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.
KS3-4 Pathways (Southfield)
GCSE Mathematics Foundation and Higher (EdExcel)
GCSE Statistics
Level 2 Further Mathematics (AQA)
KS4-5 Pathways (Southfield)
A level and AS Level Mathematics (AQA)
KS5- Higher & Further Education Pathways
Careers
Engineering, Accounting, Architecture, Financial analyst, Actuary, Computer programmer
KS4 Specification links
https://qualifications.pearson.com/en/qualifications/edexcel-gcses/mathematics-2015.html
KS5 Specification links
https://www.aqa.org.uk/subjects/mathematics/as-and-a-level/mathematics-7357
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
Word/phrase
Definition
Time series
Line graph with time plotted on the horizontal axis
Seasonal variation
Variation in a time series following a regular time period
An assessment of how strongly two sets of data are related
Positive
Positive correlation is when as one variable increases, so does the other
Negative
Negative correlation is when as one variable increases, the other decreases
Index numbers
Compare the price of an item with a base year price
Gross domestic product
The value of goods and services a country produces within a stated time period.
Recession
An economy is in recession when its GDP falls in two (or more) successive quarters.
Frequency Polygon
A line graph of class frequency plotted against midpoint
Index form
A number in index form has a base number and is raised to a power eg 2^3
Standard form
A format to write large and small numbers whereby the columns are given as a power of ten
Power
A repeated multiplication eg, 2^3 means 2 x 2 x 2
Estimate
we round to 1 significant figure to approximate a calculation, so that it is easy enough to do without the use of a calculator
Rational
A number that can be written as a fraction
Surd
An irrational number
Numerator
The number at the top of the fraction
Denominator
The number at the bottom of the fraction
Reciprocal
When you divide 1 by a number or fraction eg, the reciprocal of 3 is 1/3
Multiplier
A decimal used to find a percentage of a number. It can be used to increase and decrease by a percentage
Depreciate
when the value goes down eg, the cost of a car depreciates each year
Substitution
Swap out a variable for a number
Variable
Often a letter used to represent an unknown number, which can be changed
Factorise
To divide an expression by a term which leaves no remainders eg 10x + 5 would be 5(2x + 1) as 5 is the common factor
Expand
The opposite of factorising which is multiplication, expanding 5(2x +1) would give 10x + 5 as 5 multiplied by 2x gives 10x and 5 multiplied by 1 gives 5
Linear
Straight line equations have only single powers of x (not x^2 or above)
Subject
The subject of a formula is the letter that appears on its own next to the = sign. For example x = 4y has "x" as the subject
Rearrange
To change and move variables of an equation so that they appear on the other side
An unknown quantity given as a letter
Solve
To calculate a value for an equation which fits the rule, eg 2x = 8 would have the solution x= 4
Vertically opposite
Angles that are opposite a vertex (point) made by two straight lines
Exterior angles
Angles that are formed by extending the sides of a polygon. They form a 180 degrees wih the interior angles
Interior angles
The angles on the inside of a polygon
Bearing
An angle given from the direction of north, measured in a clockwise direction
Corresponding angles
Angles on a set of parallel lines that are in the same position when raised from one line to the next
Grouped data
When data is arranged into categories instead of having fixed values eg age could be split into 0- 10 years 11 - 20 years etc
Mean
A calculated value which distributes the total of a measure with the whole population
Range
The difference between the largest and smallest data value.
Mode
The value that occurs the most
Median
The middle value when the data has been ordered
Interquartile range
The difference between the upper quartile and lower quartile.
Skewness
The degree of asymmetry that occurs in a set of data
?Key vocabulary
Hypotenuse
The side of a right angled triangle that appears opposite the right angle
Isosceles
A triangle with two equal sides only and also two equal angles
Trigonometric ratio
The ratios of the sides of a right angled triangle, Sine, Cosine and tangent
Inverse
Meaning opposite. In trigonometry inverse sine is used to calculate an angle given the lengths of the opposite and the hypotenuse
Composite Shapes
Shapes that are formed by adding or subtracting two or more shapes
Surface area
The total area of all the faces of a 3D shape
Prism
A 3D shape with a uniform cross section
Cross-sectional Area
The face of a prism which remains constant throughout its length. Eg for a cylinder, the cross-sectional area will be the circle at the front
Vertex
The corner of a shape whereby three or more faces meet
Cylinder
A type of prism that has a circle as its cross section
Gradient
The steepness or slope of a line
y - intercept
Where the line crosses the y- axis
Perpendicular
When two lines meet at 90 degrees to one another
Parallel
Two lines that have the same gradient and will never cross
Turning point
The maximum or minimum point on a curve whereby the graph changes from increasing to decreasing or vice versa
Roots
The roots of a quadratic are the solutions when y=0. It is the intercepts with the x- axis
Origin
The centre (0,0) often used as the centre of transformations
Reflect
To flip an image over a mirror line
Rotational symmetry
Whereby a shape fits exactly over itself when rotated 360 degrees around its centre
Enlarge
To multiply a shapes lengths by a scale factor which will either make it bigger or smaller keeping the proportions the same
Translate
To move a shapes position on a coordinate axis without changing its orientation or size
Locus
A particular position or place where something occurs or is situated
Bisect
To cut equally in half
Scale
The ratio used on maps or drawings to represent the images in real life
Net
When a 3D shape is drawn in 2D as its faces connected together. The net of a cuboid could be imagined as unfolding a cereal box and the flat cardboard that is used to form it
Plan view
The view from above, often known as birds eye view
Mutually exclusive
Two events that cannot happen at the same time
Exhaustive
When all the stated probabilities sum to 1
Relative frequency
The amount of times an expected outcome is likely to occur based on the number of trials
Sample space
Diagram used to list all the possible outcomes of an experiment
Outcome
The result of doing an experiment eg getting tails is an outcome of flipping a coin, as is heads
Proportional
When two or more things are linked by a common multiple or ratio
As one quantity is increased, the other is by the common ratio eg exchanging money
Inversely proportional
When one variable is increased, the other decreases - eg temp and time for an ice cube
Best value
The cheapest per unit of weight or the highest quantity per unit weight
Calculate a value/s which makes the equation true
Coefficients
The multiple of a variable. Eg 2x has a coefficient of 2 as x is being multiplied by 2
Inequalities
The link between two expressions that are not equal, using the symbols < and > etc
Term
A number that appears in a sequence
N'th term rule
A rule for a seqeunce whereby each term has the same number added or subtracted to generate the next term
Fibbonacci
A sequence whereby the two previous terms sub to the next
Quadratic
A sequence whereby the term number is squared, will feature n^2
Term to term rule
A rule which explains how to move from one term to the next in a sequence
Bounds
The limits/range of a calculation when a number has been rounded in some way
Error Interval
Radius
The distance from the centre of a circle to the circumference
Elimination
A method of solving whereby you remove one variable by adding or subtracting simultaneous equations
A method of solving whereby you replace a variable with an equal equation. For example substituting y = 2x into 3x - y = 12 would give 3x - 2x = 12
Mixed number
A fraction with whole number and fractional parts eg 1 and one half
Improper fraction
A "top heavy" fraction where the numerator is larger than the denominator eg 5/2
A measure of distance over a measure of time eg m/s
Principle
The original amount invested into a bank account when doing repeated percentage change
When the value goes down eg, the cost of a car depreciates each year
Density
A measure of mass over a measure of volume eg g/cm^3. It is used to compare weights of objects of similar sizes
Interest
A percentage of he original amount that is added to the total
Congruent
Two shapes that are equal in size and proportions (can be mirror images of one another)
Scale factor
The multiplier which is the common ratio between two shapes length, area or volume
Similar
Whereby the proportions of two shapes are the same and there is a common ratio of their lengths
An expression where the highest power has a value of 2.
Cubic
An expression where the highest power has a value of 3
Vector
A quantity having direction as well as magnitude
Magnitude
The size of something
In the same direction, with equal gradient
Primary Data
Data that has been generated by the researcher.
Secondary Data
Data that has been sourced by the researcher but not generated by them
Sampling
Selection of a subset of individuals from a larger population
Tangent
A line that touches a curve at one place only, for a circle the tangent meets the radius at an angle of 90 degrees
Cyclic quadrilaterals
A quadrilateral whos vertices are on the circumference of a circle
Chord
A line that joins two points on the circumference however, it does not go through the centre of the circle
Segment
The part trapped by the chord often described as the shape of a piece of orange
Subtend
At a particular point when straight lines from its extremities are joined at that point
Simultaneous graphs
Two graphs that will intersect each other. The coordinates where they cross will be a solution to each equation
Completing the Square
A method of solving a quadratic equation by halving the x coefficient and writing that as a square.
Non-linear
An equation whereby the variables are raised to powers higher than 1, eg a cubic has an x^3 term which gives the graph a curved shape rather than linear.
The subject of a fomula is the letter that appears on its own next to the = sign. For example x = 4y has "x" as the subject
The opposite function eg y = 4x has an inverse of y/4 = x each swaps the output for the input
Composite function
Whereby the input of one function is a function within itself. Eg y = sin x^2 , the function of x^2 has been the input for the function y = sin x
Scalar
A quantity with no direction only size
Collinear
When two lines that are parallel share a common point
Exponent
A quantity representing the power which a number is to be raised to
Transformation
When a graph is translated or reflected
Velocity
Speed in a given direction
Acceleration
The gradient of a velocity time graph, it’s the rate of change of velocity
Normal distribution
A function that represents the distribution of many random variables as a symmetrical bell shape graph
Binomial distribution
A frequency distribution of the possible number of successful outcomes in a given number of trials in each of which there is the same probability of success.
Standard deviation
A measure of the amount of variation of a random variable expected about its mean
Primary Dat
Binomial expansion
Product rule
Simplifying Expressions
Solving linear equations
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)
Algebraic fractions
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
Quadratic equations
Sequences
Simultaneous equations
Fermat's last Theorem explained: https://www.youtube.com/watch?v=qiNcEguuFSA
Distance between points
Equation of a circle
Intersection of lines
Mid points
Parallel and perpendicular lines
Map scales and trajectory's: Try out geodesic routes using https://www.greatcirclemap.com/
Circle theorems
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
Rates of change
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
Access our current admissions information
Examinations
Details on forthcoming exams
Professional Learning Hub
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