In doing this we hope that our students will go on to use these ways of working to break down and overcome whatever problems they face in later life, whether this is mathematical or not. Our Curriculum offers students the opportunity to explore many areas of mathematics whether it is algebra or shape, number or data and aims to provide students with the ability to see and make connections between these topics as they progress through the courses.
https://qualifications.pearson.com/en/qualifications/edexcel-a-levels/mathematics-2017.html
Key questions/concepts
Squares and Square Roots
Rounding
Order of Operations
Long and Short Multiplication and Division
Calculations with measurements
Timeframe
Key vocabulary
Wider reading
Multiplying and dividing negatives
Factors and HCF
Multiples and LCM
Powers and roots
Prime factors
Angles in parallel Lines
Geometric properties of quadrilaterals
Translations
Rotations
Constructions
Probability scales
Mutually exclusive events
Venn Diagrams
Sample spaces
Experimental probability
Calculating percentages
Calculating percentage increases
Calculating percentage decreases
Calculating percentage changes
Using a multiplier to calculate a percentage
Using flow diagrams to generate sequences
The nth term of a sequence
Using the nth term
Working out the nth term
The Fibonacci sequence
Area of a triangle
Area of a parallelogram
Area of a trapezium
Surface area of cubes
Surface area of cuboids
Escher tessellations https://mcescher.com/gallery/symmetry/
http://www.shodor.org/interactivate/activities/Tessellate/
Graphs from linear equations
Gradient of a straight line
Graphs from simple quasdratic equations
Distance-time graphs
Real life graphs
Alex's Adventures in Numberland by Alex Bellos
Powers of 10
Large numbers and rounding
Significant figures
Standard form with large numbers
Multiplying with numbers in standard form
https://www.mathsisfun.com/algebra/standard-form.html
Congruent shapes
Enlargements from centre (0,0)
Enlargements from a point (x,y)
Shape and Ratio
Scales
Ted Talks maths in Pixar animations https://www.youtube.com/watch?v=_IZMVMf4NQ0
Pie charts
Creating pie charts
Scatter graphs
Correlation
Creating scatter graphs
Entertaining Mathematical Puzzles by Martin Gardner
Algebraic notation
Like terms
Expanding brackets
Using algebraic expressions
Using index notation
Polynomials https://www.youtube.com/watch?v=ffLLmV4mZwU
Adding and subtracting fractions
Multiplying fractions and integers
Dividing with integers and fractions
Mulitplication with large and small numbers
Division with large and small numbers
The Camel Problem big list - 17 camels trick - MathOverflow
Direct proportion
Graphs and direct proportion
Inverse proportion
Comparing direct and inverse proportion
Real life proportion graphs
My Best Mathematical and Logic Puzzles by Martin Gardner
The circle and its parts
Circumference of a circle investigation
Circumference of a circle formula
Area of a circle
Compound shapes with circles
The circle song https://www.youtube.com/watch?v=vppcEYLOKyI
Equations with brackets
Equations with fractions
Equations with variables on both sides
More complex equations
Rearranging formulae
The evolution of numbers https://www.mathsisfun.com/numbers/evolution-of-numbers.html
Grouped frequency tables
Drawing frequency diagrams
Comparing data
Which average to use?
Averages in real life
Geometric Mean https://www.mathsisfun.com/numbers/geometric-mean.html
Simple Interest
Percentage increase
Percentage decrease
Caluating the original
Using percentages
The Monty Hall Problem: Beyond Closed Doors by Rob Deaves
Multiplying out brackets
Factorising algebraic expressions
Rearranging Formulae
2 = 1 proof https://www.youtube.com/watch?v=upG1dIAdJqs
Angles in polygons- investigation
Angles in polygons - using angle sum
Angles in regular polygons
Tessellations and regular polygons
http://http://www.shodor.org/interactivate/activities/Tessellate/
Scatter graphs and correlations
Time-series graphs
Two-way tables
Comparing two or more data sets
Statistical Investigations
The Language of Mathematics by Keith Devlin
Adding and subtracting Fractions
Multiplying fractions
Multiplying mixed numbers
Dividing fractions
Dividing mixed numbers
November - December
50 Mathematical Ideas You Really Need to Know by Tony Crilly
More about brackets
Factorising simple expressions
Factorising expressions containing powers
Expanding single brackets
Expanding the product of two brackets
The 'Uncle Albert' Series by Russell Stannard
Standard Form
Rounding appropriately
Mental calculations
Solving problems
Multiplying by 11 https://www.youtube.com/watch?v=VT76IaPudsI
Metric Units for area and volume
Volume of a prism
Surface area of a prism
Volume of a cylinder
Surface area of a cylinder
Cone vs Sphere vs cylinder https://www.mathsisfun.com/geometry/cone-sphere-cylinder.html
Graphs from equations in the form y = mx + c
Graphs from equations in the form ax+by=c
Graphs from quadratic equations
Solving quadratic equations by drawing graphs
Solving simultaneous equations by drawing graphs
The Music of the Primes by Marcus Du Sautoy
Speed
More about proportion
Force, Mass, Area
Mass, Density, Volume
Unit Costs
Flatterland by Ian Stewart
Step graphs
Time graphs
Real-life graphs
Exponential growth graphs
Exponential decay graphs
Misleading graphs https://www.statisticshowto.com/probability-and-statistics/descriptive-statistics/misleading-graphs/
Introducing Pythagoras' Theorem
Calculating the length of the hypotenuse
Calculating the length of a shorter side
Calculating side lengths - mixed
Solving Problems with Pythagoras' Theorem
Alternative Visual proof for Pythagoras https://www.youtube.com/watch?v=tTHhBE5lYTg
Introduction to trig ratios
How to find trig ratios of angles
Using trig ratios to find angles
Using trig ratios to find lengths
Trig in context
Journey Through Genius: The Great Theorems of Mathematics by William Dunham
Practice in algebra and solving equations
Practice in graphs
Practice in geometry and measures
Practice in statistics
Practice in number
Koningsberg Bridges Problem https://www.youtube.com/watch?v=W18FDEA1jRQ
Basic algebra
Substitution
Collecting like terms
Factorisation
Quadratic expansion (different methods)
Harder quadratic expansions
Quadratic factorisation
Difference of 2 squares
Sensible estimates for scales and systems of measurement (metric)
Systems of measurement (imperial)
Conversion factors (metric to imperial)
Scale drawings
Nets
Rounding integers and decimals
Rounding with sf
Approximating calculations
Angle facts
Triangles
Angles in a polygon
Regular polygons
Angles in parallel lines
Special quadrilaterals
Bearings
Calculating with decimals (non calc)
Fractions and reciprocals
Quantity as fraction of another
Fractions on a calculator
Multiplying and dividing fractions
Solving linear equations
Fractional equations
Solving equations with brackets
Solving equations with the variable on both sides
Changing the subject of a formula
Areas of rectangles and triangles
Compound shapes
Circle parts and circumference
Answers in terms of pi
Ratio and proportion
Calculating with ratios
Speed, distance time
Best buys
3D shapes
Volume ONLY of a cuboid
Volume ONLY of a prism
Equivalent percentages, fractions and decimals
Calculating a percentage of a quantity
Increasing and decreasing quantities by a percentage
Expressing one quantity as a percentage of another
Compound measures
Graphs and equations
Linear graphs by finding points
Gradient of a line
y=mx+c
Harder graphs cover up method
Finding equation of line from graph
Equation of parallel line
Simultaneous equations graphically
Reflection
Rotational symmetry and rotation
Enlargement
Vectors
Calculating probabilities
Probability that an outcome will not happen
Mutually exclusive and exhaustive outcomes
Expectation
Choices and Outcomes
SA of a cuboid
SA of a prism
SA of a cylinder
Scale drawing and bearings
Chaos by James Gleick
Powers (indices)
Rules for multiplying and dividing powers
Standard form - using powers of 10
Standard form - writing in standard form
Standard form - calculating in standard form
The Liar Paradox and the Towers of Hanoi: 10 Greatest Math Puzzles of All Time by Marcel Danesi
Patterns in number and number sequences
Finding the nth term of a linear sequence
Special sequences
General rules from given patterns
The nth term of a quadratic sequence
Finding the nth term for a quadratic sequence
Fibbonacci and Nature https://www.youtube.com/watch?v=wTlw7fNcO-0
Quantity as frac of another
Add and subtract fractions
Multiply and divide fractions
Percentage increase and decrease
Quantity as percentage of another
Tower of Hanoi https://www.mathsisfun.com/games/towerofhanoi.html
Congruent triangles
Transformations
Bisectors
Defining a locus
Loci problems
Plans and elevations
Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace by Leonard Mlodinow
Ratio - simplifying and exressing as a fraction
Direct proportion problems
Compound measures - rates of pay and speed distance time
Density and pressure
Compound interest and repeated percentage change
Reverse Percentages
Closing the Gap: The Quest to Understand Prime Numbers by Vicky Neale
Rational numbers, reciprocals, terminating and recurring decimals
Estimating powers and roots
Negative and fractional powers
Surds - simplifying
Limits of accuracy
Problems involving limits of accuracy
Choices and outcomes
0.9 recurring = 1 https://www.youtube.com/watch?v=-tlIPvK9gmM
Pythagoras' theorem
Applying Pythagoras' theorem in real-life situations
Pythagoras' theorem and isosceles triangles
Pythagoras' theorem in 3D
Trigonometric ratios
Calculating angles
Which ratio to use
Solving problems using trigonometry (1)
Trigonometry and bearings
Trigonometry and isosceles triangles
Visual Proof of Pythagoras' Theorem https://www.youtube.com/watch?v=tTHhBE5lYTg
Probability and two-way tables
Probability and Venn diagrams
Pin codes https://www.joe.co.uk/life/somebody-has-worked-out-the-20-most-common-and-least-common-pin-numbers-35079
Drawing linear graphs from points
Drawing linear graphs by gradient-intercept
Finding the equation of a line from its graph
Real-life uses of graphs
Solving simultaneous equations using graphs
Parallel and perpendicular lines
Equation Graphing https://www.mathsisfun.com/data/graphs-index.html
Circumference and area of a circle
Sectors
Cylinders (Vol and SA)
Volume of a pyramid
Cones
Spheres
Things to Make and Do in the Fourth Dimension by Matt Parker
Linear equations - review of brackets and unknowns on both sides
Elimination method for simultaneous equations
Substitution method for simultaneous equations
Balancing coefficients to solve simultaneous equations
Using simultaneous equations to solve problems
Linear inequalities including the number line
Graphical inequalities
Trial and improvement
The Code Book by Simon Singh
Simlar triangles
Problem solving using similar triangles
Harder problems
Areas and volumes of similar shapes
Fermat's Last Theorem by Simon Singh
Powers
Multiplying and dividing by powers of 10
Standard form (calc)
How to Solve It by George Polya
Compound interest and repeated change
Reverse percentage
https://www.leonardodavinci.net/the-vitruvian-man.jsp
Constructing triangles
https://www.sciencemuseum.org.uk/see-and-do/mathematics-winton-gallery
Sampling
Scatter diagrams
Grouped data and averages
https://medium.com/however-mathematics/all-podcasts-for-mathematics-people-e684c9cac79b
Pythagoras Theorem, finding the hypotenuse
Calculating the short side
Pythagoras Theorem in real life problems
Pythagoras Theorem in isosceles triangles
Calculating lengths using trigonometry
Calculating angles using trigonometry
Trig without a calculator
Solving problems using trig
Recognising similarity
Finding unknown sides in similar shapes
Problem solving using similarity
Elimination method for harder simultaneous equations
Solving linear inequalities
Why do Buses Come in Threes? by Rob Eastaway and Jeremy Wyndham
Combined events
Tree diagrams
How many ways are there to shuffle a deck of cards? https://www.youtube.com/watch?v=uNS1QvDzCVw
Distance time graphs
Plotting and solving quadratic graphs
Solving quadratic equations by factorisation
Significant points of a quadratic curve
Cubic and reciprocal graphs
Graphing website http://www.desmos.com
Volume of Pyramids
SA of pyramids
Volume and SA cones
How Many Socks Make a Pair? by Rob Eastawa
Plotting quadratic graphs
Solving equations by using the quadratic formula
Solving quadratic equations by completing the square
The significant points of a quadratic curve
Solving one linear and one non-linear equation using graphs
Solving quadratic equations by the method of intersection
Solving linear and non-linear simultaneous equations algebraically
Quadratic inequalities
Collecting data
Frequency polygons
Cumulative frequency graphs
Box plots
Histograms
Standard deviation and variance https://www.mathsisfun.com/data/standard-deviation.html
Addition rules for outcomes of events
Independent events
Conditional probability
Circle theorems
Cyclic quadrilaterals
Tangents and chords
Alternate segment theorem
Radian Measure https://www.mathsisfun.com/geometry/radians.html
Further 2D problems
Further 3D problems
Trigonometric ratios of angles between 0o and 360o sine
Solving any triangle - sine rule
Using sine to calculate the area of a triangle
Sin Cos Hand Trick https://www.youtube.com/watch?v=PF2nmCVSUEs
Filling bottle graphs
Velocity-time graphs - interpretation and finding distance
Estimating the area under a curve
Rates of change
Equation of a circle
Other graphs - reciprocal and exponential
Transformations of the graph y=f(x) - translation
Algebraic fractions
Functions and inverses
Composite functions numeric and algebraic substitution
Iteration
How Many Socks Make a Pair? by Rob Eastaway
Properties of vectors
Vectors in geometry
Vectors https://www.mathsisfun.com/algebra/vectors.html
Binomial expansion
Product rule
Simplifying Expressions
Surds
Investigate the binomial theorem in statistics https://www.statisticshowto.com/probability-and-statistics/binomial-theorem/#:~:text=What%20is%20the%20Binomial%20Theorem,%2C%20like%20heads%20or%20tails)
Completing the square with non-unit coefficients
Factorising
Investigaet graph transformations and finding turning points using https://www.transum.org/software/SW/Functions/
Composite functions
Domains and ranges
Function notation and inverses
Graphs of functions
Used in computer programming try it at: https://scratch.mit.edu/
Algebraic proof
Factor theorem
Indices
Inequalities
Quadratic equations
Sequences
Simultaneous equations
Fermat's last Theorem explained: https://www.youtube.com/watch?v=qiNcEguuFSA
Distance between points
Intersection of lines
Mid points
Map scales and trajectory's: Try out geodesic routes using https://www.greatcirclemap.com/
Geometric proof
Trigonometry including graphs and identities
Read 'Euclid's window' by Leonard Mlodinow
Trigonometric rules
Trigonometry in 3D including planes
Try to solve these problems: https://undergroundmathematics.org/thinking-about-geometry/all-about-ratios
Differentiation - 1st and 2nd derivatives
Increasing and decreasing functions
Stationary points
Tangents and normals
Investigate the max box problem: https://www.utcsouthdurham.org/_filecache/523/fd4/838-a-level-maths-year-12-transitions-2020-worksheets.pdf
Combining transformations
Equating elements of matrices
Multiplying matrices by matrices
Multiplying matrices by scalars
The identity matrix
Problem solve at: https://undergroundmathematics.org/vector-geometry/hit-the-spot
Arguments and Proof
Index laws
Lines and circles
Quadraric equations
https://kpknudson.com/my-favorite-theorem/
Expanding and factorising
The binomial theorem
Algebraic Division
Curve Sketching
https://podcasts.ox.ac.uk/series/secrets-mathematics
The sine, Cosine and tangent graphs
The sine and Cosine rules
Differentiation from first principles
Differentiating ax^n and Leibniz notation
Tangents and Normals
Turning Points
Integration
Area under a curve
https://www.bbc.co.uk/programmes/b00srz5b/episodes/downloads
The laws of logs
Exponential Functions
Exponential Processes
Curve Fitting
Central tendancy & Spread
Single Variable Data
Bivariate Data
https://www.bbc.co.uk/programmes/p00545hk
Probability
Binomial Distribution
https://soundcloud.com/damien-adams-662584563
Formulating a test
The Critical Region
https://podcasts.ox.ac.uk/keywords/maths
Definitions and Properties
Components of a Vector
https://www.bbc.co.uk/programmes/p00cl73s
Standard Units & Basic Dimension
Motion in a Straight Line
Equations of motion for constant acceleration
Motion with variable acceleration
https://www.bbc.co.uk/programmes/b006qshd
Forces 1
Dynamics 1
Motion under Gravity
Systems of Forces
Further mathematical proof
Functions
Parametric Equations
Algebraic Fractions
Partial Fractions
The Binmoial Series
Introduction to sequences
Arithmetic Sequences
Geometric Sequence
Radians
Reciprocal & Inverse Trig functions
Compound Angles
Equivalent forms for acos θ + bsin θ
The shape of functions
Trigonometric Functions
Exponential and Log functions
The Product Rule
The Quotient Rule
The Chain Rule
Inverse Functions
Implicit Differntiation
Parametric Functions
https://www.bbc.co.uk/programmes/b00srz5b/episodes/download
Standard Integrals
Integration by Substitution
Integration by Parts
Integrating Rational Functions
Differential Equations
Simple Root Finding
Iterative Root Finding
Newton-Raphson Root Finding
Numerical Integration
Conditional Probability
Modelling with Probability
Normal Distribution
Using the Normal distribution as an approx to the binomial
Testing Correlation
Testing a Normal Distribution
2D motion with constant acceleration
2D motion with variable acceleration
Motion under gravity 2
Motion under forces
Vectors in 3D
Statics
Dynamics 2
Moments
Admissions
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Examinations
Details on forthcoming exams
Professional Learning Hub
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