YEARLY PLANNING FOR MATHEMATICS T 954 (PRAU 2 2014)

SECOND TERM: CALCULUSWeekTopicLearning OutcomeActivitiesNotePedagogy

7 Limits and ContinuityCandidates should be able to:

1

7.1 Limits1. determine the existence and values of the left-hand limit, right-hand limit and limit of a function;

2. use the properties of limits;

1. Introducing the limit of a function.

2. Teacher gives some examples, exercises and discussion.

Obeying the law

Carefulness

Rationality

Honesty

DiligenceDirective

Mastery

Metacognitive

2 7.2 Continuity1. determine the continuity of a function at a point and on an interval;

2. use the intermediate value theorem.1. Introducing the continuity of a function.

2. Teacher gives some examples, exercises and discussion.

Determinations

Cleanliness

Patience

Responsibility

8 DifferentiationCandidates should be able to:

3 4

8.1 Derivatives1. identify the derivative of a function as a limit;

2. 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;

3. perform implicit differentiation;

4. find the first derivatives of functions defined parametrically;

1. Revising the derivative of a function.

2. Teacher gives some examples, exercises and discussion.

5 7

8.2 Applications of differentiation1. determine where a function is increasing, decreasing, concave upward and concave downward;

2. determine the stationary points, extremum points and points of inflexion;

3. sketch the graphs of functions, including asymptotes parallel to the coordinate axes;1. Revising the applications of differentiation.2. Teacher gives some examples, exercises and discussion.

WeekTopicLearning OutcomeActivitiesNotePedagogy

5 7

8.2 Applications of differentiation4. find the equations of tangents and normals to curves, including parametric curves;

5. solve problems concerning rates of change, including related rates;

6. solve optimisation problems.

Obeying the law

Carefulness

Rationality

Honesty

DiligenceDirective

Mastery

Metacognitive

7UJIAN PERTENGAHAN PENGGAL 2

9 IntegrationCandidates should be able to:

8 9

9.1 Indefinite integrals1. identify integration as the reverse of differentiation;

2. integrate xn (n ), ex, sin x, cos x, sec2x, with constant multiples, sums and differences;

3. integrate rational functions by means of decomposition into partial fractions;

4. use trigonometric identities to facilitate the integration of trigonometric functions;

5. use algebraic and trigonometric substitutions to find integrals;

6. perform integration by parts;

1. Revising the integration of a function.

2. Teacher gives some examples, exercises and discussion.Determinations

Cleanliness

Patience

Responsibility

9 10

9.2 Definite integrals1. identify a definite integral as the area under a curve;

2. use the properties of definite integrals;

3. evaluate definite integrals;

4. 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;

5. calculate volumes of solids of revolution about one of the coordinate axes.

1. Revising the definite integrals.2. Teacher gives some examples, exercises and discussion.

WeekTopicLearning OutcomeActivitiesNotePedagogy

10 Differential EquationsCandidates should be able to:

10 11

10 Differential Equations1. find the general solution of a first order differential equation with separable variables;

2. find the general solution of a first order linear differential equation by means of an integrating factor;

3. transform, by a given substitution, a first order differential equation into one with separable variables or one which is linear;

4. use a boundary condition to find a particular solution;

5. solve problems, related to science and technology, that can be modelled by differential equations.

1. Introducing the differential equations.2. Teacher gives some examples, exercises and discussion.Obeying the law

Carefulness

Rationality

Honesty

DiligenceDeterminations

Cleanliness

Patience

Responsibility

Directive

Mastery

Metacognitive

CourseworkCandidates should be able to:

11

Briefing on coursework.1. plan to carry out Assignment B,

2. raise possible problems faced,

3. revise the related topics if necessary.

1. Teacher gives briefing and guideline.

11 12

Coursework proper1. carry out assignment,

2. refer to relevant sources related to the assignment,

3. seek advice and reasonable aids related to the assignment,

1. Students carry out assignment B. Teacher acts as adviser, observer, facilitator

12

Submission of coursework paper1. complete assignment report1. Teacher assesses assignment report and conducts viva.

WeekTopicLearning OutcomeActivitiesNotePedagogy

13CUTI PERTENGAHAN PENGGAL (21/3 29/3/14)

11 Maclaurin SeriesCandidates should be able to:

14

11 Maclaurin Series1. find the Maclaurin series for a function and the interval of convergence;

2. use standard series to find the series expansions of the sums, differences, products, quotients and composites of functions;

3. perform differentiation and integration of a power series;

4. use series expansions to find the limit of a function.

1. Introducing the Maclaurin series.2. Teacher gives some examples, exercises and discussion.Obeying the law

Carefulness

Rationality

Honesty

DiligenceDeterminations

Cleanliness

Patience

Responsibility

Directive

Mastery

Metacognitive

12 Numerical MethodsCandidates should be able to:

1512.1 Numerical solution of equations1. locate a root of an equation approximately by means of graphical considerations and by searching for a sign change;

2. use an iterative formula of the form xn+1 = f (xn ) to find a root of an equation to a prescribed degree of accuracy;

3. identify an iteration which converges or diverges;

4. use the Newton-Raphson method;

1. Introducing the numerical solution of equations.2. Teacher gives some examples, exercises and discussion.

16

12.2 Numerical integration1. use the trapezium rule;

2. use sketch graphs to determine whether the trapezium rule gives an over-estimate or an under-estimate in simple cases.

1. Introducing the numerical integration.2. Teacher gives some examples, exercises and discussion.

16UJIAN PRA PENTAKSIRAN STPM PENGGAL 2

WeekTopicLearning OutcomeActivitiesNotePedagogy

RevisionCandidates should be able to:

17

7 Limits and Continuity

8 Differentiation

1. To reinforce and consolidate the knowledge and skills which students have learned.

2. To expose students to the types of real STPM examination questions.

1. Revision, solving passed years examination questions , solving additional questions from reference books.

2. Doing exercises and discussing the techniques of solving problems.

Responsibility

Cooperation

Determinations

Diligence

CarefulnessCooperative

189 Integration

10 Differential Equations

1. To reinforce and consolidate the knowledge and skills which students have learned.

2. To expose students to the types of real STPM examination questions.

1. Revision, solving passed years examination questions , solving additional questions from reference books.

2. Doing exercises and discussing the techniques of solving problems.

19

11 Maclaurin Series

12 Numerical Methods

1. To reinforce and consolidate the knowledge and skills which students have learned.

2. To expose students to the types of real STPM examination questions.

1. Revision, solving passed years examination questions , solving additional questions from reference books.

2. Doing exercises and discussing the techniques of solving problems.

20

13 Past Year Papers1. To answer the questions in Paper 2 with confident.

1. Doing exercise on Past Year Papers, model Paper 1 & 2 , Trial Examination Papers from other States. Discussion.

21PEPERIKSAAN STPM PENGGAL 2 (19/5 22/5/14)

22 24 CUTI PERTENGAHAN TAHUN (27/5 14/6/14)

SCHEME OF WORK

MATHEMATICS T

PRAU 2

YEAR 2014