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

Cambridge - Mathematics - 9709

  • Overview
  • Chapters

Cambridge International A Level Mathematics develops a set of transferable skills. These include the skill of working with mathematical information, as well as the ability to think logically and independently, consider accuracy, model situations mathematically, analyse results and reflect on findings.

  • 1: Pure Mathematics 1
    1.1: Quadratics
    1.1.1: Carry out the process of completing the square
    1.1.2: Find the discriminant of a quadratic polynomial
    1.1.3: Solve quadratic equations, and quadratic inequalities, in one unknown
    1.1.4: Solve by substitution a pair of simultaneous equations
    1.1.5: Recognise and solve equations in x which are quadratic in some function of x
    1.2: Functions
    1.2.1: Understand the terms function, domain, range
    1.2.2: Identify the range of a given function in simple cases
    1.2.3: Determine whether or not a given function is one-one
    1.2.4: The relation between a one-one function and its inverse
    1.2.5: Understand and use the transformations of the graph of y = f(x)
    1.3: Coordinate geometry
    1.3.1: Find the equation of a straight line given sufficient information
    1.3.2: The forms y = mx + c, y – y1 = m(x – x1), ax + by + c = 0 in solving problems
    1.3.3: The equation (x – a) 2 + (y – b) 2 = r 2
    1.3.4: Use algebraic methods to solve problems involving lines and circles
    1.3.5: Understand the relationship between a graph & its associated algebraic equation
    1.4: Circular measure
    1.4.1: The definition of a radian, and use the relationship between radians and degrees
    1.4.2: Use the formulae s r A r 2 1 and 2 = = i i in solving problems
    1.5: Trigonometry
    1.5.1: Sketch and use graphs of the sine, cosine and tangent functions
    1.5.2: Use the exact values of the sine, cosine and tangent of 30°, 45°, 60°
    1.5.3: Use the notations sin-1 x, cos-1 x, tan-1 x
    1.5.4: Use identities
    1.5.5: The solutions of simple trigonometrical equations lying in a specified interval
    1.6: Series
    1.6.1: Use the expansion of (a + b) n , where n is a positive integer
    1.6.2: Recognise arithmetic and geometric progressions
    1.6.3: Use the formulae for the nth term and for the sum of the first n terms
    1.6.4: Use the condition for the convergence of a geometric progression
    1.7: Differentiation
    1.7.1: Understand the gradient of a curve at a point as the limit of the gradients
    1.7.2: Use the derivative of xn (for any rational n)
    1.7.3: Apply differentiation to gradients, tangents and normals
    1.7.4: Locate stationary points and determine their nature
    1.8: Integration
    1.8.1: Understand integration as the reverse process of differentiation
    1.8.2: Solve problems involving the evaluation of a constant of integration
    1.8.3: Evaluate definite integrals
    1.8.4: Use definite integration
  • 2: Pure Mathematics 2
    2.1: Algebra
    2.1.1: Understand the meaning of |x|, sketch the graph of y = |ax + b|
    2.1.2: Divide a polynomial, of degree not exceeding 4
    2.1.3: Use the factor theorem and the remainder theorem
    2.2: Logarithmic and exponential functions
    2.2.1: The relationship between logarithms and indices, and use the laws of logarithms
    2.2.2: Understand the definition and properties of e x and lnx
    2.2.3: Use logarithms to solve equations
    2.2.4: Use logarithms to transform a given relationship to linear form
    2.3: Trigonometry
    2.3.1: The secant, cosecant & cotangent functions to cosine, sine & tangent
    2.3.2: Use trigonometrical identities for the simplification
    2.4: Differentiation
    2.4.1: Use the derivatives of e x , ln x, sinx, cos x, tan x
    2.4.2: Differentiate products and quotients
    2.4.3: Find and use the first derivative of a function
    2.5: Integration
    2.5.1: Extend the idea of ‘reverse differentiation’
    2.5.2: Use trigonometrical relationships in carrying out integration
    2.5.3: Understand & use the trapezium rule to estimate the value of a definite integral
    2.6: Numerical solution of equations
    2.6.1: Locate approximately a root of an equation
    2.6.2: Understand the idea of, and use the notation for, a sequence of approximations
    2.6.3: Simple iterative formula of the form xn+1 = F (xn)
  • 3: Pure Mathematics 3
    3.1: Algebra
    3.1.1: Understand the meaning of |x|, sketch the graph of y = |ax + b|.
    3.1.2: Divide a polynomial, of degree not exceeding 4.
    3.1.3: Use the factor theorem and the remainder theorem.
    3.1.4: Recall an appropriate form for expressing rational functions
    3.1.5: Use the expansion of (1 + x) n
    3.2: Logarithmic and exponential functions
    3.2.1: Understand the relationship between logarithms and indices
    3.2.2: Understand the definition and properties of e x & lnx
    3.2.3: Use logarithms to solve equations and inequalities
    3.2.4: Use logarithms to transform a given relationship to linear form.
    3.3: Trigonometry
    3.3.1: The relationship of the secant, cosecant and cotangent functions to cosine
    3.3.2: Use trigonometrical identities for the simplification of expressions
    3.4: Differentiation
    3.4.1: Use the derivatives of ex , ln x , sin x, cos x, tan x, tan-1 x
    3.4.2: Differentiate products & quotients
    3.4.3: Find & use the first derivative of a function
    3.5: Integration
    3.5.1: Extend the idea of "reverse differentiation"
    3.5.2: Use trigonometrical relationships in carrying out integration.
    3.5.3: Integrate rational functions by means of decomposition into partial fractions
    3.5.4: Recognise an integrand of the form kf'(x)\f(x)
    3.5.5: Recognise when an integrand can usefully be regarded as a product
    3.5.6: Use a given substitution to simplify and evaluate
    3.6: Numerical solution of equations
    3.6.1: Locate approximately a root of an equation.
    3.6.2: Understand the idea of, & use the notation for, a sequence of approximations
    3.6.3: Simple iterative formula of the form xn + 1 = F(xn)
    3.7: Vectors
    3.7.1: Use standard notations for vectors
    3.7.2: Carry out addition and subtraction of vectors & multiplication of a vector
    3.7.3: Calculate the magnitude of a vector
    3.7.4: Understand the significance of all the symbols
    3.7.5: Determine whether two lines are parallel, intersect or are skew
    3.7.6: Use formulae to calculate the scalar product of two vectors
    3.8: Differential equations
    3.8.1: Formulate a simple statement involving a rate of change
    3.8.2: Find by integration a general form of solution for a differential equation
    3.8.3: Use an initial condition to find a particular solution
    3.8.4: Interpret the solution of a differential equation
    3.9: Complex numbers
    3.9.1: Understand the idea of a complex number
    3.9.2: Operations of addition, subtraction, multiplication & division
    3.9.3: Use the result that, for a polynomial equation with real coefficients
    3.9.4: Represent complex numbers geometrically by means of an Argand diagram
    3.9.5: Carry out operations of multiplication and division of two complex numbers
    3.9.6: Find the two square roots of a complex number
    3.9.7: The geometrical effects of conjugating a complex number
    3.9.8: Illustrate simple equations and inequalities involving complex numbers
  • 4: Mechanics
    4.1: Forces and equilibrium
    4.1.1: Identify the forces acting in a given situation
    4.1.2: Understand the vector nature of force, & find and use components and resultants
    4.1.3: Use the principle that, when a particle is in equilibrium
    4.1.4: Contact force between two surfaces can be represented by two components
    4.1.5: Use the model of a ‘smooth’ contact, & understand the limitations of this model
    4.1.6: Understand the concepts of limiting friction and limiting equilibrium
    4.1.7: Use Newton’s third law
    4.2: Kinematics of motion in a straight line
    4.2.1: Understand the concepts of scalar quantities & vector quantities
    4.2.2: Sketch and interpret displacement–time graphs and velocity–time graphs
    4.2.3: Use differentiation & integration with respect to time to solve simple problems
    4.2.4: Use appropriate formulae for motion with constant acceleration
    4.3: Momentum
    4.3.1: Use the definition of linear momentum & show understanding of its vector nature
    4.3.2: Use conservation of linear momentum to solve problems
    4.4: Newton’s laws of motion
    4.4.1: Apply Newton’s laws of motion to the linear motion
    4.4.2: Use the relationship between mass and weight
    4.4.3: Solve simple problems which may be modelled as the motion of a particle
    4.4.4: Solve simple problems which may be modelled as the motion of connected particles
    4.5: Energy, work and power
    4.5.1: Understand the concept of the work done by a force
    4.5.2: Understand the concepts of gravitational potential energy and kinetic energy
    4.5.3: The change in energy of a system & the work done by the external force
    4.5.4: Use the definition of power as the rate at which a force does work
    4.5.5: The instantaneous acceleration of a car moving on a hill against a resistance
  • 5: Probability & Statistics 1
    5.1: Representation of data
    5.1.1: Select a suitable way of presenting raw statistical data
    5.1.2: Draw and interpret stem-and-leaf diagrams, boxand-whisker plots, histograms
    5.1.3: Understand & use different measures of central tendency and variation
    5.1.4: Use a cumulative frequency graph
    5.1.5: Calculate and use the mean and standard deviation of a set of data
    5.2: Permutations and combinations
    5.2.1: Understand the terms permutation and combination
    5.2.2: Solve problems about arrangements of objects in a line
    5.3: Probability
    5.3.1: Evaluate probabilities in simple cases
    5.3.2: Use addition & multiplication of probabilities, as appropriate, in simple cases
    5.3.3: Understand the meaning of exclusive and independent events
    5.3.4: Calculate and use conditional probabilities in simple cases
    5.4: Discrete random variables
    5.4.1: Draw up a probability distribution table relating to a given situation
    5.4.2: Use formulae for probabilities for the binomial and geometric distributions
    5.4.3: Use formulae for the expectation and variance of the binomial distribution
    5.5: The normal distribution
    5.5.1: The use of a normal distribution to model a continuous random variable
    5.5.2: Solve problems concerning a variable X
    5.5.3: Normal distribution can be used as an approximation to the binomial distribution
  • 6: Probability & Statistics 2
    6.1: The Poisson distribution
    6.1.1: Use formulae to calculate probabilities
    6.1.2: Use facts
    6.1.3: The relevance of the Poisson distribution to the distribution of random events
    6.1.4: Use the Poisson distribution as an approximation to the binomial distribution
    6.1.5: Use the normal distribution, as an approximation to the Poisson distribution
    6.2: Linear combinations of random variables
    6.2.1: Use, when solving problems, that results
    6.3: Continuous random variables
    6.3.1: Understand the concept of a continuous random variable
    6.3.2: Use a probability density function to solve problems involving probabilities
    6.4: Sampling and estimation
    6.4.1: Understand the distinction between a sample and a population
    6.4.2: Explain in simple terms why a given sampling method may be unsatisfactory
    6.4.3: Recognise that a sample mean can be regarded as a random variable
    6.4.4: Use the fact that (X) has a normal distribution if X has a normal distribution
    6.4.5: Use the Central Limit Theorem where appropriate
    6.4.6: Calculate unbiased estimates of the population mean and variance from a sample
    6.4.7: Determine and interpret a confidence interval for a population mean
    6.4.8: Determine an approximate confidence interval for a population proportion
    6.5: Hypothesis tests
    6.5.1: Understand the nature of a hypothesis test
    6.5.2: Formulate hypotheses and carry out a hypothesis test
    6.5.3: Carry out a hypothesis test concerning the population mean
    6.5.4: The terms Type I error and Type II error in relation to hypothesis tests
    6.5.5: Calculate the probabilities of making Type I and Type II errors

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