Patricia Mogose Maths Tutor

In Year 10 preparation for sitting the GCSE examination begins.
Students sit one of two levels of exam depending on ability: Foundation or Higher.
If the Foundation tier is taken, grades G to C are possible

If the Higher tier is taken, grades D to A* are possible

The additional work covered, beyond that studied up to Year 9, for each of the 2 tiers is as follows:

Foundation Level:

• Standard Index form: mental and calculator
• Transformations: Rotation by specified angle and direction, Reflection in specified line, Translation by specified direction, Enlargement by specified scale factor and centre
• Perform basic constructions
• Constructing Loci
• Parts of circle: sector and segment
• Calculate surface area of simple 3D shapes
• Use fractional scale factors in enlargement
• Analyse formulae by considering dimensions specified
• Density, mass and volume calculations
• Factorising simple expressions
• Expanding double brackets
• Solving equations with negative solutions
• Find approximate solutions to a quadratic function through its graph
• Data collection techniques
• Pie charts, line graphs, scatter graphs, frequency diagrams, stem and leaf diagrams

Higher Level:

Fractional and negative indices: mental and calculator
Percentage: compound and simple interest, find original amount after percentage increase or decrease
Surds

• Inverse proportion
• Rationalise a denominator
• Find upper and lower bounds in calculations
• Solving linear equations with fractional coefficients and producing fractional and negative solutions
• Solve more than one linear inequaliity and express graphically
• Solving quadratic equations by factorising, completing the square and use of the formula
• Solving a pair of simultaneous equations, one linear, one quadratic or circular
• by algebraic and graphical means
• Plot cubic, reciprocal, exponential, circular, sin x and cos x functions
• Apply the tranformations, translation, reflection and stretch to linear, quadratic, sine and cosine functions
• Use Pythagoras and trigonometry in 3D problems
• Circle theorems: radius meets tangent at 90, angle in semi circle is 90, equal tangents, perpedicular chord bisector, same segment, angle at centre, cyclic quadrilateral, alternate segment
• Surface areas of further prisms, e.g. cylinder
• Problem solving involving pyramids, spheres and cones including segments of circles and frustums of cones
• Transformations using negative scale factors
• Solve problems involving the effects of enlargements on 2D and 3D shapes
• Use trigonometry for problems involving non-right angles triangles, including finding the area
• Calculate and represent graphically the sum and difference of two vectors, also the scalar multiple of a vector
• Solve 2D problems using vectors
• Problems involving arcs and sectors of circles
• Cumulative frequency tables, diagrams and box plots, find median and interquartile range
• Moving averages
• Use tree diagrams for calculating probabilities
• Data sampling methods
• Histograms