SCHEME OF WORK
MATHEMATICS T
PRE- +U 1
YEAR 2015
YEARLY PLAN FOR MATHEMATICS T 954 (PRE-U 1st Term 2015)
FIRST TERM: ALGEBRA AND GEOMETRY
Week
Date
Teaching
Period
Topic
1 Functions
28 +2
Learning Outcome
Activities
Candidates should be able to:
1
(8 periods)
15-05-2015
↓
21-05-2015
1.1 Functions
6
(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 oneto-one function;
(c) sketch the graphs of simple functions, including piecewise-defined
functions;
2
(6 periods)
22- 05-2015
↓
26-05-2015
1.2 Polynomial and
rational functions
8
(d)
(e)
(f)
(g)
Plot graphs with
computers, handphones &
calculators
use the factor theorem and the remainder theorem;
solve polynomial and rational equations and inequalities;
solve equations and inequalities involving modulus signs in simple cases;
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;
CUTI PERTENGAHAN TAHUN (28-05-2015 HINGGA 15-06-2015)
3
(6 periods)
16-06-2015
↓
19-06-2015
1.3 Exponential and
logarithmic functions
6
(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.
Week
Date
3&4
(8 periods)
20-06-2015
↓
25-06-2015
Topic
1.4 Trigonometric
functions
2 Sequences and Series
4&5
(8 periods)
5
(8 periods)
6
(8 periods)
26-06-2015
↓
01-07-2015
2.1 Sequences
02-07-2015
↓
09-07-2015
2.2 Series
10-07-2015
↓
15-07-2015
Teaching
Period
8
18 + 2
Learning Outcome
(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 θ + b cos θ in the forms r sin (θ ± α) and r cos (θ ± α);
(n) find the solutions, within specified intervals, of trigonometric equations and
inequalities.
(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;
10
(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;
(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.
2.3 Binomial expansions
3 Matrices
16+2
3.1 Matrices
8
Use some
software on
trigonometric
identities
Candidates should be able to:
10
2.2 Series
Activities
Candidates should be able to:
(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;
History of some
interesting series
(g) use the properties of determinants;
3.2 Systems of linear
equations
7
(16 periods)
7
(8 periods)
8
16-07-2015
↓
25-07-2015
21-07-2015
↓
25-07-2015
30-07-2015
↓
(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.
4 Complex Numbers
12 + 2
Candidates should be able to:
4 Complex Numbers
12 + 2
(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 Moivre’s theorem to find the powers and roots of a complex number.
Coursework
12 + 4
Candidates should be able to:
Briefing on coursework
2
Facilitating coursework
proper.
6
Submission of coursework
4
(a)
(b)
(c)
(a)
(b)
(c)
plan to carry out Assignment A,
raise possible problems faced,
revise ‘resultant velocity’, if necessary.
carry out assignment,
refer to relevant sources related to the assignment,
seek advice and reasonable aids related to the assignment
(a) complete assignment report
Teacher gives
briefing and
guideline.
Students carry
out assignment
A. Teacher acts
as adviser,
observer,
facilitator …
Teacher assesses
assignment
03-08-2015
report and
conducts viva.
CUTI HARI RAYA PUASA (28-07-2015 HINGGA 03-08-2015)
10 &11
(16
periods)
12
(8 periods)
04-08-2015
↓
15-08-2015
18-08-2015
↓
21-08-2015
5 Analytic Geometry
15 + 2
Candidates should be able to:
5 Analytic Geometry
15 + 2
(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.
6 Vectors
20 + 2
Candidates should be able to:
6.1 Vectors in two and
three dimensions
8
(a) use unit vectors and position vectors;
Some applications of dot
(b) perform scalar multiplication, addition and subtraction
product in applied science.
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;
13 & 15
(13periods)
22-08-2015
↓
29-08-2015
6.2 Vector geometry
15 & 16
01-09-2015
↓
12-09-2015
Revision
12+2
10
(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.
Revise weak topics and stress techniques of answering
questions
Cuti Pertengahan Semester 2 (15-09-15 hingga 21.09.2015)
17
07-10-2015
↓
11-10-2015
Trial examination
8
18 - 21
13-10-2015
↓
01-11-2015
Discussion and preparation
for Term 1 Exam
8
22
03-11-2015
↓
09-11-2015
STPM Term 1
Examination
8
Peer guide
Answer various sample trial papers and sharpen question
answering techniques.