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Yearly Plan Mathematics t 2013
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YEARLY PLAN FOR MATHEMATICS T 954 (PRAU 1 2013)
FIRST TERM: ALGEBRA AND GEOMETRYWeekDateTopicTeaching
PeriodLearning OutcomeActivities
1 Functions28 + 4Candidates should be able to:
1
(8 periods)
10-06-2013
14-06-20131.1 Functions6 + 2(a) state the domain and range of a function, and find composite functions;
(b) determine whether a function is one-to-one, and find the inverse of a one-to-one function;
(c) sketch the graphs of simple functions, including piecewise-defined functions;Plot graphs with computers, hand-phones & calculators
2(8 periods)
17-06-2013
21-06-20131.2 Polynomial and rational functions8(d) use the factor theorem and the remainder theorem;
(e) solve polynomial and rational equations and inequalities;
(f) solve equations and inequalities involving modulus signs in simple cases;
(g) decompose a rational expression into partial fractions in cases where the denominator has two distinct linear factors, or a linear factor and a prime quadratic factor;
3
(8 periods)
24-06-2013
28-06-20131.3 Exponential and logarithmic functions6 + 2(h) relate exponential and logarithmic functions, algebraically and graphically;
(i) use the properties of exponents and logarithms;
(j) solve equations and inequalities involving exponential or logarithmic expressions;
Search for e and its use.
WeekDateTopicTeaching
PeriodLearning OutcomeActivities
4
(8 periods)01-07-2013
05-07-20131.4 Trigonometric functions8(k) relate the periodicity and symmetries of the sine, cosine and tangent functions to their graphs, and identify the inverse sine, inverse cosine and inverse tangent functions and their graphs;
(l) use basic trigonometric identities and the formulae for sin (A B), cos (A B) and tan (A B), including sin 2A, cos 2A and tan 2A;
(m) express a sin + b cos in the forms r sin ( ) and r cos ( );
(n) find the solutions, within specified intervals, of trigonometric equations and inequalities.
Use some software on trigonometric identities
2 Sequences and Series24Candidates should be able to:
5(8 periods)08-07-2013
12-07-20132.1 Sequences2.2 Series8(a) use an explicit formula and a recursive formula for a sequence;
(b) find the limit of a convergent sequence;
(c) use the formulae for the nth term and for the sum of the first n terms of an arithmetic series and of a geometric series;
6(8 periods)15-07-2013
19-07-20132.2 Series8(d) identify the condition for the convergence of a geometric series, and use the formula for the sum of a convergent geometric series;
(e) use the method of differences to find the nth partial sum of a series, and deduce the sum of the series in the case when it is convergent;History of some interesting series
7(8 periods)22-07-2013
26-07-2013
2.3 Binomial expansions8(f) expand (a + b)n , where n Z+ ;
(g) expand (1 + x) n , where n , and identify the condition | x | < 1 for the validity of this expansion;
(h) use binomial expansions in approximations.
8(4 periods)
29-07-2013
30-07-2013
Formative test 4Test on functions and sequences & series
WeekDateTopicTeaching
PeriodLearning OutcomeActivities
6 Vectors14Candidates should be able to:
8 (6 periods)01-08-2013
02-08-20136.1 Vectors in two and three dimensions6(a) use unit vectors and position vectors;
(b) perform scalar multiplication, addition and subtraction of vectors;
(c) find the scalar product of two vectors, and determine the angle between two vectors;
(d) find the vector product of two vectors, and determine the area a parallelogram and of a triangle;
Some applications of dot product in applied science.
9 (8 periods)29-07-2013
06-08-20136.2 Vector geometry8(e) find and use the vector and cartesian equations of lines;
(f) find and use the vector and cartesian equations of planes;
(g) calculate the angle between two lines, between a line and a plane, and between two planes;
(h) find the point of intersection of two lines, and of a line and a plane;
(i) find the line of intersection of two planes.
Some interesting 3D problem solved by vectors.
CUTI PERTENGAHAN PENGGAL (07-08-2013 HINGGA 18-08-2013)
3 Matrices16Candidates should be able to:
10(8 periods)19-08-2013
23-08-2013
3.1 Matrices8(a) identify null, identity, diagonal, triangular and symmetric matrices;
(b) use the conditions for the equality of two matrices;
(c) perform scalar multiplication, addition, subtraction and multiplication of matrices with at most three rows and three columns;
(d) use the properties of matrix operations;
(e) find the inverse of a non-singular matrix using elementary row operations;
(f) evaluate the determinant of a matrix;
(g) use the properties of determinants;
11(8 periods)26-08-2013
30-08-20133.2 Systems of linear equations8(h) reduce an augmented matrix to row-echelon form, and determine whether a system of linear equations has a unique solution, infinitely many solution or no solutions;
(i) apply the Gaussian elimination to solve a system of linear equations;
(j) find the unique solution of a system of linear equations using the inverse of a matrix.
WeekDateTopicTeaching
PeriodLearning OutcomeActivities
4 Complex Numbers8Candidates should be able to:
12(8 periods)02-09-201306-09-20134 Complex Numbers8(a) identify the real and imaginary parts of a complex number;
(b) use the conditions for the equality of two complex numbers;
(c) find the modulus and argument of a complex number in cartesian form and express the complex number in polar form;
(d) represent a complex number geometrically by means of an Argand diagram;
(e) find the complex roots of a polynomial equation with real coefficients;
(f) perform elementary operations on two complex numbers expressed in cartesian form;
(g) perform multiplication and division of two complex numbers expressed in polar form;
(h) use de Moivres theorem to find the powers and roots of a complex number.
5 Analytic Geometry8Candidates should be able to:
13(8 periods)09-09-2013
13-09-2013
5 Analytic Geometry8(a) transform a given equation of a conic into the standard form;
(b) find the vertex, focus and directrix of a parabola;
(c) find the vertices, centre and foci of an ellipse;
(d) find the vertices, centre, foci and asymptotes of a hyperbola;
(e) find the equations of parabolas, ellipses and hyperbolas satisfying prescribed conditions (excluding eccentricity);
(f) sketch conics;
(g) find the cartesian equation of a conic defined by parametric equations;
(h) use the parametric equations of conics.
WeekDateTopicTeaching
PeriodLearning OutcomeActivities
Coursework8Candidates should be able to:
14(8 periods)
16-09-2013
20-09-2013Briefing on coursework Facilitating coursework proper.
Facilitating coursework proper. Submission of coursework22
2
2(a) plan to carry out Assignment A,
(b) raise possible problems faced,
(c) revise resultant velocity, if necessary.(d) carry out assignment,
(e) refer to relevant sources related to the assignment,
(f) seek advice and reasonable aids related to the assignment,
(g) complete assignment reportTeacher gives briefing and guideline.Students carry out assignment A. Teacher acts as adviser, observer, facilitator
Students carry out assignment A. Teacher acts as adviser, observer, facilitator Teacher assesses assignment report and conducts viva.
15(8 periods)23-09-2013
27-09-2013Revision8
16(8 periods)30-09-2013
4-10-2013Trial examination and
revision8
17(8 periods)7-10-2013
11-10-2013Discussions and refinement8
WeekDateTopicTeaching
PeriodLearning OutcomeActivities
18 22
14-10-2013
15-11-2013
Revision40
2319-11-2013
25-11-2013
Pep. Bertulis STPM Baharu Penggal 1
YEARLY PLANNING FOR MATHEMATICS T 954 (PRAU 2 2013)
SECOND TERM: CALCULUSWeekDateTopicTeaching
PeriodLearning OutcomeActivities
7 Limits and Continuity12Candidates should be able to:
1
(6 periods)02-01-2013
04-01-2013
7.1 Limits6(a) determine the existence and values of the left-hand limit, right-hand limit and limit of a function;
(b) use the properties of limits;
1
(2 periods)
2
(4 periods)
07-01-2013
11-01-2013
7.2 Continuity6(c) determine the continuity of a function at a point and on an interval;
(d) use the intermediate value theorem.
8 Differentiation28Candidates should be able to:
2
(4 periods)
3
(8 periods) 14-01-2013
18-01-2013
8.1 Derivatives12(a) identify the derivative of a function as a limit;
(b) find the derivatives of xn (n ), ex, ln x, sin x, cos x, tan x, sin1x, cos1x, tan1x, with constant multiples, sums, differences, products, quotients and composites;
(c) perform implicit differentiation;
(d) find the first derivatives of functions defined parametrically;
4
(8 periods)
5
(8 periods) 21-01-2013
31-01-2013
8.2 Applications of differentiation16(e) determine where a function is increasing, decreasing, concave upward and concave downward;
(f) determine the stationary points, extremum points and points of inflexion;
(g) sketch the graphs of functions, including asymptotes parallel to the coordinate axes;
(h) find the equations of tangents and normals to curves, including parametric curves;
(i) solve problems concerning rates of change, including related rates;
(j) solve optimisation problems.
WeekDateTopicTeaching
PeriodLearning OutcomeActivities
9 Integration28Candidates should be able to:
6
(8 periods)
7
(6 periods)04-02-2013
15-02-2013
9.1 Indefinite integrals14(a) identify integration as the reverse of differentiation;
(b) integrate xn (n ), ex, sin x, cos x, sec2x, with constant multiples, sums and differences;
(c) integrate rational functions by means of decomposition into partial fractions;
(d) use trigonometric identities to facilitate the integration of trigonometric functions;
(e) use algebraic and trigonometric substitutions to find integrals;
(f) perform integration by parts;
7
(2 periods), 8
(8 periods)
9
(4 periods)18-02-2013
28-02-2013
9.2 Definite integrals14(g) identify a definite integral as the area under a curve;
(h) use the properties of definite integrals;
(i) evaluate definite integrals;
(j) calculate the area of a region bounded by a curve (including a parametric curve) and lines parallel to the coordinate axes or between two curves;
(k) calculate volumes of solids of revolution about one of the coordinate axes.
10 Differential Equations14Candidates should be able to:
9
(4 periods),
10
(8 periods)
11
(2 periods)04-03-2013
15-03-2013
10 Differential Equations14(a) find the general solution of a first order differential equation with separable variables;
(b) find the general solution of a first order linear differential equation by means of an integrating factor;
(c) transform, by a given substitution, a first order differential equation into one with separable variables or one which is linear;
(d) use a boundary condition to find a particular solution;
(e) solve problems, related to science and technology, that can be modelled by differential equations.
11
(2 periods)
05-03-2013
06-03-2013
Formative test 2Test on limits & continuity, differentiation, integration and differential equations.
WeekDateTopicTeaching
PeriodLearning OutcomeActivities
Coursework12Candidates should be able to:
11
(2 periods)
11-03-2013
15-03-2013
Briefing on coursework.2(a) plan to carry out Assignment B,
(b) raise possible problems faced,
(c) revise the related topics if necessary.
Teacher gives briefing and guideline.
11
(2 periods)
12
(5 periods)
18-03-2013
22-03-2013
Coursework proper7(a) carry out assignment,
(b) refer to relevant sources related to the assignment,
(c) seek advice and reasonable aids related to the assignment,
Students carry out assignment B. Teacher acts as adviser, observer, facilitator
12
(3 periods)
18-03-2013
22-03-2013
Submission of coursework paper3(a) complete assignment reportTeacher assesses assignment report and conducts viva.
11 Maclaurin Series12Candidates should be able to:
13
(8 periods)
14
(4 periods)25-03-2013
29-03-2013
11 Maclaurin Series12(a) find the Maclaurin series for a function and the interval of convergence;
(b) use standard series to find the series expansions of the sums, differences, products, quotients and composites of functions;
(c) perform differentiation and integration of a power series;
(d) use series expansions to find the limit of a function.
WeekDateTopicTeaching
PeriodLearning OutcomeActivities
12 Numerical Methods14Candidates should be able to:
14
(4 periods)
15
(6 periods)01-04-2013
05-04-2013
12.1 Numerical solution of equations10(a) locate a root of an equation approximately by means of graphical considerations and by searching for a sign change;
(b) use an iterative formula of the form xn+1 = f (xn ) to find a root of an equation to a prescribed degree of accuracy;
(c) identify an iteration which converges or diverges;
(d) use the Newton-Raphson method;
15
(2 periods)
16
(2 periods)
08-04-2013
19-04-2013
12.2 Numerical integration4(e) use the trapezium rule;
(f) use sketch graphs to determine whether the trapezium rule gives an over-estimate or an under-estimate in simple cases.
17(6 periods)
22-04-2013
26-04-2013Trial examination 6
18(8 periods)
19(8 periods) 20(8 periods)
29-04-2013
17-05-2013
Revision
2120-05-2013
23-05-2013Pep. Bertulis STPM Baharu Penggal 2
YEARLY PLANNING FOR MATHEMATICS T 954 (PRAU 3 2013)
THIRD TERM: STATISTICSWeekDateTopicTeaching
PeriodLearning OutcomeActivities
13 Data Description16Candidates should be able to:
1 2
(16periods)10-06-2013
21-06-201313 Data Description16(a) identify discrete, continuous, ungrouped and grouped data;
(b) construct and interpret stem-and-leaf diagrams, box-and-whisker plots, histograms and cumulative frequency curves;
(c) state the mode and range of ungrouped data; (d) determine the median and interquartile range of ungrouped and grouped data;
(e) calculate the mean and standard deviation of ungrouped and grouped data, from raw data and from given totals such as
(f) select and use the appropriate measures of central tendency and measures of dispersion;
(g) calculate the Pearson coefficient of skewness;
(h) describe the shape of a data distribution.
14 Probability14Candidates should be able to:
3 4
(14periods)24-06-2013
03-07-201314 Probability14(a) apply the addition principle and the multiplication principle;
(b) use the formulae for combinations and permutations in simple cases;
(c) identify a sample space, and calculate the probability of an event;
(d) identify complementary, exhaustive and mutually exclusive events;
(e) use the formula P(A B) = P(A) + P(B) P(A B);
(f) calculate conditional probabilities, and identify independent events;
(g) use the formulae P(A B) = P(A) P(B|A) = P(B) P(A|B);
(h) use the rule of total probability.
WeekDateTopicTeaching
PeriodLearning OutcomeActivities
15 Probability Distributions26Candidates should be able to:
4
(4 periods)
5
(2 periods)04-07-2013
08-07-201315.1 Discrete random variables6(a) identify discrete random variables;
(b) construct a probability distribution table for a discrete random variable;
(c) use the probability function and cumulative distribution function of a discrete random variable;
(d) calculate the mean and variance of a discrete random variable;
5
(6 periods)10-07-2013
12-07-201315.2 Continuous random variables6(e) identify continuous random variables;
(f) relate the probability density function and cumulative distribution function of a continuous random variable;
(g) use the probability density function and cumulative distribution function of a continuous random variable;
(h) calculate the mean and variance of a continuous random variable;
6
(4 periods)15-07-2013
16-07-201315.3 Binomial distribution4(i) use the probability function of a binomial distribution, and find its mean and variance;
(j) use the binomial distribution as a model for solving problems related to science and technology;
6
(4 periods)17-07-2013
19-07-201315.4 Poisson distribution4(k) use the probability function of a Poisson distribution, and identify its mean and variance;
(l) use the Poisson distribution as a model for solving problems related to science and technology;
7
(6 periods)22-07-2013
26-07-201315.5 Normal distribution6(m) identify the general features of a normal distribution, in relation to its mean and standard deviation;
(n) standardise a normal random variable and use the normal distribution tables;
(o) use the normal distribution as a model for solving problems related to science and technology;
(p) use the normal distribution, with continuity correction, as an approximation to the binomial distribution, where appropriate.
WeekDateTopicTeaching
PeriodLearning OutcomeActivities
8(4 periods)
29-07-2013
30-07-2013Formative test 4Test on data description, probability and probability distributions.
16 Sampling and Estimation26Candidates should be able to:
8
(6 periods)
9
(8 periods)01-08-2013
06-08-201316.1 Sampling14(a) distinguish between a population and a sample, and between a parameter and a statistic;
(b) identify a random sample;
(c) identify the sampling distribution of a statistic;
(d) determine the mean and standard deviation of the sample mean;
(e) use the result that X has a normal distribution if X has a normal distribution;
(f) use the central limit theorem;
(g) determine the mean and standard deviation of the sample proportion;
(h) use the approximate normality of the sample proportion for a sufficiently large sample size;
CUTI PERTENGAHAN PENGGAL (07-08-2013 HINGGA 18-08-2013)
10
(8 periods)
11
(4 periods)19-08-2013
27-08-201316.2 Estimation12(i) calculate unbiased estimates for the population mean and population variance;
(j) calculate an unbiased estimate for the population proportion;
(k) determine and interpret a confidence interval for the population mean based on a sample from a normally distributed population with known variance;
(l) determine and interpret a confidence interval for the population mean based on a large sample;
(m) find the sample size for the estimation of population mean;
(n) determine and interpret a confidence interval for the population proportion based on a large sample;
(o) find the sample size for the estimation of population proportion.
WeekDateTopicTeaching
PeriodLearning OutcomeActivities
17 Hypothesis Testing12Candidates should be able to:
11
(4 periods)
12
(8 periods)28-08-2013
06-09-201317 Hypothesis Testing12(a) explain the meaning of a null hypothesis and an alternative hypothesis;
(b) explain the meaning of the significance level of a test;
(c) carry out a hypothesis test concerning the population mean for a normally distributed population with known variance;
(d) carry out a hypothesis test concerning the population mean in the case where a large sample is used;
(e) carry out a hypothesis test concerning the population proportion by direct evaluation of binomial probabilities;
(f) carry out a hypothesis test concerning the population proportion using a normal approximation.
18 Chi-squared Tests14Candidates should be able to:
13
(8 periods)
14
(6 periods)09-09-2013
18-09-2013
18 Chi-squared Tests14(a) identify the shape, as well as the mean and variance, of a chi-squared distribution with a given number of degrees of freedom;
(b) use the chi-squared distribution tables;
(c) identify the chi-squared statistic;
(d) use the result that classes with small expected frequencies should be combined in a chi-squared test;
(e) carry out goodness-of-fit tests to fit prescribed probabilities and probability distributions with known parameters;
(f) carry out tests of independence in contingency tables (excluding Yates correction).
WeekDateTopicTeaching
PeriodLearning OutcomeActivities
Coursework10Candidates should be able to:
14
(2 periods)
15 (8 periods)
19-09-2013
27-09-2013
Briefing on coursework.
Coursework proper
Passing up coursework
2
62
(a) plan to carry out Assignment C,
(b) raise possible problems faced,
(c) revise the related topics if necessary.
(d) carry out assignment,
(e) refer to relevant sources related to the assignment,
(f) seek advice and reasonable aids related to the assignment,
(h) complete assignment report
Teacher gives briefing and guideline.
Students carry out assignment C. Teacher acts as adviser, observer, facilitator
Teacher assesses assignment report and conducts viva.
16(8 periods)30-09-2013
4-10-2013Trial examination and
revision8
17(8 periods)7-10-2013
11-10-2013Discussions and refinement8
18 20
14-10-2013
01-11-2013
Revision24
2106-11-2013
14-11-2013
Pep. Bertulis STPM Baharu Penggal 3
SCHEME OF WORK
MATHEMATICS T
PRAU 1
YEAR 2013
SCHEME OF WORK
MATHEMATICS T
PRAU 2
YEAR 2013
SCHEME OF WORK
MATHEMATICS T
PRAU 3
YEAR 2013