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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.


  • Polynomial functions and equations; graphical representation
  • Simple rational algebraic functions and their graphs
  • Summation of finite series
  • Further mathematical induction


  • 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


  • 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


  • 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.


  • 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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