Stpm Mathematics T Notes Pdf
[PPU] Semester 2 Topics-Syllabus
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954
MATHEMATICS T
Sources from:
SECOND TERM: CALCULUS
Topic Teaching Period Learning Outcome
7 Limits and Continuity 12
Candidates should be able to:
7.1 Limits
6
(
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; 7.2 Continuity 6 (
c
) determine the continuity of a function at a point and on an interval; (
d
) use the intermediate value theorem.
8 Differentiation
28
Candidates should be able to: 8.1 Derivatives
12
(
a
) identify the derivative of a function as a limit; (
b
) find the derivatives of
x
n
(
n
), e
x
, ln
x
, sin
x
, cos
x
, tan
x
, sin
1
x
, cos
1
x
, tan
1
x
, with constant multiples, sums, differences, products, quotients and composites; (
c
) perform implicit differentiation; (
d
) find the first derivatives of functions defined parametrically; 8.2 Applications of differentiation 16 (
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.
9 Integration 28
Candidates should be able to: 9.1 Indefinite integrals
14
(
a
) identify integration as the reverse of differentiation; (
b
) integrate
x
n
(
n
), e
x
, sin
x
, cos
x
, sec
2
x
, with constant multiples, sums and differences;
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Topic Teaching Period Learning Outcome
(
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;
9.2 Definite integrals
14
(
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 Equations
14
Candidates should be able to:
(
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 Maclaurin Series
12
Candidates should be able to:
(
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;
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Stpm Mathematics T Notes Pdf
Source: https://www.scribd.com/document/112831187/954-Math-T-PPU-Semester-2-Topics-Syllabus
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