British (UK)

The National Curriculum of England (UK) is a very structured curriculum that is designed to meet the needs of all students, stretching brighter children and supporting those who need it through differentiated teaching and learning activities. The curriculum extends and excites all students, whatever their interests or ability. Through it, teachers are able to identify, celebrate and nurture the talents and intelligences of students.

British education is renowned for concerning itself with the development of the whole personality.

In the British education system, students are taught to learn by questioning, problem-solving and creative thinking rather than by the mere retention of facts, hence giving them analytical and creative thinking skills that they will need in the working world. A variety of teaching and assessment methods designed to develop independent thought as well as a mastery of the subject matter is used.

The National Curriculum of England has a clearly defined series of academic and other objectives at every level. mydrasa focuses on Key stage 3 (Year 7-9), Key stage 4 IGCSE/GCSE (Year 10-11) and Key stage 5 A-Level (Year 12-13).

mydrasa added subjects related to Key stage 4 to Year 9, and added subjects related to Key stage 5 to Year 11 for student preparation.

IGCSE stands for the "International General Certificate of Secondary Education". It is a program leading to externally set, marked and certificated examinations from the University of Cambridge. Any student who takes an IGCSE subject will be gaining a qualification that is recognized globally.

The exam boards covered under the International GCSE are Cambridge, Edexcel, and Oxford AQA.

SUbjects

Subjects

Edexcel - Further Mathematics - AL - YFM01

  • Overview
  • Chapters

The Pearson Edexcel International Advanced Subsidiary in Mathematics, Further Mathematics and Pure Mathematics and the Pearson Edexcel International Advanced Level in Mathematics, Further Mathematics and Pure Mathematics are modular qualifications.

The Advanced Subsidiary and Advanced Level qualifications can be claimed on completion of the required units, as detailed in the Qualification overview section.


Content

• A variety of 14 equally weighted units allowing many different combinations, resulting in flexible delivery options.

• Core mathematics content separated into four Pure Mathematics units.

• From the legacy qualification:

o Decision Mathematics 1 has been updated for a more balanced approach to content.

o The Further, Mechanics and Statistics units have not changed.


Assessment

• Fourteen units tested by written examination.

• Pathways leading to International Advanced Subsidiary Level and International Advanced Level in Mathematics, Further Mathematics and Pure Mathematics.

  • 1: Unit FP1: Further Pure Mathematics 1
    1.1: Complex numbers
    1.1.1: Definition of complex numbers
    1.1.2: Sum, product and quotient of complex numbers
    1.1.3: Geometrical representation of complex numbers
    1.1.4: Complex solutions of quadratic equations
    1.1.5: Conjugate complex roots and a real root of a cubic equation
    1.1.6: Finding conjugate complex roots and/or real roots of a quartic equation
    1.2: Roots of quadratic equations
    1.2.1: Sum of roots and product of roots of a quadratic equation
    1.2.2: Manipulation of expressions
    1.2.3: Forming quadratic equations with new roots
    1.3: Numerical solution of equations
    1.3.1: Equations of the form f(x) = 0
    1.4: Coordinate systems
    1.4.1: Cartesian equations
    1.4.2: Idea of parametric equation
    1.4.3: The focus-directrix property of the parabola
    1.4.4: Tangents and normals to these curves
    1.5: Matrix algebra integration
    1.5.1: Addition and subtraction of matrices
    1.5.2: Multiplication of a matrix by a scalar
    1.5.3: Products of matrices
    1.5.4: Evaluation of 2 × 2 determinants
    1.5.5: Inverse of 2 × 2 matrices
    1.6: Transformations using matrices
    1.6.1: Linear transformations of column vectors in two dimensions
    1.6.2: Geometrical transformations
    1.6.3: Combinations of transformations
    1.6.4: The inverse (when it exists) of a given transformation
    1.7: Series
    1.7.1: Summation of simple finite series
    1.8: Proof
    1.8.1: Proof by mathematical induction
  • 2: Unit FP2: Further Pure Mathematics 2
    2.1: Inequalities
    2.1.1: The manipulation and solution of algebraic inequalities
    2.2: Series
    2.2.1: Summation of simple finite series using the method of differences
    2.3: Further complex numbers
    2.3.1: Euler’s relation
    2.3.2: De Moivre’s theorem
    2.3.3: Elementary transformations
    2.4: First order differential equations
    2.4.1: Further solution of first order differential equations
    2.4.2: linear differential equations
    2.4.3: Differential equations
    2.5: Second order differential equations
    2.5.1: The linear second order differential equation
    2.5.2: Differential equations reducible to the above types
    2.6: Maclaurin and Taylor series
    2.6.1: Third and higher order derivatives
    2.6.2: Derivation and use of Maclaurin series
    2.6.3: Derivation and use of Taylor series
    2.6.4: Use of Taylor series method for series solutions of differential equations
    2.7: Polar coordinates
    2.7.1: Polar coordinates
    2.7.2: Use of the formula for area
  • 3: Unit FP3: Further Pure Mathematics 3
    3.1: Hyperbolic functions
    3.1.1: The six hyperbolic functions
    3.1.2: Inverse hyperbolic functions
    3.2: Further coordinate systems
    3.2.1: Cartesian and parametric equations
    3.2.2: The focus-directrix properties
    3.2.3: Tangents and normals
    3.2.4: Simple loci problems
    3.3: Differentiation
    3.3.1: Differentiation of hyperbolic functions
    3.3.2: Differentiation of inverse functions
    3.4: Integration
    3.4.1: Integration of hyperbolic functions
    3.4.2: Integration of inverse trigonometric and hyperbolic functions
    3.4.3: Integration using hyperbolic and trigonometric substitutions
    3.4.4: Substitution for integrals
    3.4.5: The derivation and use of simple reduction formulae
    3.4.6: The calculation of arc length and the area of a surface of revolution
    3.5: Vectors
    3.5.1: The vector product a × b and the triple scalar product a . b × c
    3.5.2: Use of vectors in problems involving points, lines and planes
    3.5.3: The equation of a plane
    3.6: Further matrix algebra
    3.6.1: Linear transformations of column vectors
    3.6.2: Combination of transformations.
    3.6.3: Transpose of a matrix
    3.6.4: Evaluation of 3 × 3 determinants
    3.6.5: Inverse of 3 × 3 matrices
    3.6.6: The inverse of a given transformation
    3.6.7: Eigenvalues and eigenvectors of 2 × 2 and 3 × 3 matrices
    3.6.8: Reduction of symmetric matrices to diagonal form
  • 4: Unit M1: Mechanics 1
    4.1: Mathematical models in mechanics
    4.1.1: The basic ideas of mathematical modelling as applied in Mechanics
    4.2: Vectors in mechanics
    4.2.1: Magnitude and direction of a vector
    4.2.2: Application of vectors
    4.3: Kinematics of a particle moving in a straight line
    4.3.1: Motion in a straight line with constant acceleration
    4.4: Dynamics of a particle moving in a straight line or plane
    4.4.1: The concept of a force
    4.4.2: Simple applications including the motion of two connected particles
    4.4.3: Momentum and impulse
    4.4.4: Coefficient of friction.
    4.5: Statics of a particle
    4.5.1: Forces treated as vectors
    4.5.2: Equilibrium of a particle under coplanar forces
    4.5.3: Coefficient of friction
    4.6: Moments
    4.6.1: Moment of a force.
  • 5: Unit M2: Mechanics 2
    5.1: Kinematics of a particle moving in a straight line or plane
    5.1.1: Motion in a vertical plane with constant acceleration
    5.1.2: Simple cases of motion of a projectile
    5.1.3: Velocity and acceleration when the displacement is a function of time
    5.1.4: Differentiation and integration of a vector with respect to time
    5.2: Centres of mass
    5.2.1: Centre of mass of a discrete mass distribution
    5.2.2: Centre of mass of uniform plane figures
    5.2.3: Simple cases of equilibrium of a plane lamina.
    5.3: Work and energy
    5.3.1: Kinetic and potential energy, work and power
    5.4: Collisions
    5.4.1: Momentum as a vector
    5.4.2: Direct impact of elastic particles
    5.4.3: Successive impacts of up to three particles and a smooth plane surface
    5.5: Statics of rigid bodies
    5.5.1: Moment of a force
    5.5.2: Equilibrium of rigid bodies
  • 6: Unit M3: Mechanics 3
    6.1: Further kinematics
    6.1.1: Kinematics of a particle moving in a straight line
    6.2: Elastic strings and springs
    6.2.1: Elastic strings and springs
    6.2.2: Energy stored in an elastic string or spring
    6.3: Further dynamics
    6.3.1: Newton’s laws of motion
    6.3.2: Simple harmonic motion
    6.3.3: Oscillations of a particle attached to the end of an elastic string or spring
    6.4: Motion in a circle
    6.4.1: Angular speed
    6.4.2: Radial acceleration in circular motion
    6.4.3: Uniform motion of a particle moving in a horizontal circle
    6.4.4: Motion of a particle in a vertical circle
    6.5: Statics of rigid bodies
    6.5.1: Centre of mass of uniform rigid bodies and simple composite bodies
    6.5.2: Simple cases of equilibrium of rigid bodies
  • 7: Unit S1: Statistics 1
    7.1: Mathematical models in probability and statistics
    7.1.1: The basic ideas of mathematical modelling
    7.2: Representation and summary of data
    7.2.1: Histograms, stem and leaf diagrams, box plots
    7.2.2: Measures of location – mean, median, mode
    7.2.3: Measures of dispersion
    7.2.4: Skewness. Concepts of outliers
    7.3: Probability
    7.3.1: Elementary probability
    7.3.2: Exclusive and complementary events
    7.3.3: Independence of two events
    7.3.4: Sum and product laws
    7.4: Correlation and regression
    7.4.1: Scatter diagrams. Linear regression
    7.4.2: Explanatory (independent) and response (dependent) variables
    7.4.3: The product moment correlation coefficient
    7.5: Discrete random variables
    7.5.1: The concept of a discrete random variable
    7.5.2: The probability function and the cumulative distribution function
    7.5.3: Mean and variance of a discrete random variable
    7.5.4: The discrete uniform distribution
    7.6: The Normal distribution
    7.6.1: The Normal distribution including the mean, variance
  • 8: Unit S2: Statistics 2
    8.1: The Binomial and Poisson distributions
    8.1.1: The binomial and Poisson distributions
    8.1.2: The mean and variance of the binomial and Poisson distributions
    8.1.3: The use of the Poisson distribution
    8.2: Continuous random variables
    8.2.1: The concept of a continuous random variable
    8.2.2: The probability density function and the cumulative distribution function
    8.2.3: Relationship between density and distribution functions
    8.2.4: Mean and variance of continuous random variable
    8.2.5: Mode, median and quartiles of continuous random variables
    8.3: Continuous distributions
    8.3.1: The continuous uniform (rectangular) distribution
    8.3.2: Use of the Normal distribution
    8.4: Hypothesis tests
    8.4.1: Population, census and sample. Sampling unit, sampling frame
    8.4.2: Concepts of a statistic and its sampling distribution
    8.4.3: Concept and interpretation of a hypothesis test
    8.4.4: Critical region
    8.4.5: One-tailed and two-tailed tests
    8.4.6: Hypothesis tests
  • 9: Unit S3: Statistics 3
    9.1: Combinations of random variables
    9.1.1: Distribution of linear combinations of independent Normal random variables
    9.2: Sampling
    9.2.1: Methods for collecting data
    9.2.2: Other methods of sampling
    9.3: Estimation, confidence intervals and tests
    9.3.1: Concepts of standard error, estimator, bias
    9.3.2: The distribution of the sample mean
    9.3.3: Concept of a confidence interval and its interpretation
    9.3.4: Confidence limits for a Normal mean, with variance known
    9.3.5: Hypothesis tests for the mean of a Normal distribution with variance known
    9.3.6: Use of Central Limit theorem
    9.3.7: Hypothesis test for the difference between the means
    9.3.8: Use of large sample results
    9.4: Goodness of fit and contingency tables
    9.4.1: The null and alternative hypotheses
    9.4.2: Degrees of freedom
    9.5: Regression and correlation
    9.5.1: Spearman’s rank correlation coefficient
    9.5.2: Testing the hypothesis that a correlation is zero
  • 10: Unit D1: Decision Mathematics 1
    10.1: Algorithms
    10.1.1: The general ideas of algorithms
    10.1.2: Bin packing, bubble sort, quick sort, binary search
    10.2: Algorithms on graphs
    10.2.1: The minimum spanning tree
    10.2.2: Dijkstra’s algorithm for finding the shortest path
    10.3: Algorithms on graphs II
    10.3.1: Algorithm for finding the shortest route around a network
    10.3.2: The practical and classical Travelling Salesman problems
    10.3.3: Determination of upper and lower bounds using minimum spanning tree methods
    10.3.4: The nearest neighbour algorithm
    10.4: Critical path analysis
    10.4.1: Modelling of a project by an activity network
    10.4.2: Completion of the precedence table for a given activity network
    10.4.3: Algorithm for finding the critical path
    10.4.4: Total float. Gantt (cascade) charts. Scheduling
    10.5: Linear programming
    10.5.1: Formulation of problems as linear programs
    10.5.2: Graphical solution of two variable problems
    10.5.3: Consideration of problems where solutions must have integer values

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