Mathematics

Department vision

Mathematics is important in our everyday life, allowing us to make sense of the world around us and to manage our lives. Using mathematics enables us to model real-life situations and make connections and informed predictions. It equips us with the skills we need to interpret and analyse information, simplify and solve problems, assess risk and make informed decisions.”

We aim to encourage students to develop lively, creative and enquiring minds.  To be capable of independent thought and to enjoy Mathematics through problem solving and perseverance.  To appreciate that Mathematics is inherent to everyday life.

Year 7

 

Topic 

Learning Outcomes 

Term 1   

Number Skill;  

 

 

 

 

 

 

 

 

 

 

Equations, Functions & Formulae;  

 

 

 

 

 

Fractions 

2.1 - Understand the difference between multiples, factors and primes. Find all the factor pairs of any whole number. Find the HCF and LCM of two numbers. 

2.2 – Add, subtract, multiply and divide positive and negative numbers. 

2.3 – Use mental and written strategies for multiplication. Divide a 3-digit integer by a single or 2-digit integer. 

2.4 – Use index notation for squares and square roots. Calculate with squares and square roots. 

2.5 – Carry out calculations involving squares, cubes, square roots and cube roots. Use factorising to work out square roots and cube roots. Solve word problems using square roots and cube roots. 

2.6 – Estimate answers to complex calculations. Carry out calculations involving brackets. 

3.1 – Simplify expressions by collecting like terms. 

3.2 – Construct expressions using four operations.  

3.3 – Substitute into formulae. 

3.4 – Derive formulae from a description. 

3.5 – Expand expressions involving brackets. Substitute into expressions involving powers.  

3.6 – Factorise an algebraic expression. 

4.1 – Compare and simplify fractions. Write one number as a fraction of another. Work out simple fractions of amounts. 

4.2 – Write an improper fraction as a mixed number. Add and subtract fractions. 

4.3 – Work with equivalent fractions, decimals and percentages. Use division to write a fraction as a decimal. 

Term 2 

Fractions (cont); 

 

 

 

Analysing and Displaying Data; 

 

 

 

 

 

 

 

 

 

Angles and Shapes. 

4.4 – Work out fractions of amounts. Divide an integer and a fraction by a fraction. Multiply a fraction by a fraction. 

4.5 – Add and subtract mixed numbers. Enter time as a mixed number into a calculator. Multiply and divide a mixed number by a fraction. 

  1. – Use two-way tables. Interpret and draw dual bar charts and compound bar charts. 

  1. – Choose the most appropriate average for a set of data. Find the mode, median, mean and range for a set of data. Compare sets of data using averages and the range.  

  1. – Group discrete and continuous data. Draw and interpret grouped frequency diagrams. 

  1. – Interpret and draw line graphs. Recognise when a graph is misleading. 

  1. – Draw and interpret pie charts.  

  1. – Interpret and draw scatter graphs. Describe the correlation between two sets of data. Draw a line of best fit and use it to estimate values. 

5.1 – Work out unknown angles when two or more lines meet or cross at a point. Work out unknown angles involving parallel lines. 

5.2 – Describe the line and rotational symmetry of triangles. Understand how to prove that a result is true. Use properties of a triangle to work out unknown angles. Use the properties of isosceles and equilateral triangles to solve problems.  

5.3 – Describe the line and rotational symmetry or quadrilaterals. Describe the properties of quadrilaterals. Solve problems involving quadrilaterals. 

5.4 – Work out the interior and exterior angles of a polygon.   

 

Term 3 

Decimals; 

 

 

 

 

 

 

 

Equations. 

 

6.1 – Write decimals in ascending and descending order.  

6.2 – Round to decimal places.  

6.3 – Add and subtract decimals.  

6.4 – Multiply a decimal by an integer. Use place value to multiply decimals. 

6.5 – Divide a decimal by a whole number. Divide a number by a decimal. 

6.6 – Convert between fractions, decimals and percentages. Compare different proportions using percentages. 

6.7 – Calculate percentages with and without a calculator. Calculate percentages increases and decreases. Work backwards to solve a percentage problem. 

7.1 – Write and solve simple equations. Solve problems using equations.  

7.2 – Write and solve two-step equations. 

 

Term 4 

Equations (cont.); 

 

 

Multiplicative Reasoning. 

 

 

 

 

7.3 – Write and solve equations with letters on both sides.  

7.4 – Solve equations that include 

x2x2

and 

x3x3

. Use trial and improvement to find solutions to 1 decimal place.  

8.1 – Convert between metric and imperial units. Use metric units.  

8.2 – Write a ratio in its simplest form. Simplify a ration expressed in fractions or decimals.  

8.3 – Share a quantity in 2 or more parts in a given ratio. 

8.4 – Understand the relationship between ratio and proportion. 

  

Term 5 

Multiplicative Reasoning (cont.); 

 

 

 

Sequences and Graphs. 

 

 

8.5 – Solve simple word problems involving ratio and direct proportion. Solve simple word problems involving ratio and inverse proportion.  

8.6 – Solve problems involving ratio and proportion using the unitary method. Write ratios in the form 1:n. Solve best buy problems.  

10.1 – Work out the terms of an arithmetic sequence using the term-to-term rule. Work out a given term in a simple arithmetic sequence.  

10.2 – Work out and use expressions for the nth term in an arithmetic sequence. 

Term 6 

Sequences and Graphs;  

 

 

 

 

 

Perimeter, Area and Volume 

10.3 – Generate sequences and predict how they will continue. Recognise geometric sequences and work out the term-to-term rule.  

10.4 – Use positive and negative coordinates. Work out the midpoint of a line segment. 

10.5 – Draw straight-line graphs. Recognise straight-line graphs parallel to the axes. Recognise graphs of y=x and y=-x. 

9.1 – Calculate the area of triangles, parallelograms and trapeziums.  

9.2 – Calculate the area and perimeter of shapes made from rectangles and triangles. 

9.3 – Identify nets of different 3D solids. Know the properties of 3D solids. 

9.4 – Calculate the surface area of cubes and cuboids. 

9.5 – Calculate the volume of a cube or a cuboid. Convert between cm³, ml and litres.  

9.6 – Convert between metric measures for area and volume. 

Year 8

 

Topic 

Learning Outcomes 

Term 1     

Factors and Powers; 

 

 

 

 

 

 

Working with powers (Algebra); 

 

 

 

 

 

 

 

Graphs. 

  1. – Write the prime factor decomposition of a number.  Use prime factor decomposition to find the HCF and LCM of two numbers. 

  1. – Use the laws of indices for positive powers for multiplying and dividing. 

  1. – Use and understand powers of 10.  Understand the effect of multiplying and dividing by any integer power of 10. 

  1. – Round to a number of significant figures. 

 

2.1 – Simplify expressions involving powers and brackets.  Understand the meaning of an identity. 

2.2 – Use the index laws in algebraic calculations and expressions.  Simplify expressions with powers. 

2.3 – Write and simplify expressions involving brackets and powers.  Factorise an algebraic expression. 

2.4 – Substitute integers into expressions.  Construct and solve equations. 

 

10.1 – Plotting straight line graphs.  Finding the y-intercept of a straight-line graph. 

10.2 – Find the gradient of a straight-line graph.  Plotting graphs using the gradient and y-intercept. 

10.3 – Use y = mx + c.  Find the equation of a straight-line graph. 

10.4 – Identify parallel and perpendicular lines. 

10.5 – Find the inverse of a linear function. 

 

Term 2   

Graphs (cont.); 

 

Real-life Graphs; 

 

 

 

 

 

 

 

Transformations. 

10.6 – Plot and use non-linear graphs. 

 

4.1 – Recognise when values are in direct proportion.  Plot graphs and read values to solve problems. 

4.2 – Interpret graphs from different sources.  Understand financial graphs. 

4.3 – Draw and interpret distance-time graphs.  Use distance-time graphs to solve problems. 

4.4 – Interpret graphs that are curved.  Interpret real-life graphs. 

4.5 – Understand when graphs are misleading. 

 

5.1 – Describe and carry out translations and reflections. 

5.2 – Describe and carry out rotations. 

5.3 – Describe and carry out enlargements. 

5.4 – Enlarge a shape using a negative or fractional scale factor. 

5.5 – Transform 2D shapes using a combination of reflection, rotation, enlargement and translation. 

 

Term 3   

Transformations (cont); 

 

 

 

Fractions, Decimals and Percentages; 

 

 

 

 

 

 

Probability. 

5.6 – Identify planes of reflection symmetry in 3D solids.  Find the perimeter and area of 2D shapes after enlargements.  Find the volume of 3D solids after enlargements. 

6.1 – Recognise fractional equivalents to some recurring decimals.  Change a recurring decimal into a fraction. 

6.2 – Calculate percentages.  Calculating an original quantity before a percentage increase or decrease. 

6.3 – Calculate percentage change. 

6.4 – Calculate the effect of repeated percentage changes. 

 

8.1 – Calculate and compare probabilities.  Decide if a game is fair. 

8.2 – Identify mutually exclusive outcomes and events.  Find the probability of mutually exclusive outcomes and events.  Find the probability of an event not happening. 

8.3 – Calculate the relative frequency of a value.  Use relative frequency to estimate the probability of an event.  Use estimated probability to calculate expected frequencies. 

8.4 – Carry out a probability experiment.  Estimate probability using data from an experiment.  Work out the expected results when an experiment is repeated. 

8.5 – List all the possible outcomes in sample space diagrams or Venn diagrams.  Calculate probabilities of repeated events. 

 

 

Term 4   

Probability; 

 

Scale Drawings and Measures; 

 

 

 

 

 

 

 

8.6 – Use tree diagrams to find the probabilities of two or more events. 

 

9.1 – Use scales in maps and plans.  Use and interpret maps. 

9.2 – Measure and use bearings.  Draw diagrams to scale using bearings. 

9.3 – Draw diagrams to scale.  Use and interpret scale drawings. 

9.4 – Identify congruent and similar shapes.  Use congruence to solve problems in triangles and quadrilaterals. 

9.5 – Use similarity to solve problems in 2D shapes. 

 

 

Term 5 

Constructions and Loci 

 

 

 

 

 

 

 

 

 

2D Shapes and 3D Solids 

7.1 – Draw triangles accurately using a ruler and protractor.  Draw diagrams to scale. 

7.2 – Draw accurate nets of 3D solids.  Construct triangles using a ruler and compasses.  Construct nets of 3D solids using a ruler and compasses. 

7.3 – Bisect a line using a ruler and compasses.  Construct perpendicular lines using a ruler and compasses. 

7.4 – Bisect angles using a ruler and compasses.  Draw accurate diagrams to solve problems. 

7.5 – Draw a locus.  Use loci to solve problems. 

 

3.1 – Use 2D representations of 3D solids. 

3.2 – Sketch nets of 3D solids.  Calculate the surface area of prisms. 

 

Term 6 

2D Shapes and 3D Solids 

 

 

 

 

 

 

 

Revision and preparation for the PPE’s.  

 

Consolidation for work completed and areas of weakness identified from the PPE’s. 

 

Time allowed for those topics not completed during Terms 1-5.  

 

 

3.3 – Calculate the volume of prisms. 

3.4 – Name different parts of a circle.  Calculate the circumference of a circle or arc length.  Calculate the radius or diameter given the circumference. 

3.5 – Calculate the area of a circle or sector.  Calculate the radius or diameter when given the area. 

3.6 – Calculate the volume and surface area of a cylinder. 

3.7 – Use Pythagoras’ Theorem in right-angled triangles. 

 

 

Years 9

 

Topic 

Learning Outcomes 

Term 1   

Algebra Review 

 

 

 

 

Unit 1 – Number. Topics covered:  

 

Expanding brackets, factorising by common factors, expanding the product of two brackets. Factorising by grouping, factorising quadratics including with coefficient of x2

>1, >1, 

factorising difference of two squares. Algebraic Fractions, Simplify, multiply and divide. Linear equations, setting up equations, and solving. 

 

  1. – Work out the total number of ways of performing a series of tasks.  

  1. – Estimate an answer. Use place value to answer questions.  

  1. – Write a number as the product of its prime factors. Find the HCF and LCM of two numbers. 

  1. – Use powers and roots in calculations. Multiply and divide using index laws. Work out a power raised to a power.  

  1. – Use negative indices. Use fractional indices. 

  1. – Write a number in standard form. Calculate with numbers in standard form.  

 

Term 2   

Unit 1 – Number, cont. Topics covered:  

 

 

Unit 5 – Angles and Trigonometry. Topics covered:  

 

  1. – Understand the difference between rational and irrational numbers. Simplify a surd. Rationalise a denominator. 

 

5.1 – Derive and use the sum of angles in a triangle and in a quadrilateral. Derive and use the fact that the exterior angle of a triangle is equal to the sum of the two opposite interior angles. 

5.2 – Calculate the sum of the interior angles of a polygon. Use the interior angles of polygons to solve problems.  

5.3 – Know the sum of the exterior angles of a polygon. Use the angles of polygons to solve problems.  

5.4 – Calculate the length of the hypotenuse in a right-angled triangle. Solve problems using Pythagoras’ theorem. 

5.5 – Calculate the length of a shorter side in a right-angled triangle. Solve problems using Pythagoras’ theorem. 

5.6 – Use trigonometric ratios to find lengths in a right-angled triangle. Use trigonometric ratios to solve problems.  

5.7 – Use trigonometric ratios to calculate an angle in a right-angled triangle. Find angles of elevation and angles of depression. Use trigonometric ratios to solve problems. Know the exact values of the sine, cosine, and tangent of some angles. 

 

Term 3   

Unit 3 – Interpreting and representing data. Topics Covered:  

 

 

 

 

 

 

 

 

 

 

 

 

 

Unit 2 – Algebra. Topics Covered:  

 

3.1 – Construct and use back-to-back stem and leaf diagrams. Construct and use frequency polygons and pie charts. 

3.2 – Plot and interpret time series graphs. Use trends to predict what might happen in the future.  

3.3 – Plot and interpret scatter graphs. Determine whether or not there is a linear relationship between two variables. 

3.4 – Draw a line of best fit on a scatter graph. Use the line of best fit to predict values. 

3.5 – Decide which average is best for a set of data. Estimate the mean and range from a grouped frequency table. Find the modal class and the group containing the median.  

3.6 – Construct and use two-way tables. Choose appropriate diagrams to display data. Recognise misleading graphs. 

 

2.1 – Use the rules of indices to simplify algebraic expressions.  

2.4 – Substitute numbers into formulae. Rearrange formulae. Distinguish between expressions, equations, formulae and identities. 

 

Term 4   

Unit 2 – Algebra. Topics Covered:  

 

 

 

 

Unit 4 – Fractions, ratio, proportion. Topics Covered:  

 

2.5 – Find a general formula for the nth term of an arithmetic sequence. Determine whether a particular number is a term of a given arithmetic sequence. 

2.6 – Solve problems using geometric sequences. Work out terms in Fibonacci-like sequences. Find the nth term of a quadratic sequence.  

 

4.1 – Add, subtract, multiply and divide fractions and mixed numbers. Find the reciprocal of an integer, decimal or fraction. 

4.2 – Write ratios in the form 1:n or n:1. Compare ratios. Find quantities using rations. Solve problems involving ratios.  

4.3 – Convert between currencies and measures. Recognise and use direct proportion. Solve problems involving rations and proportion.  

4.4 – Work out percentage increases and decreases. Solve real-life problems involving percentages. 

4.5 – Calculate using fractions, decimals and percentages. Convert a recurring decimal to a fraction.  

 

Term 5   

Unit 6 – Graphs. Topics Covered: 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Unit 8 – Transformations. Topics Covered: 

 

6.1 – Find the gradient and y-intercept from a linear equation. Rearrange an equation into the form y=mx+c. Compare two graphs from their equations. Plot graphs with equations ax+by=c. 

6.2 – Sketch graphs using the gradient and intercepts. Find the equation of a line, given its gradient and one point on the line. Find the gradient of a line through two points. 

6.3 – Draw and interpret distance-time graphs. Calculate average speed from a distance-time graph. Understand velocity-time graphs. Find acceleration and distance from velocity-time graphs. 

6.4 – Draw and interpret real-life linear graphs. Recognise direct proportion. Draw and use a line of best fit.  

6.5 – Find the coordinates of the midpoint of a line segment. Find the gradient and length of a line segment. Find the equations of lines parallel or perpendicular to a given line.  

6.6 – Draw quadratic graphs. Solve quadratic equations using graphs. Identify the line of symmetry of a quadratic graph. Interpret quadratic graphs relating to real-life situations.  

6.7 – Draw graphs of cubic functions. Solve cubic equations using graphs. Draw graphs of reciprocal functions. Recognise a graph from its shape.  

6.8 – Interpret linear and non-linear real-life graphs. Draw the graph of a circle. 

 

8.1 – Draw plans and elevations of 3D solids.  

8.2 – Reflect a 2D shape in a mirror line. Rotate a 2D shape about a centre of rotation. Describe reflections and rotations.  

8.3 – Enlarge shapes by fractional and negative scale factors about a centre of enlargement. 

8.4 – Translate a shape using a vector. Carry out and describe combinations of transformations.  

8.5 – Draw and use scales on maps and scale drawings. Solve problems involving bearings.  

8.6 – Construct triangles using a ruler and compasses. Construct the perpendicular bisector of a line. Construct the shortest distance from a point to a line using a ruler and compasses.  

 

Term 6 

Unit 8 – Transformations. Topics Covered: 

 

 

 

Unit 7 – Area and Volume. Topics Covered: 

8.7 – Bisect an angle using a ruler and compasses. Construct angles using a ruler and compasses. Construct shapes made from triangles using a ruler and compasses.  

8.8 – Draw a locus. Use loci to solve problems.  

 

7.1 – Find the area and perimeter of compound shapes. Recall and use the formula for area of a trapezium.  

7.2 – Convert between metric units of area. Calculate the maximum and minimum possible values of a measurement.  

7.3 – Convert between metric units of volume. Calculate volumes and surface areas of prisms.  

7.4 – Calculate the area and circumference of a circle. Calculate area and circumference in terms of pi. 

7.5 – Calculate the perimeter and area of semicircles and quarter circles. Calculate arc lengths, angles and areas of sectors of circles. 

7.6 – Calculate volume and surface area of a cylinder and a sphere. Solve problems involving volumes and surfaces areas.  

7.7 – Calculate volume and surface area of pyramids and cones. Solve problems involving pyramids and cones.  

 

Years 10 & 11

Year 10

 

Topic 

Learning Outcomes 

Term 1   

Unit 2 – Algebra. Topics Covered:  

 

 

 

 

 

 

 

Unit 6 – Graphs. Topics Covered: 

2.1 – Use the rules of indices to simplify algebraic expressions.  

2.4 – Substitute numbers into formulae. Rearrange formulae. Distinguish between expressions, equations, formulae and identities. 

2.5 – Find a general formula for the nth term of an arithmetic sequence. Determine whether a particular number is a term of a given arithmetic sequence. 

2.6 – Solve problems using geometric sequences. Work out terms in Fibonacci-like sequences. Find the nth term of a quadratic sequence.  

 

6.1 – Find the gradient and y-intercept from a linear equation. Rearrange an equation into the form y=mx+c. Compare two graphs from their equations. Plot graphs with equations ax+by=c. 

6.2 – Sketch graphs using the gradient and intercepts. Find the equation of a line, given its gradient and one point on the line. Find the gradient of a line through two points. 

6.3 – Draw and interpret distance-time graphs. Calculate average speed from a distance-time graph. Understand velocity-time graphs. Find acceleration and distance from velocity-time graphs. 

6.4 – Draw and interpret real-life linear graphs. Recognise direct proportion. Draw and use a line of best fit.  

6.5 – Find the coordinates of the midpoint of a line segment. Find the gradient and length of a line segment. Find the equations of lines parallel or perpendicular to a given line.  

6.6 – Draw quadratic graphs. Solve quadratic equations using graphs. Identify the line of symmetry of a quadratic graph. Interpret quadratic graphs relating to real-life situations.  

6.7 – Draw graphs of cubic functions. Solve cubic equations using graphs. Draw graphs of reciprocal functions. Recognise a graph from its shape.  

6.8 – Interpret linear and non-linear real-life graphs. Draw the graph of a circle. 

 

Term 2   

Unit 8 – Transformation and Construction. Topics Covered: 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Unit 9 – Equations and Inequalities. Topics Covered: 

 

8.1 – Draw plans and elevations of 3D solids. 

8.2 – Reflect a 2D shape in a mirror line.  Rotate a 2D shape about a centre of rotation.  Describe reflections and rotations. 

8.3 – Enlarge shapes by fractional and negative scale factors about a centre of enlargement. 

8.4 – Translate a shape using a vector.  Carry out and describe combinations of transformations. 

8.5 – Draw and use scales on maps and scale drawings.  Solve problems involving bearings. 

8.6 – Construct triangles using a ruler and compasses.  Construct the perpendicular bisector of a line.  Construct the shortest distance from a point to a line using a ruler and compasses. 

8.7 – Bisect an angle, construct angles and construct shapes made from triangles using a ruler and compasses. 

8.8 – Draw a locus.  Use loci to solve problems. 

 

9.1 – Find roots of quadratic functions.  Rearrange and solve simple quadratic equations. 

9.2 – Solve more complex quadratic equations.  Use the quadratic formula to solve quadratic equations. 

9.3 – Complete the square for a quadratic expression.  Solve quadratic equations by completing the square. 

9.4 – Solve simple simultaneous equations.  Solve simultaneous equations for real-life situations. 

9.5 – Use simultaneous equations to find the equation of a straight line.  Solve linear simultaneous equations where both equations are multiplied.  Interpret real-life situations involving two unknowns and solve them. 

9.6 – Solve simultaneous equations with one quadratic equation.  Use real-life situations to construct quadratic and linear equations and solve them. 

9.7 – Solve inequalities and show the solution on a number line using set notation. 

 

Term 3   

Unit 11 – Multiplicative Reasoning. Topics Covered: 

 

 

 

 

 

 

Unit 10 – Probability. Topics Covered: 

11.1 – Find an amount after repeated percentage changes.  Solve growth and decay problems. 

11.2 – Calculate rates.  Convert between metric speed measures.  Use a formula to calculate speed and acceleration. 

11.3 – Solve problems involving compound measures. 

11.4 – Use relationships involving ratio.  Use direct and inverse proportion. 

 

10.1 – Use the product rule for finding the number of outcomes for two or more events.  List all the possible outcomes of two events in a sample space diagram. 

10.2 – Identify mutually exclusive events.  Find the probabilities of mutually exclusive events.  Find the probability of an event not happening. 

10.3 – Work out the expected results for experimental and theoretical probabilities.  Compare real results with theoretical expected values to decide if a game is fair. 

10.4 – Draw and use frequency trees.  Calculate probabilities of repeated events.  Draw and use probability tree diagrams. 

10.5 – Decide if two events are independent.  Draw and use tree diagrams to calculate conditional probability.  Draw and use tree diagrams without replacement.  Use two-way tables to calculate conditional probability. 

Term 4   

Unit 10 – Probability, cont. 

 

Unit 12 – Similarity and Congruence.  

 

10.6 – Use Venn diagrams to calculate conditional probability.  Use set notation. 

 

12.1 – Show that two triangles are congruent.  Know the conditions of congruence. 

12.2 – Prove shapes are congruent.  Solve problems involving congruence.   

12.3 – Use the ratio of corresponding sides to work out scale factors.  Find missing lengths on similar shapes. 

12.4 – Use similar triangles to work out lengths in real life.  Use the link between linear scale factor and area scale factor to solve problems. 

12.5 – Use the links between scale factors for length, area and volume to solve problems. 

 

Term 5   

Unit 13 – More Trigonometry. Topics Covered: 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Unit 14 – Further Statistics. Topics Covered: 

13.1 – Understand and use upper and lower bounds in calculations involving trigonometry. 

13.2 – Understand how to find the sine of any angle.  Know the graph of the sine function and use it to solve equations. 

13.3 – Understand how to find the cosine of any angle.  Know the graph of the cosine function and use it to solve equations. 

13.4 – Understand how to find the tangent of any angle.  Know the graph of the tangent function and use it to solve equations. 

13.5 – Find the area of a triangle and a segment of a circle.  Use the sine rule to solve 2D problems. 

13.6 – Use the cosine rule to solve 2D problems.  Solve bearings problems using trigonometry. 

13.7 – Use Pythagoras’ theorem in 3D.  Use trigonometry in 3D. 

13.8 – Recognise how changes in a function affect trigonometric graphs. 

 

14.1 – Understand how to take a simple random sample.  Understand how to take a stratified sample. 

 

Term 6   

Unit 14 – Further Statistics. Cont.  

 

 

 

 

 

 

 

Unit 15 – Equations and Graphs.  

 

14.2 – Draw and interpret cumulative frequency tables and diagrams.  Work out median, quartiles and interquartile range from a cumulative frequency diagram. 

14.3 – Find the quartiles and the interquartile range from stem-and-leaf diagrams.  Draw and interpret box plots. 

14.4 – Understand frequency density.  Draw histograms. 

14.5 – Interpret histograms. 

14.6 – Compare two sets of data. 

 

15.1 – Solve simultaneous equations graphically. 

15.2 – Represent inequalities on graphs.  Interpret graphs of inequalities. 

15.3 – Recognise and draw quadratic functions. 

15.4 – Find approximate solutions to quadratic equations graphically.  Solve quadratic equations using an iterative process. 

15.5 – Find the roots of cubic equations.  Sketch graphs of cubic functions.  Solve cubic equations using an iterative process. 

 

Year 11 

 

Topic 

Learning Outcomes 

Term 1   

Unit 16 – Circle Theorems. Topics Covered: 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Unit 17 – More Algebra. Topics Covered: 

 

16.1 – Solve problems involving angles, triangles and circles.  Understand and use facts about chords and their distance from the centre of a circle.  Solve problems involving chords and radii. 

16.2 – Understand and use facts about tangents at a point and from a point.  Give reasons for angle and length calculations involving tangents. 

16.3 – Understand, prove and use facts about angles subtended at the centre and the circumference of circles.  Understand, prove and use facts about the angle in a semicircle being a right angle.  Find missing angles using these theorems and give reasons for answers. 

16.4 – Understand, prove and use facts about angles subtended at the circumference of a circle.  Understand, prove and use facts about cyclic quadrilaterals.  Prove the alternate segment theorem. 

16.5 – Solve angle problems using circle theorems.  Give reasons for angle sizes using mathematical language.  Find the equation of the tangent to a circle at a given point. 

 

17.1 – Change the subject of a formula where the power of the subject appears.  Change the subject of a formula where the subject appears twice. 

17.2 – Add, subtract, multiply and divide algebraic fractions.  Change the subject of a formula involving fractions where all the variables are in denominators. 

17.3 – Simplify algebraic fractions. 

17.4 – Add, subtract, multiply and divide more complex algebraic fractions. 

17.5 – Simplify and expand expressions involving surds.  Rationalise the denominator of a fraction. 

17.6 – Solve equations that involve algebraic fractions. 

 

Term 2   

Unit 17 – More Algebra  

 

 

Unit 18 – Vectors and Geometric Proof. Topics Covered: 

 

 

17.7 – Use function notation.  Find composite and inverse functions. 

17.8 – Prove a result using algebra. 

 

18.1 – Understand and use vector notation.  Work out the magnitude of a vector. 

18.2 – Calculate using vectors and represent the solutions graphically.  Calculate the resultant of two vectors. 

18.3 – Solve problems using vectors.  Use the resultant of two vectors to solve vector problems. 

18.4 – Express points as position vectors.  Prove lines are parallel.  Prove points are collinear. 

18.5 – Solve geometric problems in 2D using vector methods.  Apply vector methods for simple geometric proofs. 

 

Term 3   

Unit 19 – Proportion and Graphs. Topics Covered: 

 

19.1 – Write and use equations to solve problems involving direct proportion. 

19.2 – Solve problems involving square and cubic proportionality. 

19.3 – Write and use equations to solve problems involving inverse proportion.  Use and recognise graphs showing inverse proportion. 

19.4 – Recognise and sketch graphs of exponential functions. 

19.5 – Calculate the gradient of a tangent at a point.  Estimate the area under a non-linear graph. 

19.6 – Understand the relationship between translating a graph and the change in its function notation. 

19.7 – Understand the effect stretching a curve parallel to one of the axes has on its function form.  Understand the effect reflecting a curve in one of the axes has on its function form. 

 

Term 4    

Revision & Preparation 

Review of previously taught topics in preparation for summer examination.  Individual teachers to teach specific content to their class based on gap analysis of their class / groups within their class as a result of recent assessment. 

 

Term 5   

Revision & Preparation 

Review of previously taught topics in preparation for summer examination.  Individual teachers to teach specific content to their class based on gap analysis of their class / groups within their class as a result of recent assessment. 

 

Term 6   

External Examinations 

 

 

Post 16 at WG6

Year 12

 

Topic 

Learning Outcomes 

Term 1   

Pure 1: Algebraic Expressions 

 

 

 

 

 

 

Pure 2: Quadratics  

 

 

 

 

 

 

Pure 3: Equations and Inequalities 

 

 

 

 

 

 

Pure 4: Graphs and Transformations 

 

 

 

 

 

 

 

Pure 12: Differentiation 

 

 

 

 

 

 

 

 

 

 

 

Pure 5: Straight Line Graphs 

  1. Index Laws 

  1. Expanding Brackets 

  1. Factorising 

  1. Negative and Fractional Indices 

  1. Surds 

  1. Rationalising Denominators 

 

2.1 Solving Quadratic Equations 

2,2 Completing the Square 

2.3 Functions 

2.4 Quadratic Graphs 

2.5 The Discriminant 

2.6 Modelling with Quadratics 

 

3.1 Linear Simultaneous Equations 

3.2 Quadratic Simultaneous Equations 

3.3 Simultaneous Equations on Graphs 

3.4 Linear Inequalities 

3.5 Quadratic Inequalities 

3.6 Inequalities on Graphs 

 

4.1 Cubic Graphs 

4.2 Quartic Graphs 

4.3 Reciprocal Graphs 

4.4 Points of Intersection 

4.5 Translating Graphs 

4.6 Stretching Graphs 

4.7 Transforming Functions 

 

12.1 Gradients of Curves 

12.2 Finding the Derivative 

12.3 Differentiation 

xnxn

 

12.4 Differentiation Quadratics 

12.5 Differentiation functions with two or more terms 

12.6 Gradients, tangents and normal 

12.7 Increasing and decreasing functions 

12.8 Second order derivatives 

12.9 Stationary Points 

12.10 Sketching gradient functions 

12.11 Modelling with differentiation 

 

5.1 

y=mx+cy=mx+c

 

5.2 Equations of straight lines 

5.3 Parallel and perpendicular lines 

5.4 Length and area 

5.5 Modelling with straight lines 

 

Term 2 

Pure 11: Vectors 

 

 

 

 

 

 

Stats 1: Data Collection 

 

 

 

 

 

Stats 2: Measures of Location and Spread 

 

 

 

 

Stats 3: Representations of Data 

 

 

 

 

 

Stats 4: Correlation 

 

 

Mechs 8: Modelling in Mechanics 

 

 

 

 

Mechs 9: Constant Acceleration 

 

 

 

 

 

Pure 6: Circles 

11.1 Vectors 

11.2 Representing vectors 

11.3 Magnitude and direction 

11.4 Position vectors 

11.5 Solving geometric problems 

11.6 Modelling with vectors 

 

  1. Populations and samples 

  1. Sampling 

  1. Non-random sampling 

  1. Types of data 

  1. The large data set 

 

2.1 Measures of Central Tendency 

2.2 Other Measures of Location 

2.3 Measures of Spread 

2.4 Variance and Standard Deviation 

2.5 Coding 

3.1 Outliers 

3.2 Box Plots 

3.3 Cumulative Frequency 

3.4 Histograms 

3.5 Comparing Data 

 

4.1 Correlation 

4.2 Linear Regression 

 

8.1 Constructing a Model 

8.2 Modelling Assumptions 

8.3 Quantities and Units 

8.4 Working with Vectors 

 

9.1 Displacement-time Graphs 

9.2 Velocity-time Graphs 

9.3 Constant Acceleration Formulae 1 

9.4 Constant Acceleration Formulae 2 

9.5 Vertical Motion Under Gravity 

 

6.1 Midpoints and Perpendicular Bisectors 

6.2 Equation of a Circle 

6.3 Intersections of Straight Lines and Circles 

6.4 Use Tangent and Chord Properties 

6.5 Circles and Triangles 

 

Term 3 

Pure 13: Integration 

 

 

 

 

 

 

 

Pure 9: Trigonometric Ratios 

 

 

 

 

 

 

Pure 10: Trigonometric Identities and Equations 

 

 

 

 

 

 

Pure 14: Exponentials and Logarithms 

 

 

 

 

 

 

 

 

Mechs 10: Forces and Motion 

13.1 Integrating 

xnxn

 

13.2 Indefinite Integrals 

13.3 Finding Functions 

13.4 Definite Integrals 

13.5 Areas under Curves 

13.6 Areas under the x-axis 

13.7 Areas between Curves and Lines 

 

9.1 The cosine rule 

9.2 The sine rule 

9.3 Areas of Triangles 

9.4 Solving triangle problems 

9.5 Graphs of sine, cosine, and tangent 

9.6 Transforming trigonometric graphs 

 

10.1 Angles in all four Quadrants 

10.2 Exact values of trigonometrical ratios 

10.3 Trigonometric Identities 

10.4 Simple Trigonometric Equations 

10.5 Harder Trigonometric Equations 

10.6 Equations and Identities 

 

14.1 Exponential Functions 

14.2 

y=exy=ex

 

14.3 Exponential Modelling 

14.4 Logarithms 

14.5 Laws of Logarithms 

14.6 Solving Equations using Logarithms 

14.7 Working with Natural Logarithms 

14.8 Logarithms and Non-Linear Data 

 

10.1 Force Diagrams 

10.2 Forces as Vectors 

10.3 Forces and Acceleration 

10.4 Motion in 2 Dimensions 

10.5 Connected Particles 

10.6 Pulleys 

 

Term 4 

Stats 5: Probability 

 

 

 

 

Stats 6: Statistical Distributions 

 

 

 

 

Mechs 11: Variable Acceleration 

 

 

 

 

 

Pure 7: Algebraic Methods 

 

 

 

 

 

 

5.1 Calculating Probabilities 

5.2 Venn Diagrams 

5.3 Mutually Exclusive and Independent Events 

5.4 Tree Diagrams 

 

6.1 Probability Distributions 

6.2 The Binomial Distributions 

6.3 Cumulative Probabilities 

 

 

11.1 Functions of time 

11.2 Using differentiation 

11.3 Maxima and minima problems 

11.4 Using integration 

11.5 Constant acceleration formulae 

 

7.1 Algebraic Fractions 

7.2 Dividing Polynomials 

7.3 The factor theorem 

7.4 Mathematical Proof 

7.5 Methods of Proof 

 

 

Term 5 

Stats 7: Hypothesis Testing 

 

 

 

 

Pure 8: The Binomial Expansion 

 

7.1 Hypothesis Testing 

7.2 Finding Critical Values 

7.3 One-tailed tests 

7.4 Two-tailed tests 

 

8.1 Pascal’s Triangle 

8.2 Factorial Notation 

8.3 The Binomial Expansion 

8.4 Solving Binomial Problems 

8.5 Binomial Estimation 

 

Term 6 

(Y13) Pure 5: Radians 

 

 

 

 

 

(Y13) Pure 1: Algebraic Methods 

 

 

 

 

 

(Y13) Pure 2: Functions and Graphs 

 

 

 

 

 

 

 

(Y13) Pure 4: Binomial Expansion 

5.1 Radian Measure 

5.2 Arc Length 

5.3 Areas of Sectors and Segments 

5.4 Solving Trigonometric Equations 

5.5 Small Angle Approximations 

 

  1. Proof by Contradiction 

  1. Algebraic Fractions 

  1. Partial Fractions 

  1. Repeated Factors 

  1. Algebraic Division 

 

2.1 The Modulus Function 

2.2 Functions and Mapping 

2.3 Composite Functions 

2.4 Inverse Functions 

2.5 

y=|f(x)|y=f(x)

 and 

y=f(|x|)y=f(x)

 

2.6 Combining Transformations 

2.7 Solving Modulus Problems  

 

4.1 Expanding 

(1+x)n(1+x)n

 

4.2 Expanding 

(a+bx)n(a+bx)n

 

4.3 Using Partial Fractions 

 

Year 13 

 

Topic 

Learning Outcomes 

Term 1   

Pure 2: Functions and Graphs 

 

 

 

 

 

 

 

Pure 3: Sequences and Series 

 

 

 

 

 

 

 

 

Pure 4: Binomial Expansion 

 

 

 

Mechs 5: Forces and Friction 

 

 

 

Mechs 6: Projectiles 

 

 

 

 

Pure 6: Trigonometric Functions 

2.1 The Modulus Function 

2.2 Functions and Mapping 

2.3 Composite Functions 

2.4 Inverse Functions 

2.5 

y=|f(x)|y=f(x)

 and 

y=f(|x|)y=f(x)

 

2.6 Combining Transformations 

2.7 Solving Modulus Problems  

 

3.1 Arithmetic Sequences 

3.2 Arithmetic Series 

3.3 Geometric Sequences 

3.4 Geometric Series 

3.5 Sum to Infinity 

3.6 Sigma Notation 

3.7 Recurrence Relations 

3.8 Modelling with Series 

 

4.1 Expanding 

(1+x)n(1+x)n

 

4.2 Expanding 

(a+bx)n(a+bx)n

 

4.3 Using Partial Fractions 

 

5.1 Resolving Forces 

5.2 Inclined Planes 

5.3 Friction 

 

6.1 Horizontal Projection 

6.2 Horizontal and Vertical Components 

6.3 Projection at any Angle 

6.4 Projectile motion formulae 

 

6.1 Secant, cosecant and cotangent 

6.2 Graphs of sec x, cosec x and cot x 

6.3 Using sec x, cosec x and cot x 

6.4 Trigonometric Identities 

6.5 Inverse Trigonometric Functions 

 

Term 2   

Pure 7: Trigonometry and Modelling 

 

 

 

 

 

 

 

Pure 8: Parametric Equations 

 

 

 

 

 

Pure 9: Differentiation 

 

 

 

 

 

 

 

 

 

 

Stats 1: Regression, correlation and hypothesis testing 

 

 

 

Stats 2: Conditional Probability 

7.1 Addition Formulae 

7.2 Using the angle addition formulae 

7.3 Double-angle formulae 

7.4 Solving Trigonometric Equations 

7.5 Simplifying 

acosx ±bsinxacos⁡x ±bsin⁡x

 

7.6 Proving Trigonometric Identities 

7.7 Modelling with Trigonometric Functions 

 

8.1 Parametric Equations 

8.2 Using Trigonometric Identities 

8.3 Curve Sketching 

8.4 Points of Intersection 

8.5 Modelling with Parametric Equations 

 

9.1 Differentiating 

sinx andcosxsin⁡x andcos⁡x

 

9.2 Differentiation exponentials and logarithms 

9.3 The chain rule 

9.4 The product rule 

9.5 The quotient rule 

9.6 Differentiating trigonometric functions 

9.7 Parametric differentiation 

9.8 Implicit differentiation 

9.9 Using second derivatives 

9.10 Rates of change 

 

  1. Exponential models 

  1. Measuring correlation 

  1. Hypothesis testing for zero correlation 

 

2.1 Set Notation 

2.2 Conditional Probability 

2.3 Conditional Probabilities in Venn Diagrams 

2.4 Probability Formulae 

2.5 Tree Diagrams 

 

Term 3 

Stats 3: The Normal Distribution 

 

 

 

 

 

 

 

 

3.1 The normal distribution 

3.2 Finding probabilities for normal distributions 

3.3 The inverse normal distributions 

3.4 The standard normal distribution 

3.5 Finding 

μ

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