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GCE Advanced Level Further Mathematics Curriculum For 11th Grade And
12th Grade / GCE A Level
Our Singapore Math books for 11th Grade And
12th Grade / GCE A Level are written in English and based on GCE A
Level Further Maths curriculum for 11th Grade And 12th Grade / GCE A
Level, which covers the following topics.
Algebra
- Polynomial functions and equations; graphical representation
- Simple rational algebraic functions and their graphs
- Summation of finite series
- Further mathematical induction
Analysis
- Further differentiation and integration
- Applications of integration to mean values, centroids, lengths of
curves and areas of surfaces of revolution
- Solution of linear differential equations (constant coefficients);
reduction of a given differential equation by means of a given
substitution
Complex numbers
- Proof of de Moivre's theorem for a positive integral exponent;
application of de Moivre's theorem for a rational exponent
- Loci in the Argand diagram
Matrices and linear spaces
- Basic properties of a linear (vector) space; subspaces spanned by a
set of vectors
- Linear dependence and independence
- Row space and column space of a matrix; the basis of a subspace
- Matrices as linear transformations
- Eigenvalues and eigenvectors of 2 x 2 and 3 x 3 matrices
Vectors
- The ratio theorem and geometrical applications
- Vector equations of lines and planes
- The vector product a x b and its properties
- Applications of scalar and vector products
Polar coordinates
- Polar coordinates; sketching simple curves; area of a sector
Mechanics
- Equilibrium of a rigid body under a coplanar set of forces. The
interaction principle applied to rigid bodies in contact.
- Centre of mass of a system of particles and of a rigid body. Moments
of inertia.
- Motion in a vertical circle
- Simple harmonic motion; small oscillations which approximate to
simple harmonic motion, including those of a simple and a compound
pendulum.
- Impulse and momentum. Coefficient of restitution. Direct impact of
smooth spheres. Oblique impact of a smooth sphere with a fixed plane.
Statistics
- Further simple distributions, including the geometric distribution
and the negative exponential distribution
- The use of the t-distribution and tables. Test of significance of
the sample mean. The two-sample estimate of variance and the
two-sample t-test. The paired-sample t-test.
- Use of the x2 distribution and tables; the x2-testl
contingency tables
- Bivariate samples: scatter diagrams; linear (product moment)
correlation coefficient (r), regression coefficient (b),
regression lines and least squares. Confidence limits for regression
coefficient ß.
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