SMK SERI BANDAR PONTIAN

SEMESTER PLAN

FOR

MATHEMATICS TFIRST TERM

YEAR 2015

YEARLY PLAN FOR MATHEMATICS T 954 (PRAU 1 2015)

FIRST TERM: ALGEBRA AND GEOMETRYWeekTopicLearning OutcomeActivitiesNotePedagogy

1 FunctionsCandidates should be able to:

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1.1 Functions1. state the domain and range of a function, and find composite functions;

2. determine whether a function is one-to-one, and find the inverse of a one-to-one function;

3. sketch the graphs of simple functions, including piecewise-defined functions;1. Revising the concept of function.

2. Teacher gives some examples, exercises and discussion.

Obeying the law

Carefulness

Rationality

Honesty

DiligenceDirective

Mastery

Metacognitive

26

1.2 Polynomial and rational functions1. use the factor theorem and the remainder theorem;

2. solve polynomial and rational equations and inequalities;

3. solve equations and inequalities involving modulus signs in simple cases;

4. 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;

1. Introducing the factor theorem and remainder theorem.

2. Teacher gives some examples, exercises and discussion.

Determinations

Cleanliness

Patience

Responsibility

26

1.3 Exponential and logarithmic functions1. relate exponential and logarithmic functions, algebraically and graphically;

2. use the properties of exponents and logarithms;

3. solve equations and inequalities involving exponential or logarithmic expressions;

1. Revising the properties of exponents and logarithms.

2. Teacher gives some examples, exercises and discussion.

WeekTopicLearning OutcomeActivitiesNotePedagogy

27

1.4 Trigonometric functions1. 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;

2. 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;

3. express a sin + b cos in the forms r sin ( ) and r cos ( );

4. find the solutions, within specified intervals, of trigonometric equations and inequalities.

1. Revising the use of basic trigonometric identities.

2. Teacher gives some examples, exercises and discussion.

Obeying the law

Carefulness

Rationality

Honesty

DiligenceDeterminations

Cleanliness

Patience

Responsibility

Directive

Mastery

Metacognitive

2 Sequences and SeriesCandidates should be able to:

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2.1 Sequences2.2 Series1. use an explicit formula and a recursive formula for a sequence;

2. find the limit of a convergent sequence;

3. 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;

1. Introducing the use an explicit formula and a recursive formula.

2. Teacher gives some examples, exercises and discussion.

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2.2 Series1. identify the condition for the convergence of a geometric series, and use the formula for the sum of a convergent geometric series;

2. 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;1. Introducing the convergence of series.

2. Teacher gives some examples, exercises and discussion.

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2.3 Binomial expansions1. expand (a + b)n , where n Z+ ;

2. expand (1 + x) n , where n , and identify the condition | x | < 1 for the validity of this expansion;

3. use binomial expansions in approximations.

1. Introducing Binomial expansions.

2. Teacher gives some examples, exercises and discussion.

3 MatricesCandidates should be able to:

303.1 Matrices1. identify null, identity, diagonal, triangular and symmetric matrices;1. Revising the concept of matrices.

WeekTopicLearning OutcomeActivitiesNotePedagogy

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3.1 Matrices2. identify null, identity, diagonal, triangular and symmetric matrices;

3. use the conditions for the equality of two matrices;

4. perform scalar multiplication, addition, subtraction and multiplication of matrices with at most three rows and three columns;5. use the properties of matrix operations;

6. find the inverse of a non-singular matrix using elementary row operations;

7. evaluate the determinant of a matrix;

8. use the properties of determinants;

2. Teacher gives some examples, exercises and discussion.

Obeying the law

Carefulness

Rationality

Honesty

DiligenceDeterminations

Cleanliness

Patience

Responsibility

Directive

Mastery

Metacognitive

30

3.2 Systems of linear equations1. 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;

2. apply the Gaussian elimination to solve a system of linear equations;

3. find the unique solution of a system of linear equations using the inverse of a matrix.1. Introducing the Gaussian elimination.

2. Teacher gives some examples, exercises and discussion.

31UJIAN PERTENGAHAN PENGGAL 1 27/7/2015 28/7/2015

4 Complex NumbersCandidates should be able to:

32 33

4 Complex Numbers1. identify the real and imaginary parts of a complex number;

2. use the conditions for the equality of two complex numbers;

3. find the modulus and argument of a complex number in cartesian form and express the complex number in polar form;

4. represent a complex number geometrically by means of an Argand diagram;

5. find the complex roots of a polynomial equation with real coefficients;

6. perform elementary operations on two complex numbers expressed in cartesian form;

7. perform multiplication and division of two complex numbers expressed in polar form;

8. use de Moivres theorem to find the powers and roots of a complex number.1. Introducing the complex number.

2. Teacher gives some examples, exercises and discussion.

WeekTopicLearning OutcomeActivitiesNotePedagogy

5 Analytic GeometryCandidates should be able to:

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5 Analytic Geometry1. transform a given equation of a conic into the standard form;

2. find the vertex, focus and directrix of a parabola;

3. find the vertices, centre and foci of an ellipse;

4. find the vertices, centre, foci and asymptotes of a hyperbola;

5. find the equations of parabolas, ellipses and hyperbolas satisfying prescribed conditions (excluding eccentricity);

6. sketch conics;

7. find the cartesian equation of a conic defined by parametric equations;

8. use the parametric equations of conics.

1. Introducing the analytic geometry.

2. Teacher gives some examples, exercises and discussion.

Obeying the law

Carefulness

Rationality

Honesty

DiligenceDeterminations

Cleanliness

Patience

Responsibility

Directive

Mastery

Metacognitive

6 VectorsCandidates should be able to:

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6.1 Vectors in two and three dimensions1. use unit vectors and position vectors;

2. perform scalar multiplication, addition and subtraction of vectors;

3. find the scalar product of two vectors, and determine the angle between two vectors;

4. find the vector product of two vectors, and determine the area a parallelogram and of a triangle;1. Introducing vectors in two and three dimensions.

2. Teacher gives some examples, exercises and discussion.

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6.2 Vector geometry1. find and use the vector and cartesian equations of lines;

2. find and use the vector and cartesian equations of planes;

3. calculate the angle between two lines, between a line and a plane, and between two planes;

4. find the point of intersection of two lines, and of a line and a plane;

5. find the line of intersection of two planes.

1. Introducing vectors geometry.

2. Teacher gives some examples, exercises and discussion.

CourseworkCandidates should be able to:

37Briefing on coursework1. plan to carry out Assignment A,

2. raise possible problems faced,

3. revise resultant velocity, if necessary.

1. Teacher gives briefing and guideline.

WeekTopicLearning OutcomeActivitiesNotePedagogy

CourseworkCandidates should be able to:

37 38

Facilitating coursework proper.

Facilitating coursework proper. Submission of coursework4. carry out assignment,

5. refer to relevant sources related to the assignment,

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

7. complete assignment report2. Students carry out assignment A. Teacher acts as adviser, observer, facilitator.3. Students carry out assignment A. Teacher acts as adviser, observer, facilitator.

4. Teacher assesses assignment report and conducts viva.Obeying the law

Carefulness

Rationality

Honesty

DiligenceDeterminations

Cleanliness

Patience

Responsibility

Directive

Mastery

Metacognitive

39

CUTI PERTENGAHAN PENGGAL (18/9/2015 26/9/2015)

40UJIAN PRA PENTAKSIRAN STPM PENGGAL 1 (28/9/2015 1/10/2015)

RevisionCandidates should be able to:

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1 Functions 2 Sequences and Series 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

WeekTopicLearning OutcomeActivitiesNotePedagogy

423 Matrices 4 Complex Numbers

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

43

5 Analytic Geometry

6 Vectors 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.

44 45

13 Past Year Papers1. To answer the questions in Paper 1 with confident.

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

46 47 PEPERIKSAAN STPM PENGGAL 1 (10/11/2015 18/11/2015)

47 53 CUTI AKHIR TAHUN (20/11/2015 2/1/2016)

PREPARED BY TAN CHIN HUAT