Preparation for GCSE and A-level exams
in Peterborough
Whether you are preparing for GCSE or A-level exams, you can rely on t Patricia Mogose Maths Tutor in Peterborough. I offer personalised maths tuitions at affordable rates. You can also contact me for primary and secondary school maths tuition.
Professional tutor
GCSE maths tuition
BSc Honours and PGCE qualified
The Foundation level covers:
Foundation tier students sit the GCSE exam at the end of Year 11 and exam grades fall between 1 – 5. They will take 3 exams, one of which is a non-calculator paper, and the the other 2 are calculator papers. The exam will focus on material learnt in previous years, as well as the new work they will cover in the last 2 years, as follows:
- Standard Index form: mental and calculator
- Working with fractions in ratio problems
- Find exact solutions in terms of pi
- Use inequality notation to express error intervals
- Understand limits of accuracy in calculations
- Substitute numerical values into expressions and forrmulae
- Recognise expressions, equations, formulae, terms and identities
- Work with surds
- Show algebraic expressions are equivalent
- Factorising simple expressions
- Expanding double brackets
- Solving equations with negative solutions
- Find approximate solutions and turning points of a quadratic function graphically
- Recognise cubic and reciprocal functions
- Work with graphs involving speed, distance, time and acceleration
- Extend sequences to recognise squares, cubes, Fibonacci-type and simple geometric sequences
- Use compound units of speed, density, pressure and rates of pay
- Percentage increase/decrease, simple interest and percentages more than 100%
- Growth, decay and compound interest
- Work with direct and inverse proportion
- Constructions and loci using compass and ruler
- Transformations: rotation by angle and direction, reflection in specified line, translation by vector, enlargement by scale factor, maybe fractional and the centre
- Circle: sector, segment, tangent and chord, arc length and sector area
- Plan and elevation of 3D shapes
- vectors: addition, subtraction, simple multiplication and graphical illustration
- Probability: relative frequency, combined events and tree diagrams
- Venn diagrams
- Statistics: samples and populations
- Pie charts, line graphs, scatter graphs, frequency diagrams, stem and leaf diagrams
- Interpret and calculate various statistical measures
Higher level topics:
Higher tier students sit the GCSE exam at the end of Year 11 and exam grades fall between 4 – 9. They will take 3 exams, one of which is a non-calculator paper, and the the other 2 are calculator papers. The exam will focus on material learnt in previous years, as well as the new work they will cover in the last 2 years. This will include all material described in the Foundation tier, and additional material as follows:
- Estimation of powers and roots for any positive number
- Work with fractional indices
- Further surd work involving rationalising a denominator
- Find the exact conversion of a recurring decimal as a fraction
- Determine upper and lower bounds of a calculation
- Simplify algebraic expressions involving surds and fractions
- Factorising more complex quadratic expressions
- Prove mathematically that 2 expressions are equivalent
- Inverse functions
- Identify and find equations for perpendicular and parallel lines
- Determine the turning point of a quadratic by completing the square
- Exponential and trigonometric graphs
- Transformation of graphs
- Areas under graphs
- Equation of a circle and of a tangent to a circle
- Solve quadratic equations by formula and square completion
- Solve simultaneous equations, one linear, one quadratic
- Approximate the solution to an equation by iteration
- Solve quadratic inequalities
- nth term of a quadratic sequence
- Gradients of curves
- Combined transformations
- Further circle theorems
- Using the relationship between area, length and volume in similar shapes
- Trigonometry in 3D shapes and non-right angled triangles
- Vectors in geometric proof
- Conditional probability
- Histograms
- Cumulative frequency