different numbers of trials 3.3.2 recognise that a first-stage result in a two-stage experiment may or may not affect a second stage result Chapter 5 EPW 4 Preliminary Chapter 6 Chapter 6 contd. Test 5 (Chapter 4-6) Chapter 7 EPW 5 Chapter 8 3.3.3 7 2DMAT estimate population size using the capture-recapture technique. 2.1 2.1.1 Measurement use sine, cosine and tangent ratios to determine sides and angles of right triangles, degree measure only 2.1.2 use the formula area ΔABC = 1 absin C 2 2.1.3 use sine and cosine rules to determine sides and angles of acute contexts only) 8 2DMAT 3.5 3.5.4 3.5.5 3.5.6 8-9 TEST 6 (Chapter 7-9) triangles (two-dimensional Interpret data read information from frequency tables, nested and layered tables, frequency graphs and time-series graphs and scatterplots discern the suitability of mean, median and mode for indicating central location calculate numbers of data in categories from relative frequencies and proportions Mock exams Preliminary ( Pythag) Chapter 9 Preliminary Assessment outline: Unit 2C MAT/2DMAT ASSESSMENT WEIGHTINGS TIME T1 W 5 RESPONSE 27% T1W 9 T2 W 4 T2 W 6 UNIT 2C TEST 1 Chapter 1 – 3 2 C TEST 2 Chapter 4 – 6 2 C TEST 3 Chapter 7 – 10 2 C SEMESTER 1 Exam Semester 1 TASK WEIGHTING NUMBER AND ALGEBRA T1 W 3 T2 W 2 CHANCE AND DATA 3% √ √ 4% √ √ 5% √ 15% √ INVESTIGATION 8% SPACE AND MEASUREMENT Investigation1 Take home part with in-class validation 3% Investigation 2 Take home part with in-class validation 5% TOTAL 35% √ √ √ √ √ Assessment outline: Unit 2C MAT/2DMAT ASSESSMENT WEIGHTINGS TIME T2 W11 RESPONSE 48% T3W4 T3 W7 T3 W10 UNIT 2D TEST 4 Chapter 1 – 3 2 D TEST 5 Chapter 4 – 6 2D TEST 6 Chapter 7-9 2D SEMESTER 2 exam (mock) Semester 2 TASK WEIGHTING NUMBER AND ALGEBRA CHANCE AND DATA 5% √ √ √ 6% √ √ 7% √ 30% √ INVESTIGATION T2 W9 17% Investigation 3 Take home part with in-class validation 5% T3 W2 Investigation 4 Take home part with in-class validation 6% Investigation 5 Take home part with in-class validation 6% TOTAL 65% T3 W5 SPACE AND MEASUREMENT √ √ √ √ √