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SEKOLAH MENENGAH KEBANGSAAN RAJA PEREMPUAN, IPOH SCHEME OF WORK MATHEMATICS S (PAPER 2) PRA-U1 2010 WEEK/DATE 18 10.5.10-14.5.10 19 – 21 17.5.10-4.6.10 TOPIC/CONTENT LEARNING OUTCOMES ACTIVITIES & VALUES TEACHING AID Induction set Explaining relevant examples. White-board Grid board Soft wares Calculator CD and LCD ORIENTATION WEEK 1. DATA DESCRIPTION 1.1 Representation of data i) Discrete and continuous data ii) Frequency distribution iii) Stemplots iv) Frequency polygon v) Histogram vi) Ogive /cumulative frequency curve. 5.6.10 – 20.6.10 22 – 24 21.6.10-9.7.10 LEARNING OBJECTIVES 1.2 Measures of central tendency i) mean ii) mode iii) median iv) Boxplot v) Relative frequency distribution Pupils should be able to a) To distinguish between discrete and continuous data, grouped and ungrouped data. b) To construct and interpret stemplots. c) To construct and interpret frequency polygon. d)To construct and interpret histogram. i) with equal class width ii) with unequal class width e) To construct and interpret cumulative frequency curve( ogive). i) “less than “ ogive ii) “more than” ogive Pupils should be able to a) identify the types of data given. b) apply the properties of a stemplot. c) apply the properties of frequency polygon, histogram and cumulative frequency curve FISRT SEMESTER BREAK a) To calculate mean, mode & a) use the correct formula to median of ungrouped data. determine the value of mean, b) To calculate mean, mode & median mode and median of grouped data. c) To determine the median & mode from histogram. d) To determine median & quartiles from ogive. e) To construct boxplots. Show the correct method of drawing frequency polygon, histogram and ogive. Moral Value: Cooperation Systematic Concentrate Discuss the calculation of mean, mode and median for ungrouped and grouped data. Graph paper CD and LCD Calculator 25 – 27 12.7.10- 30.7.10 1.3 Measures Of Dispersion i) Range ii) Quartiles iii) Interquartiles range iv) Semi-interquartiles range v) Variance vi) Standard deviation a) To calculate the range, first and third quartile, interquartile and semiinterquartile range for ungrouped data. b)To calculate the variance and standard deviation c) To derive and use the formula i ( x x) 2 = x 2 - n(x) 2 a) apply the correct formula a) differentiate the value of interquartile and semiinterquartile range. c) identify the properties of a boxplot. d) determine the upper and lower outlier e) answer STPM questions Induction set. Discuss the calculation of the measure of dispersion. Graph paper CD & LCD Calculator d) To determine the shape of distribution. e) To construct a boxplot. f) To identify the outliers. 28 2.8.10 – 6.8.10 29 - 30 9.8.10 – 20.8.10 USBF 2 Teacher explains the rule of sets 2. PROBABILITY 2.1 Techniques of counting i) Sets ii) Permutation iii) Combination Pupils should be able to a) Counting rules for finite sets. b) To apply the properties of sets. c) To apply the formula of permutation of i) n different objects ii) n objects taking r objects iii) objects in a circular arrangement. d) To apply the formula of combination of n different objects taking r objects each time Pupils should be able to a) the value of n factorial. b) use the calculation of n Pr c) use the calculation of n Cr Discuss how to solve problems involving permutations and combinations Moral Value: Concern Cooperation Unity Calculator CD & LCD 31 - 32 23.8.10-3.9.10 4.9.10-12.9.10 2.2 Events and Probabilities i) Mutually exclusive events. ii) Independent events iii) Conditional events iv) Probability of conditional events v) Problems solving a) To understand the concept of sample space, event and probabilities b) To calculate the probability of an event. c) To distinguish between exclusive and non-exclusive event. d) To apply the formula P(A B)=P(A) +P(B)-P(A B). e) To apply the formula of independent event f) To apply the formula of conditional event. g) To calculate P(A/B) or P(B/A) h) To apply the formula P(A B)= P(A) x P(B/A) a) determine the probability of a given event. b) identify the relation between independent and conditional event. SECOND MID TERM BREAK HARI RAYA AIDILFITRI Teacher explains the rule of sets Discuss how to solve problems involving permutations and combinations Use of P(A B) = P(A) + P(B) – P(A B) Teacher discuss the meaning of conditional and independent events and shows how to use the formula P(A B) = P(A) x P(B/A) Calculator CD & LCD 33 - 34 13.9.10-24.9.10 3. DISCRETE PROBABILITY DISTRIBUTIONS 3.1 Random Variables i) Discrete Random Variables (DRV) ii) Continuous Random Variables iii) Probability distribution table iv) Probability distribution 3.2 Mathematical Expectation i) Mean, variance and standard deviation ii) Expected values and Variance Pupils should be able to a) understand the concept of a DRV b) construct a probability distribution table for DRV a) Understand the concept of mathematical expectation b) Calculate the expected value of X, E(X) c) Use the Expectation formula : E(g(x)) = Σ g(x). P(X = x) d) Show that E(a) = a, E(aX b) = aE(X) b e) Derive and use the formula E(X - µ)2 = E(X2) - µ2 f) Calculate Var(X), Var( g(x) ) g) Use the formula to find the expected and variance of linear combination of two DRV, X , Y Pupils should be able to a) calculate the probability of discrete random variable b) solve problems on DRV a) Calculate the mean and variance of a discrete random variable. b) Use formulae : E(aX b) = aE(X) b Var (aX b) = a 2 Var(X) E(aX bY) = aE(X) bE(Y) Var(aX bY) = a Var(X) + 2 2 b Var(Y) Explanation on DRV and how to construct the probability distribution table for DRV Teacher explains the mathematical expectation and how to determine E(X) Students are asked to prove all the mathematical expectations Discuss the proof of E(X - µ)2 = E(X2) - µ2 Teacher shows how to calculate variance of X and how to find the expected and variance of linear combination of two DRV, X , Y Moral Value: Gratitude Systematic Politeness Calculator CD & LCD Reference book 35 27.9.10-1.10.10 3.3 The Binomial Distribution X ~ B(n, p) a) Understand the concept of the Binomial Distribution, X~ B(n, p) b) Use the probability function of X ~ B(n, p) c) Find the mean and variance of X. d) Determine the value of X that most likely to occur. a) Determine the probability of an event that follows a binomial distribution. b) Determine the mean, variance and standard deviation of a binomial distribution. c) Solve problems involving Binomial Distribution. Teacher explains the Binomial Distribution and how to solve the problems involving X ~ B(n, p) Calculator CD & LCD 36 4.10.10-8.10.10 3.4 Normal Distribution a) Understand the concept of the a) Find the probability of zscores for standard normal distribution. b) Convert a random variable of a normal distribution , X, to the standardised variable, Z. c) Determine the probability of an event that follows a Normal Distribution. d) Solve problems involving Normal Distribution. Teacher explains the Normal Distribution and how to solve the problems involving Calculator CD & LCD X ~ N( , ) 2 Normal Distribution, X ~ N( , ). b) Understand the use of the standard normal distribution table. c) Standardise a normal variable. d) Use the normal distributions as models for solving problems. 2 37 11.10.10 – 15.10.10 Revision 38 – 39 18.10.10 - 29.10.10 YEAR-END EXAMINATION 40 1.11.10 – 5.11.10 Post-Test Discussion X ~ N( , 2) 41 – 42 8.11.10 – 19.11.10 Pupils should be able to 4. Network Planning 4.1 Network diagram 4.2 Critical path 4.2.1 Calculation of the earliest event time 4.2.2 Calculation of the latest event time 4.2.3 Calculation of project completion time 4.3 Floats a.) To understand the concepts of activities, events and networks b.) To construct and interpret networks c.) To identify the critical activities and critical paths d.) To calculate the minimum completion times e.) To calculate and explain total, free and independent floats. a.) Use the ruler for constructing the activity network b.) To determine the hanging activity c.) To trace the critical path d.) To calculate the earliest event time e.) To calculate the latest event time f.) To calculate the completion time g.) To determine the types of floats a.) Set induction b.) Explaining the use of symbols c.) Explaining how to construct an activity network d.) Explaining the contents e.) Discussion f.) Attempt past year STPM questions g.) Ex 2.1 - 2.3 h.) Revision exercises Moral Value: Cooperation Systematic Concentrate Prepared by, ………………………… (PN.FONG EE LIN) Checked by, ………………………… (PN. HJH. AZIAH BT SHAMSUDDIN) Certified by, ………………………… Verified by, …………………………