 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 �.

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