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• In this course students will learn exactly what they need to know for their high school maths exams using the GCSE maths and iGCSE maths curricula.
• This course covers many GCSE maths and IGCSE maths curricula including Cambridge CIE 0580 (Core & Extended) and Pearson Edexcel Maths A (Foundation & Higher)
• The details of the content covered are as follows:
• Use letters to express generalised numbers and express basic arithmetic processes algebraically. Substitute numbers for words and letters in formulae.
• Use letters to express generalised numbers and express basic arithmetic processes algebraically. Substitute numbers for words and letters in formulae.
• Rearrange simple formulae.
• Construct simple expressions and set up simple equations.
• Manipulate directed numbers. Use brackets and extract common factors.
• Expand products of algebraic expressions.
• Use and interpret positive, negative and zero indices. Use the rules of indices.
• Derive and solve simple linear equations in one unknown. Derive and solve simultaneous linear equations in two unknowns.
• Use letters to express generalised numbers and express basic arithmetic processes algebraically.
• Construct and rearrange complicated formulae and equations.
• Manipulate directed numbers. Use brackets and extract common factors.
• Expand products of algebraic expressions.
• Manipulate algebraic fractions. Factorise and simplify rational expressions.
• Use and interpret positive, negative and zero indices. Use and interpret fractional indices. Use the rules of indices.
• Derive and solve linear equations in one unknown. Derive and solve simultaneous linear equations in two unknowns.
• Derive and solve simultaneous equations, involving one linear and one quadratic.
• Derive and solve quadratic equations by factorisation, completing the square and by use of the formula. Derive and solve linear inequalities.
• Continue a given number sequence. Recognise patterns in sequences including the term to term rule and relationships between different sequences.
• Interpret and use graphs in practical situations including travel graphs and conversion graphs. Draw graphs from given data.
• Draw and interpret these graphs. Solve linear and quadratic equations approximately, including finding and interpreting roots by graphical methods.
• Recognise, sketch and interpret graphs of functions.
• Represent inequalities graphically and use this representation to solve simple linear programming problems.
• Continue a given number sequence. Recognise patterns in sequences including the term to term rule and relationships between different sequences.
• Express direct and inverse proportion in algebraic terms and use this form of expression to find unknown quantities.
• Interpret and use graphs in practical situations including travel graphs and conversion graphs. Draw graphs from given data.
• Apply the idea of rate of change to simple kinematics involving distance–time and speed–time graphs, acceleration and deceleration.
• Calculate distance travelled as area under a speed–time graph.
• Solve associated equations approximately, including finding and interpreting roots by graphical methods.
• Draw and interpret graphs representing exponential growth and decay problems. Recognise, sketch and interpret graphs of functions.
• Estimate gradients of curves by drawing tangents.
• Discriminate between maxima and minima by any method.
• Understand that symbols may be used to represent numbers in equations or variables in expressions and formulae.
• Understand that algebraic expressions follow the generalised rules of arithmetic.
• Use index notation for positive and negative integer powers (including zero).
• Use index laws in simple cases.
• Evaluate expressions by substituting numerical values for letters.
• Collect like terms.
• Multiply a single term over a bracket.
• Take out common factors.
• Expand the product of two simple linear expressions.
• Understand that a letter may represent an unknown number or a variable.
• Use correct notational conventions for algebraic expressions and formulae.
• Substitute positive and negative integers, decimals and fractions for words and letters in expressions and formulae.
• Use formulae from mathematics and other real-life contexts expressed initially in words or diagrammatic form and convert to letters and symbols.
• Derive a formula or expression.
• Change the subject of a formula where the subject appears once.
• Solve linear equations, with integer or fractional coefficients, in one unknown in which the unknown appears on either side or both sides of the equation.
• Set up simple linear equations from given data.
• Calculate the exact solution of two simultaneous equations in two unknowns.
• Solve quadratic equations by factorisation (limited to x2 + bx + c = 0).
• Understand and use the symbols >,<.
• Understand and use the convention for open and closed intervals on a number line.
• Solve simple linear inequalities in one variable and represent the solution set on a number line.
• Represent simple linear inequalities on rectangular Cartesian graphs.
• Identify regions on rectangular Cartesian graphs defined by simple linear inequalities.
• Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence.
• Find subsequent terms of an integer sequence and the rule for generating it.
• Use linear expressions to describe the nth term of arithmetic sequences.
• Interpret information presented in a range of linear and non-linear graphs.
• Understand and use conventions for rectangular Cartesian coordinates.
• Plot points (x, y) in any of the four quadrants or locate points with given coordinates.
• Determine the coordinates of points identified by geometrical information.
• Determine the coordinates of the midpoint of a line segment, given the coordinates of the two end points.
• Draw and interpret straight line conversion graphs.
• Find the gradient of a straight line.
• Recognise that equations of the form y = mx + c are straight line graphs with gradient m and intercept on the y-axis at the point (0, c).
• Recognise, generate points and plot graphs of linear and quadratic functions.
• Use index notation involving fractional, negative and zero powers.
• Expand the product of two or more linear expressions.
• Understand the concept of a quadratic expression and be able to factorise such expressions.
• Manipulate algebraic fractions where the numerator and/or the denominator can be numeric, linear or quadratic.
• Complete the square for a given quadratic expression.
• Use algebra to support and construct proofs.
• Understand the process of manipulating formulae or equations to change the subject.
• Set up problems involving direct or inverse proportion and relate algebraic solutions to graphical representation of the equations.
• Calculate the exact solution of two simultaneous equations in two unknowns.
• Interpret the equations as lines and the common solution as the point of intersection.
• Solve quadratic equations by factorisation.
• Solve quadratic equations by using the quadratic formula or completing the square.
• Form and solve quadratic equations from data given in a context.
• Solve simultaneous equations in two unknowns, one equation being linear and the other being quadratic.
• Solve quadratic inequalities in one unknown and represent the solution set on a number line.
• Identify harder examples of regions defined by linear inequalities.
• Understand and use common difference (d) and first term (a) in an arithmetic sequence.
• Know and use nth term =+ − an d.
• Find the sum of the first n terms of an arithmetic series (Sn).
• Understand the concept that a function is a mapping between elements of two sets.
• Understand the terms ‘domain’ and ‘range’ and which values may need to be excluded from a domain.
• Understand and find the composite function fg and the inverse function f -1.
• Recognise, plot and draw graphs.
• Apply to the graph of y = f(x) the transformations y = f(x) + a, y = f(ax), y = f(x + a), y = af(x) for linear, quadratic, sine and cosine functions.
• Interpret and analyse transformations of functions and write the functions algebraically.
• Find the gradients of non-linear graphs.
• Find the intersection points of two graphs, one linear 1 ( ) y and one non-linear 2 ( ) y , and and recognise that the solutions.
• Calculate the gradient of a straight line given the coordinates of two points.
• Find the equation of a straight line parallel to a given line; find the equation of a straight line perpendicular to a given line.
• Understand the concept of a variable rate of change.
• Differentiate integer powers of x.
• Determine gradients, rates of change, stationary points, turning points (maxima and minima) by differentiation and relate these to graphs.
• Distinguish between maxima and minima by considering the general shape of the graph only.
• Apply calculus to linear kinematics and to other simple practical problems.