Maths – Key Stage 4

Year 9

Half TermTopics to be coveredKey skills covered
Autumn HT 11. Integers
2. Decimals
3. Fractions
4. Percentages
1. Ordering integers, decimals including inequality notation.
2. Converting between fractions decimals and percentages.
3. Four operations with integers, decimals and fractions.
4. Calculating percentages of amounts, percentage change, simple interest, compound interest and decay and reverse percentages.
Autumn HT 21. Number types.
2. Factors, multiples and primes.
3. Rounding and estimation.
4. Bounds.
5. Indices
6. Standard form
7. Surds
1. Identify factors, multiples, primes, squares, cubes and associated roots.
2. Round to a specified degree of accuracy and use to estimate calculations or calculate bounds.
3. Apply laws of indices to simplifying expressions and calculating in standard form.
4. Apply know of square roots and square numbers to simplifying surds.
Spring HT 11. Ratio
2. Proportion
3. Shape
1. Express ratio in its simplest form and share in a ratio.
2. Solve proportion problems including recipes, exchange rates and best buy.
3. Solve direct and indirect proportion problems.
4. Define shapes by their properties and apply basic angle rules.
Spring HT 21. Angles
2. Plans and elevations
3. Area & Perimeter
1. Find missing angles in parallel lines and polygons.
2. Use and calculate bearings.
3. Draw and interpret 3D shapes using their elevations.
4. Calculate the area and perimeter of 2D shapes and the surface area of 3D shapes.
Summer HT 11. Area and volume
2. Similarity and congruence
1. Calculate the area and circumference of circles.
2. Find the surface area and volume of 3D shapes.
3. Define similarity and congruence and use to find missing sides in shapes.
Summer HT 21. Measure
2. Constructions and loci
3. Transformations
1. Convert between different metric units of measure.
2. Convert between imperial and metric units.
3. Construct angles and bisectors and apply to loci problems.
4. Rotate, reflect, translate and enlarge 2D shapes.

Year 10

Half TermTopics to be coveredKey skills covered
Autumn HT 11. Scatter graphs
2. Interpreting charts
3. Box plots
4. Histograms
5. Averages
1. Understand correlation
2. Recognise different charts
3. Draw and analyse box plots
4. Draw and read from histograms
5. Calculate all the averages
Autumn HT 21. Probability
2. Venn diagrams
3. Linear graphs
4. Parallel and perpendicular lines
1. Calculate a variety of probabilities
2. Populate and interpret a Venn diagram
3. Draw and recognise linear graphs and their equation
4. Work out the equation of missing lines
Spring HT 11. Sequences
2. Algebraic techniques
3. Solving linear equations
1. Calculating an nth term
2. Factorising and multiplying out brackets
3. Rearranging to get a solution
4. Factorising and completing the square
Spring HT 21. Sketching graphs
2. Gradients and rates of change
3. Iteration
1. Drawing a wide range of graphs
2. Using a tangent to calculate and interpret the gradient
3. Solving equations by iteration
Summer HT 11. Simultaneous equations
2. Inequalities
3. Transforming functions
1. Finding solutions of a combination of equations
2. Solving inequalities, algebraically and graphically
3. Sketching transformations
Summer HT 21. Pythagoras theorem
2. Trigonometry
1. 2D and 3D problems
2. Finding missing lengths and angles

Year 11

Half TermTopics to be coveredKey skills covered
Autumn HT 1Algebra – revision and consolidation of key concepts1. Use and interpret algebraic notation, including coefficients written as fractions rather than as decimals, brackets.
2. Use conventional notation for priority of operations, including brackets, powers, roots and reciprocals.
3. Understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factors
4. Simplify and manipulate algebraic expressions (including those involving surds) by: collecting like terms, multiplying a single term over a bracket, taking out common factors
5. Substitute numerical values into formulae and expressions, including scientific formulae
6. Solve linear equations in one unknown algebraically including those with the unknown on both sides of the equation
7. Find approximate solutions using a graph
8. Solve quadratic equations algebraically by factorising
9. Translate simple situations or procedures into algebraic expressions or formulae; derive an equation and the solve the equation and interpret the solution
10. Simplify and manipulate algebraic expressions (including those involving surds) by: expanding products of two or more binomials, factorising quadratic expressions (including the difference of two squares), simplifying expressions involving sums, products and powers, including the laws of indices
11. Understand and use standard mathematical formulae
12. Rearrange formulae to change the subject
13. Know the difference between an equation and an identity
14. Argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments and proofs
15. Where appropriate, interpret simple expressions as functions with inputs and outputs
16. Interpret the reverse process as the ‘inverse function’
17. Interpret the succession of two functions as a ‘composite function’
18. Solve quadratic equations (including those that require rearrangement) algebraically by factorising, by completing the square and by using the quadratic formula
19. Recognise, sketch and interpret graphs of linear and quadratic functions
20. Identify and interpret roots, intercepts and turning points of quadratic functions graphically; deduce roots algebraically and turning points by completing the square
21. Derive an equation, solve the equation and interpret the solution
22. Solve two simultaneous equations in two variables (linear / linear or linear/quadratic) algebraically
23. Derive two simultaneous equations
24. Solve the equations and interpret the solution
Autumn HT 21. Trig recap
2. Sine and cosine rules
3. Vectors
4. Circle theorems
1. Using the trigonometric identities to finding missing lengths and angles on right-angled triangles and problem solving; know the exact values of sin(x) and cos(x) for x=0°, 30°, 45°, 60° and 90°, and tan(x) for x=0°, 30°, 45° and 60°.
2. Know and apply the Sine rule and Cosine rule to find unknown lengths and angles.
3. Know and apply 0.5absinC to calculate the area, sides or angles of any triangle; apply addition and subtraction of vectors.
4. Apply multiplication of vectors by a scalar; use vectors to construct geometric arguments and proofs.
5. Apply and prove the standard circle theorems. This includes: angles at a centre is twice the angle at the circumference; angle in a semi-circle is 90°; angles in the same segment are equal; opposite angles in a cyclic quadrilateral sum to 180°; tangent at any point on a circle is perpendicular to the radius at that point; tangents from an external point are equal in length; the perpendicular from the centre to a chord bisects the chord; alternate segment theorem.
Spring HT 11. Trig recap
2. Sine and cosine rules
3. Vectors
4. Circle theorems
1. Using the trigonometric identities to finding missing lengths and angles on right-angled triangles and problem solving; know the exact values of sin(x) and cos(x) for x=0°, 30°, 45°, 60° and 90°, and tan(x) for x=0°, 30°, 45° and 60°.
2. Know and apply the Sine rule and Cosine rule to find unknown lengths and angles.
3. Know and apply 0.5absinC to calculate the area, sides or angles of any triangle; apply addition and subtraction of vectors.
4. Apply multiplication of vectors by a scalar; use vectors to construct geometric arguments and proofs.
5. Apply and prove the standard circle theorems. This includes: angles at a centre is twice the angle at the circumference; angle in a semi-circle is 90°; angles in the same segment are equal; opposite angles in a cyclic quadrilateral sum to 180°; tangent at any point on a circle is perpendicular to the radius at that point; tangents from an external point are equal in length; the perpendicular from the centre to a chord bisects the chord; alternate segment theorem.
Spring HT 2Revision, consolidation and exam practice
Summer HT 1Revision, consolidation and exam practice
Summer HT 2Revision, consolidation and exam practice