**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