Nottingham High School


		Schemes of Work

		6.1 Mechanics

		6.1 Statistics

		6.1 Pure

		6.2 Mechanics

		6.2 Statistics

		6.2 Pure

		Further Maths

		Year 7 Teaching Summary

		Year 8 Teaching Summary

		Year 9 Teaching Summary

		Year 10 and 11 Teaching Summary

Home : Senior School : Academic Departments : Maths : Schemes of Work : Year 10 and 11 Teaching Summary

Year 10 and 11 Teaching Summary

Year 10/11 Teaching Summary

Statistics and Probability I
Mean, median and mode, Collecting data, Discrete and continuous data, Grouping data, Histograms with unequal class widths, Mean, Median and Mode of a distribution, Using a calculator to find means, Stem and Leaf diagrams.	The terms : census, sample, random sample, stratified sample. Area scales drawn on histograms. Use of mid-points in grouped data.
Algebra I
Basic factorising, Expansion of brackets, Simplifying fractions, Solving equations, Rearranging formulae, Multiplying out pairs of brackets, Perfect squares and difference between two squares, Direct, inverse and non-linear proportion, Index form, Finding rational powers without a calculator.	Revision of Year 9 work. Use of the a symbol to mean “is proportional to”. .
Trigonometry I
Use of three main ratios in solving problems involving right-angled triangles.	Revision of Year 9 work.
Statistics II
Measures of spread, Upper and lower quartiles, Median, Boxplots, Scatter Diagrams, Cumulative frequency curves, Standard Deviation, Questionnaires, Comparing Distributions	Range and Interquartile range. Standard deviation on a calculator (no use of formula – no longer on syllabus). Skew and Normal distribution shape.
Graphs I
Graphs of the form y = mx + c, y = ax²+ bx + c, y = a/(x-b) + c and , Use of graphs to solve simultaneous equations, Shading regions satisfying linear inequalities.	Revision of Year 9 work. The term asymptote.
End of First Term
(The next two sections are interchangeable.)
Graphs II
Distance-time and speed-time graphs, Drawing and using tangents to non-linear graphs, Exponential growth and decay, Use of a given graph to solve an equation by drawing another line, Transformations of graphs, Sketching graphs using transformations, Use of factorised forms of quadratics and cubics to produce sketches.	Significance of gradients (not area yet). Transformations such as y = f(x) + k, y = f(x+ k), y =kf(x), y = f(kx)

Algebra II
Solution of simultaneous equations, Problem solving, Factorising quadratics, Solving quadratics by factorising and use of formula, Problem solving.	Elimination and substitution methods. Quadratics such as 3x² – 2x - 16

Vectors
Vector quantities, Vectors given as columns and as size and direction, Displacement and position vectors, Multiplication by scalar and addition/subtraction, Parallel and equivalent vectors, Use in geometric problems, Magnitude and direction of a column vector.	Vectors only met to define translations previously.
Geometry I
Areas and perimeters, A = ½ ab sinc for a triangle, Length of arcs, Area of sectors, Surface area and volume, Dimension of a formula, Conditions for congruent triangles, Use of congruent triangles in geometric problems, Ratios between lengths, areas and volumes for similar solids.	Revision of Year 9 work. New shapes : Pyramid, Cone, Sphere.
End of Year 10 – Intermediate set follow different course in Year 11
Geometry II
Loci and constructions.	Some introduced to this in Year 9. Perpendicular and angle bisectors. Constructions of angles without protractors.
Sequences and Iteration
Flow charts, Arithmetic and geometric progressions, Recurrence relations, Difference method, Trial and improvement solutions, Convergence, divergence and oscillation of infinite series, Graphical approaches, Paradoxes with infinite series.	Formulae for nth terms : u_n = a + (n – 1) d and u_n = ar^n-1 Formulae by patterns in differences for quadratic and cubic sequences. Use of spreadsheet to look at convergence.
Probability II
Probability, Tree Diagrams.	Independent and mutually exclusive events. The law P(A or B) = P(A) + P(B) – P(A and B) for non-mutually exclusive events.

Matrix Transformations
Transformation review, Composite and inverse transformations, Adding and subtracting matrices, Multiplying by scalars, Multiplying two matrices, Matrices to describe transformations, Finding transformation matrices, Inverse matrices.	The notations Afor a transformation, AB for B followed by A and A^-1 for the inverse of A.
Trigonometry II
Trigonometric ratios for any angle, Graphs of sine, cosine and tangent, Sine rule and cosine rule, Problems in 2D and 3D, Solving simple trigonometric equations, Transformations of trigonometric graphs.	Use of CAST diagram. Including the ambiguous case for sine rule.
Circle Geometry
Angle properties of a circle, Constructions.	Chords, semicircles, angles at centre, alternate segment.
Travel Graphs
Speed-time and distance-time graphs, Area under speed time graph, Underestimate and overestimate for areas by rectangles, Trapezium rule.
Rational Numbers and Accuracy
Rational numbers, Irrational numbers, Percentage error.
End of Year 11

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Trigonometry I

Statistics II

Measures of spread, Upper and lower quartiles, Median, Boxplots, Scatter Diagrams, Cumulative frequency curves, Standard Deviation, Questionnaires, Comparing Distributions

Graphs I

End of First Term

(The next two sections are interchangeable.)

Graphs II

Algebra II

Geometry I

End of Year 10 – Intermediate set follow different course in Year 11

Geometry II

Sequences and Iteration

Flow charts, Arithmetic and geometric progressions, Recurrence relations, Difference method, Trial and improvement solutions, Convergence, divergence and oscillation of infinite series, Graphical approaches, Paradoxes with infinite series.

Formulae for nth terms : un = a + (n – 1) d and un = arn-1

Probability II

Probability, Tree Diagrams.

Matrix Transformations

Transformation review, Composite and inverse transformations, Adding and subtracting matrices, Multiplying by scalars, Multiplying two matrices, Matrices to describe transformations, Finding transformation matrices, Inverse matrices.

The notations Afor a transformation, AB for B followed by A and A-1 for the inverse of A.

Trigonometry II

Trigonometric ratios for any angle, Graphs of sine, cosine and tangent, Sine rule and cosine rule, Problems in 2D and 3D, Solving simple trigonometric equations, Transformations of trigonometric graphs.

Use of CAST diagram.

Circle Geometry

Angle properties of a circle, Constructions.

Chords, semicircles, angles at centre, alternate segment.

Travel Graphs

Speed-time and distance-time graphs, Area under speed time graph, Underestimate and overestimate for areas by rectangles, Trapezium rule.

Rational Numbers and Accuracy

Rational numbers, Irrational numbers, Percentage error.

End of Year 11

Formulae for nth terms : u_n = a + (n – 1) d and u_n = ar^n-1

The notations Afor a transformation, AB for B followed by A and A^-1 for the inverse of A.