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GCE Advanced Level Further Mathematics Curriculum For 11th Grade And 12th Grade / GCE A LevelOur 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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