Mathematics

The mathematics department at Southfield School aims to develop and instil confidence in problem solving and critical thinking.

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 (AQA), Level 2 Further Mathematics (AQA)
KS4-5 Pathways (Southfield) A level and AS Level Mathematics (AQA)
KS5- Higher & Further Education
Pathways		 A level and AS Level Mathematics (AQA)
Careers  Engineering, Accounting, Architecture, Financial analyst, Actuary, Computer programmer 
KS4 Specification links  https://www.aqa.org.uk/subjects/mathematics/gcse/mathematics-8300/specification-at-a-glance 
https://www.aqa.org.uk/subjects/mathematics/aqa-certificate/further-mathematics-8365
KS5 Specification links

https://www.aqa.org.uk/subjects/mathematics/as-and-a-level/mathematics-7357
Year 7

Unit 1 - Working with Numbers

Key questions/concepts

  • Squares and Square Roots

  • Rounding

  • Order of Operations

  • Long and Short Multiplication and Division

  • Calculations with measurements 

Timeframe

  • September - October

Key vocabulary

Word/phrase Definition
Metric units The metric system
Conversion Expression
Rounding Convenient number of decimals
Decimal places Fraction
Power The power (or exponent) of a number says how many times to use the number in a multiplication

 

 

 

 

 

Wider reading

  • The Boy Who Loved Math: The Improbable Life of Paul Erdös

 

Unit 2 - Perimeter, area, volume

Key questions/concepts

  • Perimeter & Area
  • Perimeter & Area of rectangles
  • Perimeter & area of compound shapes
  • Volume of cubes & cuboids 

Timeframe

  • September - October

Key vocabulary

Word/phrase Definition
Surface area The surface the object occupies
Capacity Something can contain
Perpendicular At an angle of 90° to a given line, plane, or surface or to the ground
Formula Expressed in symbols
Compound shapes Shapes joined together

 

Wider reading

 

Unit 3 - Decimal numbers

Key questions/concepts

  • Multiplying and Dividing by 10,100,1000
  • Ordering decimals
  • Estimates
  • Adding and Subtracting decimals
  • Adding negative mumbers
  • Subtracting negative numbers

Timeframe

  • October - November

Key vocabulary

Word/phrase Definition
Reciprocal Divided by number
Estimate Roughly calculate or judge the value, number, quantity, or extent of
Approximation A value or quantity that is nearly but not exactly correct
Inverse A reciprocal quantity, mathematical expression, geometric figure, etc. which is the result of inversion.
Place value The value of each digit in a number

 

Wider reading

  • Can you Solve my Problems? by Alex Bellos

 

Unit 4 - Using numbers

Key questions/concepts

  • Timetables, charts and money
  • Positive and nagative numbers
  • Adding negative numbers
  • Subtracting negative numbers

Timeframe

  • October - November

Key vocabulary

Word/phrase Definition
Debit An amount of money taken out of an account: the opposite of credit.
Credit The ability of a customer to obtain goods or services before payment, based on the trust that payment will be made in the future.
Inequality A relation which makes a non-equal comparison between two numbers or other mathematical expression
Timetable A number
Analogue Change

 

Wider reading

 

Unit 5 - Algebra

Key questions/concepts

  • Expressions and substitution
  • Simplifying expressions
  • Using formulae
  • Writing formulae

Timeframe

  • October - November

Key vocabulary

Word/phrase Definition
Expression A finite combination of symbols that is well-formed according to rules that depend on the context
Substitute Means to put in the place of another
Variable A variable is a symbol which works as a placeholder for expression or quantities that may vary or change
Term Variable
Equivalent Equal in value, amount, function, meaning, etc.

 

Wider reading

  • A Mathematical Pandora's Box by Brian Bolt

 

Unit 6 - Statistics

Key questions/concepts

  • Mode, median, range and meaning
  • Statistics diagrams
  • Collecting and using data
  • Grouped frequency
  • Data collection

Timeframe

  • November - December

Key vocabulary

Word/phrase Definition
Grouped Frequency The frequency is the number of times a particular data point occurs in the set of data. Grouped data is data given in intervals.
Continuous Data Any value
Sample A  small part or quantity intended to show what the whole is like
Discrete data Values
Outlier Significant from other

 

Wider reading

Unit 7 - Fractions

Key questions/concepts

  • Equivalent fractions
  • Comparing fractions
  • Adding and substracting fractions
  • Mixed numbers and improper fractions
  • Calculations with mixed numbers

Timeframe

  • January - February

Key vocabulary

Word/phrase Definition
Common factor A number that can be divided into two different numbers, without leaving a remainder.
Mixed number A whole number, and a proper fraction represented together
Improper fractions A fraction in which the numerator is greater than the denominator
Convert Function of something
Equivalent Equal in value, amount, function, meaning, etc.

 

Wider reading

  • Epyptian fractions

 

Unit 8 - Sequences

Key questions/concepts

  • Function machines
  • Sequences and rules
  • Working out missing terms
  • Other sequences

Timeframe

  • January - February

Key vocabulary

Word/phrase Definition
nth term A formula with 'n' in it which enables you to find any term of a sequence without having to go up from one term to the next.
Algebraic Rule A mathematical expression that relates two variables and is written in the form of an equation
Triangular Numbers Any of the series of numbers (1, 3, 6, 10, 15, etc.) obtained by continued summation of the natural numbers 1, 2, 3, 4, 5, etc.
Input The known variable
Output The solution

 

Wider reading

  • Blockhead: The Life of Fibonacci

 

Unit 9 - Coordinated and graphs

Key questions/concepts

  • Coordinates
  • Horizonal and vertical lines
  • Graphs of the form y=ax
  • Graphs from the relationships
  • Real life graphs

Timeframe

  • January - February

Key vocabulary

Word/phrase Definition
Graph A pictorial representation or a diagram that represents data
Rule Rule is the procedure that a count must follow
Conversion graphs A conversion graph is used to change one unit into another
Quadrant Any of the 4 areas made when we divide up a plane by an x and y axis
Origin The origin is the point where the axes of the system intersect

 

Wider reading

  • Infinity and Me

 

Unit 10 - Percentages

Key questions/concepts

  • Fractions, decimals and percentages
  • Franctions of a quantity
  • Percentages of a quantity
  • Percentages with a calculator
  • Percentage increase and decrease

Timeframe

  • February - March

Key vocabulary

Word/phrase Definition
Deposit The act of putting money into a bank account
Reduction Reduction refers to the rewriting of an expression into a simpler form
Increase Make something bigger (in size or quantity)
Decrease Make something smaller (in size or quantity)
Quantity The origin is the point where the axes of the system intersect

Wider reading

 

Unit 11 - Equations

Key questions/concepts

  • Finding unknown numbers
  • Solving equations
  • Solving more complex equations
  • Setting up and solving equations

Timeframe

  • February - March

Key vocabulary

Word/phrase Definition
Variable A symbol which works as a placeholder for expression or quantities that may vary or change
Operation A function which takes zero or more input values to a well-defined output value
Inverse Inverse refers to the opposite of another operation
Solve To solve something is to find a solution
Algebra Algebra is the study of mathematical symbols and the rules for manipulating these symbol

Wider reading

 

Unit 12 - Angles

Key questions/concepts

  • Measuring and drawing angles
  • Calculating angles
  • Angles in a triangle
  • Angles in a quadrilateral
  • Properties of triangles and quadrilaterals

Timeframe

  • March - April

Key vocabulary

Word/phrase Definition
Vertices The points where two or more curves, lines, or edges meet
Parallel Lines in a plane which do not meet
Perpendicular The relationship between two lines which meet at a right angle
Intersect When two or more lines cross each other in a plane
Compass An instrument with two arms, one sharp and one with a pencil that can be used to draw circles or arcs

Wider reading

 

Unit 13 - Ratio

Key questions/concepts

  • Intro to ratios
  • Simplifying ratios
  • Ratios and sharing
  • Solving Problems

Timeframe

  • April - May

Key vocabulary

Word/phrase Definition
Quantity How much there is of something
Simplify To make simpler, such as, to reduce to basic essentials

Wider reading

  • On a Beam of Light: A Story of Albert Einstein

 

Unit 14 - Symmetry

Key questions/concepts

  • Line symmetry and Rotational Symmetry
  • Reflections
  • Tessellations

Timeframe

  • April - May

Key vocabulary

Word/phrase Definition
Tessellation The covering of a plane using one or more geometric shapes
Object An object is anything that has been (or could be) formally defined
Image The image of a function is the set of all output values it may produce
Mirror Line A systematic (built-in) error which makes all values wrong by a certain amount
Reflect An image or shape as it would be seen in a mirror

Wider reading

 

Unit 15 - Probability

Key questions/concepts

  • Probability Words
  • Probability Scales
  • Experimental Probability

Timeframe

  • June - July

Key vocabulary

Word/phrase Definition
Trial A single performance of well-defined experiment
Theoretical Probability Probability that is determined on the basis of reasoning
Event A set of possible outcomes resulting from a particular experiment
Biased A systematic (built-in) error which makes all values wrong by a certain amount
Fair A probability experiment may be considered "fair" if all outcomes are equally likely

Wider reading

 

Unit 17 - Interpreting Data

Key questions/concepts

  • Pie Charts
  • Comparing mean and range
  • Statistical Surveys

Timeframe

  • June - July

Key vocabulary

Word/phrase Definition
Data Data is a collection of facts, such as numbers, words, measurements, observations or just descriptions of things
Tally A way of keeping count by drawing marks
Frequency The number of times an event or a value occurs
Sector The portion of a disk enclosed by two radii and an arc
Pie Charts A pie chart is a circular statistical graphic, which is divided into slices to illustrate numerical proportion

Wider reading

 

Year 8

Unit 1 - Working with Numbers

Key questions/concepts

  • Multiplying and dividing negatives

  • Factors and HCF

  • Multiples and LCM

  • Powers and roots

  • Prime factors

Timeframe

  • September - October

Key vocabulary

Word/phrase Definition
Negative Less than zero
Positive More than zero
Factor A number which divides perfectly into another number
Multiple The result of multiplying a number by an integer
Prime A number that is divisible by itself and 1

 

 

 

 

 

Wider reading

 

Unit 2 - Geometry

Key questions/concepts

  • Angles in parallel Lines

  • Geometric properties of quadrilaterals

  • Translations

  • Rotations

  • Constructions

Timeframe

  • September - October

Key vocabulary

Word/phrase Definition
Allied Angles enclosed by the parallel lines and transversal which sum to 180 degrees
Alternate Angles which are on opposite sides of the transversal. These can be interior or exterior
Corresponding The angles which occupy the same relative position at each intersection where a straight line crosses two others
Transversal A line that crosses at least two other lines.
Parallel  

 

 

 

 

 

 

Wider reading

  • The Math Book by Clifford A Pickover

 

Unit 3 - Probability

Key questions/concepts

  • Probability scales

  • Mutually exclusive events

  • Venn Diagrams

  • Sample spaces

  • Experimental probability

Timeframe

  • September - October

Key vocabulary

Word/phrase Definition
Intersection A new set which contains all the elements that are common to both the sets
Mutually Exclusive Two events which can never happen at the same time
Set A collection of items or data
Union A new set that contains all of the elements that are in at least one of the two sets
Venn diagram A diagram consisting of multiple curves, usually circles, each respresenting a set

 

 

 

 

 

Wider reading

 

Unit 4 - Percentages

Key questions/concepts

  • Calculating percentages

  • Calculating percentage increases

  • Calculating percentage decreases

  • Calculating percentage changes 

  • Using a multiplier to calculate a percentage

Timeframe

  • November - December

Key vocabulary

Word/phrase Definition
Percentage A rate, number or amount in each hundred
Multiplier The number by which another is multiplied
Increase To become or make greater in size, amount or degree
Decrease To become or make smaller in size, amount or degree
Tax An added amount to the original price

 

 

 

 

 

Wider reading

 

Unit 5 - Sequences

Key questions/concepts

  • Using flow diagrams to generate sequences

  • The nth term of a sequence

  • Using the nth term

  • Working out the nth term 

  • The Fibonacci sequence

Timeframe

  • November - December

Key vocabulary

Word/phrase Definition
Finite Limited in size or extent
Infinite Unlimited in size or extent
Flow diagram A diagram of the sequence of movements or actions of people or things involved in a complex system or activity
Generate To produce or create
Fibonacci An Italian mathematician considered to be "the most talented Western mathematician of the middle ages"

 

 

 

 

 

 

Wider reading

  • Snowflake Seashell Star by Alex Bellos and Edmund Harriss

 

Unit 6 - Area

Key questions/concepts

  • Area of a triangle

  • Area of a parallelogram

  • Area of a trapezium

  • Surface area of cubes

  • Surface area of cuboids

Timeframe

  • November - December

Key vocabulary

Word/phrase Definition
Base The bottom line of a shape
Height The vertical distance from the top of the shape to the base
Compound Shape Any shape which is made up of two or more geometric shapes
Perpendicular height The height when measured from a 90o intersection with the base
Surface area The total area that the surface of the object occupies

 

 

 

 

 

Wider reading

 

Unit 7 - Graphs

Key questions/concepts

  • Graphs from linear equations

  • Gradient of a straight line

  • Graphs from simple quasdratic equations

  • Distance-time graphs

  • Real life graphs

Timeframe

  • November - December

Key vocabulary

Word/phrase Definition
Linear equation An equation which makes a straight line when drawn on a graph
Variable A symbol for a number which we don't know yet
Rule A step by step procedure which must be followed
Gradient How steep a line is
Quadratic An equation where the highest exponent of the vasiable is a square

 

 

 

 

 

Wider reading

  • Alex's Adventures in Numberland by Alex Bellos

 

Unit 8 - Number

Key questions/concepts

  • Powers of 10

  • Large numbers and rounding

  • Significant figures

  • Standard form with large numbers

  • Multiplying with numbers in standard form

Timeframe

  • January - February

Key vocabulary

Word/phrase Definition
Indices Shows how many times a number or letter has been multiplied by itself
Significant figure The number of digits in a value that contribute to the degree of accuracy of the value
Estimate To find something close to the correct answer
Standard form Any number that we can write as a decimal number, between 1 and 10, multiplied by a power of 10
Rounding Making a number simpler but keeping its value close to what it was

 

 

 

 

 

Wider reading

 

Unit 9 - Congruence and Scaling

Key questions/concepts

  • Congruent shapes

  • Enlargements from centre (0,0)

  • Enlargements from a point (x,y)

  • Shape and Ratio 

  • Scales

Timeframe

  • January - February

Key vocabulary

Word/phrase Definition
Congruent Being the same shape and size after rotation, reflection or translation
Transformation Changing a shape using rotation, reflection, translation or enlargement
Congruent triangles Triangles with exactly the same three sides and exactly the same three angles
Scale factor By how much a shape has been enlarged
Rays Part of a line that has a fixed starting point but no end point

 

 

 

 

 

Wider reading

 

Unit 10 - Interpreting Data

Key questions/concepts

  • Pie charts

  • Creating pie charts

  • Scatter graphs

  • Correlation

  • Creating scatter graphs

Timeframe

  • February - March

Key vocabulary

Word/phrase Definition
Pie chart A type of graph which represents the data in a circular format
Sector The area between an arc and two radii of a circle
Correlation A measure of the relationship between two variables
Scatter graph A graph of plotted points that show the relationship between two sets of data
Frequency table A frequency table is a table that lists items and shows the number of times the items occur

 

 

 

 

 

Wider reading

  • Entertaining Mathematical Puzzles by Martin Gardner

 

Unit 11 - Algebra

Key questions/concepts

  • Algebraic notation

  • Like terms

  • Expanding brackets

  • Using algebraic expressions

  • Using index notation

Timeframe

  • February - March

Key vocabulary

Word/phrase Definition
Index notation A way of representing repeated multiplications of the same number
Algebraic expression Numbers, symbols and operations grouped together that show the value of something
Term A single number or variable, or numbers and variables muliplied together
Like terms Terms whose variables, with any exponents, are the same
Substitution Putting numbers in place of letters to calculate the value of an expression

 

 

 

 

 

Wider reading

 

Unit 12 - Fractions and Decimals

Key questions/concepts

  • 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

Timeframe

  • February - March

Key vocabulary

Word/phrase Definition
Denominator The bottom number in a fraction
Numerator The top number in a fraction
Integer A positive or negative whole number
Mixed number A number consisting of a whole number and a proper fraction
Improper fraction A fraction in which the numerator is greater than or equal to the denominator

 

 

 

 

 

Wider reading

  • The Camel Problem big list - 17 camels trick - MathOverflow 

 

Unit 13 - Proportion

Key questions/concepts

  • Direct proportion

  • Graphs and direct proportion

  • Inverse proportion

  • Comparing direct and inverse proportion

  • Real life proportion graphs

Timeframe

  • April - May

Key vocabulary

Word/phrase Definition
Direct proportion A relationship between two variables whose ratio is equal to a constant value
Variable A quantity that may change
Proportional A relationship in which two quantities vary directly with each other
Inverse proportion When one value increases as the other decreases or vice versa
Formula A rule or fact written with mathematical symbols

 

 

 

 

 

Wider reading

  • My Best Mathematical and Logic Puzzles by Martin Gardner

 

Unit 14 - Circles

Key questions/concepts

  • The circle and its parts

  • Circumference of a circle investigation

  • Circumference of a circle formula

  • Area of a circle

  • Compound shapes with circles

Timeframe

  • April - May

Key vocabulary

Word/phrase Definition
Circumference The distance around the edge of a circle
Diameter The distance from one point on a circle through the center to another point on the circle
Radius The distance from the center to the circumference. It is half of the circle's diameter
Chord A line segment connecting two points on a curve.
Pi A mathematical constant defined as the ratio of a circle's circumference to its diameter

 

 

 

 

 

Wider reading

 

Unit 15 - Equations and Formulae

Key questions/concepts

  • Equations with brackets

  • Equations with fractions

  • Equations with variables on both sides

  • More complex equations

  • Rearranging formulae

Timeframe

  • June - July

Key vocabulary

Word/phrase Definition
Inverse Operation The operation which reverses the effect of another operation
Simplify To reduce to the lowest terms by cancelling to the lowest common factor
Equation The statement that the values of two mathematical expressions are equal
Subject The variable you are solving for
Rearrange To change the order of one or more terms

 

 

 

 

 

Wider reading

 

Unit 16 - Comparing Data

Key questions/concepts

  • Grouped frequency tables

  • Drawing frequency diagrams

  • Comparing data

  • Which average to use?

  • Averages in real life

Timeframe

  • June - July

Key vocabulary

Word/phrase Definition
Class A group of objects with something in common
Continuous Data that can take any value
Discrete Information that can only take certain values
Frequency Frequency refers to the number of times an event or a value occurs
Grouped frequency table The grouped frequency table is a statistic method to organize and simplify a large set of data in to smaller groups

 

 

 

 

 

 

Wider reading

Year 9

Unit 1 - Percentages

Key questions/concepts

  • Simple  Interest

  • Percentage increase 

  • Percentage decrease

  • Caluating the original 

  • Using percentages

Timeframe

  • September - October

Key vocabulary

Word/phrase Definition
Simple interest A percentage of the loan that is paid at regular intervals for the life of the loan
Increase The new value is larger that the original value
Decrease The new value is smaller that the original value
Multiplier A method to increase or decrease by a given  percentage
Original value The value before any percentage increase or decrease

 

 

 

 

 

Wider reading

  • The Monty Hall Problem: Beyond Closed Doors by Rob Deaves

 

Unit 2 - Equations and Formulae

Key questions/concepts

  • Multiplying out brackets

  • Factorising algebraic expressions

  • Equations with brackets

  • Equations with fractions

  • Rearranging Formulae

Timeframe

  • September - October

Key vocabulary

Word/phrase Definition
Expand To multiply out a term with brackets
Factorise The opposite of expanding.  Put a common factor of the terms before the bracket
Expression An expression is a collection of terms
Equation A statement where two expressions are equal to each other as they have the same value
Subject The subject is the variable to the left of the = sign that everything else is equal to

 

 

 

 

 

Wider reading

 

Unit 3 - Polygons

Key questions/concepts

  • Angles in polygons- investigation

  • Angles in polygons - using angle sum

  • Angles in regular polygons

  • Tessellations and regular polygons

  • Constructions

Timeframe

  • September - October

Key vocabulary

Word/phrase Definition
Polygon A closed 2D shape that has straight sides
Concave A concave polygon is one that has at least one diagonal outside the polygon
Convex A convex polygon is one that has all diagonals inside the polygon
Regular A polygon with all interior angles equal and side lengths equal
Tessellation Repeating pattern of a 2D shape where the shapes fit together exactly, leaving no gaps

 

 

 

 

 

Wider reading

 

Unit 4 - Using Data

Key questions/concepts

  • Scatter graphs and correlations

  • Time-series graphs

  • Two-way tables

  • Comparing two or more data sets

  • Statistical Investigations

Timeframe

  • November - December

Key vocabulary

Word/phrase Definition
Correlation 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
Mean An average found by adding together all data values and dividing by how many there are
IQR A measure of spread of the data. 75th percentile - 25th percentile

 

 

 

 

 

Wider reading

  • The Language of Mathematics by Keith Devlin

 

Unit 5 - Fractions

Key questions/concepts

  • Adding and subtracting Fractions

  • Multiplying fractions 

  • Multiplying mixed numbers

  • Dividing fractions

  • Dividing mixed numbers

Timeframe

November - December

Key vocabulary

Word/phrase Definition
Denominator The bottom number in a fraction
Numerator The top number in a fraction
Equivalent Having the same value
Proper A fraction where the numerator is smaller that the denominator
Improper A fraction where the numerator is larger than the denominator

 

 

 

 

 

Wider reading

  • 50 Mathematical Ideas You Really Need to Know by Tony Crilly

 

Unit 6 - Algebra

Key questions/concepts

  • More about brackets

  • Factorising simple expressions

  • Factorising expressions containing powers 

  • Expanding single brackets

  • Expanding the product of two brackets

Timeframe

  • November - December

Key vocabulary

Word/phrase Definition
Variable A symbol for a value we don't know yet
Coefficient A number used to multiply a variable which appears in front of the variable
Term Either a single number, variable or numbers and variables multiplied together
Quadratic Where the highest power of a variable is a square i.e. a power of 2
Product The result when multiplying

 

 

 

 

 

Wider reading

  • The 'Uncle Albert' Series by Russell Stannard

 

Unit 7 - Decimal Numbers

Key questions/concepts

  • Powers of 10

  • Standard Form

  • Rounding appropriately

  • Mental calculations

  • Solving problems

Timeframe

  • November - December

Key vocabulary

Word/phrase Definition
Decimal A system of numbers based on the number ten, tenth parts and powers of ten
Integer A whole number which can be positive, negative or zero
Standard form A concise way of writing very large or very small numbers
Rounding Making a number simpler but keeping its value close to what it was
Significant figures The number of digits that contribute to the degree of accuracy of the value

 

 

 

 

 

Wider reading

 

Unit 8 - Volume and Surface Area

Key questions/concepts

  • Metric Units for area and volume

  • Volume of a prism

  • Surface area of a prism

  • Volume of a cylinder

  • Surface area of a cylinder

Timeframe

  • January - February

Key vocabulary

Word/phrase Definition
Prism A solid object with two identical end faces and all other faces are rectangles
Cube A prism with 6 identical square faces
Cuboid A prism with 6 rectangular faces 
Cylinder A shape with two identical circular end faces and one curved face
Volume The amount of 3-dimensional space an object takes up

 

 

 

 

 

Wider reading

 

Unit 9 - Solving Equations Graphically

Key questions/concepts

  • 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

Timeframe

  • January - February

Key vocabulary

Word/phrase Definition
Gradient A measure of the slope of a line
Intercept The point at which a graph crosses an axis
Constant A numerical value
Linear Forms a straight line when graphed
Roots Where the graph crosses the x-axis i.e. thex- values which give a y-value of zero

 

 

 

 

 

Wider reading

  • The Music of the Primes by Marcus Du Sautoy

 

Unit 10 - Compound Units

Key questions/concepts

  • Speed

  • More about proportion

  • Force, Mass, Area

  • Mass, Density, Volume

  • Unit Costs

Timeframe

  • January - February

Key vocabulary

Word/phrase Definition
Compound unit A measurement that uses more than one quantity 
Speed Distance divided by time
Distance Length. A measure of how far
Mass A measure of how much matter is in an object
Density Mass divided by volume

 

 

 

 

 

Wider reading

  • Flatterland by Ian Stewart

 

Unit 11 - Applications of Graphs

Key questions/concepts

  • Step graphs

  • Time graphs

  • Real-life graphs

  • Exponential growth graphs

  • Exponential decay graphs

Timeframe

  • February - March

Key vocabulary

Word/phrase Definition
Discontinuous Not in one continuous line
Step-graph Also called piece-wise. A line graph made up of lines in horizontal intervals or "steps"
Exponential growth Where a value increases in proportion to its current value, such as always doubling
Axes Axes often means the "x" and "y" lines that cross at right angles to make a graph
Exponential decay Decrease at a fixed rate 

 

 

 

 

 

Wider reading

 

Unit 12 - Pythagoras' Theorem

Key questions/concepts

  • 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

Timeframe

  • February - March

Key vocabulary

Word/phrase Definition
Right-angle An angle of 90 degrees
Hypotenuse Side opposite the right-angle in a triangle. It is also the longest side of a right-angled triangle
Square number The result of multiplying a number by itself
Square-root The square root of a number is the value that, when multiplied by itslef, gives you the number
Pythagoras The mathematician after whom the theorem a2 + b2 = c2 is named

 

 

 

 

 

Wider reading

 

Unit 13 - Right-angled Triangles

Key questions/concepts

  • 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

Timeframe

  • February - March

Key vocabulary

Word/phrase Definition
Adjacent side Next to. In this topic it is the side next to the angle being used
Opposite side The side opposite the angle of interest in the triangle
Sine The length of the side opposite the angle divided by the length of the hypotenuse
Cosine The length of the adjacent side divided by the length of the hypotenuse
Tangent The length of the side opposite the angle divided by the length of the adjacent side

 

 

 

 

 

Wider reading

  • Journey Through Genius: The Great Theorems of Mathematics by William Dunham

 

Unit 14 - GCSE Preparation

Key questions/concepts

  • Practice in algebra and solving equations

  • Practice in graphs

  • Practice in geometry and measures

  • Practice in statistics

  • Practice in number

Timeframe

  • March - April - GCSE course starts June/July

 

Wider reading

Year 10 Foundation

Unit 1 - Expressions and formulae

Key questions/concepts

  • Basic algebra

  • Substitution

  • Expanding brackets

  • Collecting like terms

  • Factorisation

  • Quadratic expansion (different methods)

  • Harder quadratic expansions

  • Quadratic factorisation

  • Difference of 2 squares

Timeframe

  • September - October

Key vocabulary

Word/phrase Definition
Solve Calculate a value/s which makes the equation true
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, expaning 5(2x +1) would give 10x + 5  as 5 multiplied by 2x gives 10x and 5 multiplied by 1 gives 5

 

 

 

 

 

 

Wider reading

  • How to Cut a Cake: and Other Mathematical Conundrums by Ian Stewart

 

Unit 2 - Measures and scale drawing

Key questions/concepts

  • Sensible estimates for scales and systems of measurement (metric)

  • Systems of measurement (imperial)

  • Conversion factors (metric to imperial)

  • Scale drawings

  • Nets

Timeframe

  • September - October

Key vocabulary

Word/phrase Definition
Metric A system of units whereby the common ratio is often 1000. eg 1000g is equal to 1kg
Imperial  The old units of measure such as pounds and ounces, inches and yards and gallons and pints
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

 

 

 

 

 

 

Wider reading

  • Thinking Mathematically by Mason, Burton & Stacey

 

Unit 3 - Approximations

Key questions/concepts

  • Rounding integers and decimals

  • Rounding with sf

  • Approximating calculations

Timeframe

  • September - October

Key vocabulary

Word/phrase Definition
Decimal places The decimal columns a number has Eg 2.5 has 1 decimal place as the 5 appears after the decimal place
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

 

 

 

 

Wider reading

 

Unit 4 - Angles

Key questions/concepts

  • Angle facts

  • Triangles

  • Angles in a polygon

  • Regular polygons

  • Angles in parallel lines

  • Special quadrilaterals

  • Bearings

Timeframe

  • November - December

Key vocabulary

Word/phrase Definition
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

 

 

 

 

 

 

Wider reading

  • Chaos by James Gleick

 

 

Unit 5 - Decimals and fractions

Key questions/concepts

  • Calculating with decimals (non calc)

  • Fractions and reciprocals

  • Quantity as fraction of another 

  • Fractions on a calculator

  • Adding and subtracting fractions

  • Multiplying and dividing fractions

Timeframe

  • November - December

Key vocabulary

Word/phrase Definition
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
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

 

 

 

 

 

Wider reading

 

Unit 6 - Linear Equations

Key questions/concepts

  • Solving linear equations

  • Fractional equations 

  • Solving equations with brackets

  • Solving equations with the variable on both sides

  • Changing the subject of a formula

Timeframe

  • January - February

Key vocabulary

Word/phrase Definition
Linear Straight line equations have only single powers of x (not x^2 or above)
Subject 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
Rearrange To change and move variables of an equation so that they appear on the other side
Variable  An unknown quanitiy 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

 

 

 

 

 

 

Wider reading

  • Mathematics for the Imagination by Peter Higgins

 

 

Unit 7 - Perimeter and area

Key questions/concepts

  • Areas of rectangles and triangles

  • Compound shapes

  • Area of a parallelogram

  • Area of a trapezium

  • Circle parts and circumference

  • Area of a circle

  • Answers in terms of pi

Timeframe

  • January - February

Key vocabulary

Word/phrase Definition
Circumference The length around the perimeter of a circle
Arc A fraction of the circumference - also a length with an "arch" shape
Sector A fraction of the area of a circle - pizza slice shape
Compound Shapes Shapes that are formed by adding or subtracting two or more shapes
Diameter The widest part of the circle measured from one side to the other and through the centre of the circle

 

 

 

 

 

Wider reading

 

Unit 8 - Ratio, speed and proportion

Key questions/concepts

  • Ratio and proportion

  • Calculating with ratios

  • Speed, distance time

  • Direct proportion

  • Best buys

Timeframe

  • February - March

Key vocabulary

Word/phrase Definition
Proportional When two or more things are linked by a common multiple or ratio
Speed 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
Best value The cheapest per unit of weight or the highest quantity per unit weight
Simple interest When a percentage of the initial amount invested is added each year as a fixed amount

 

 

 

 

 

Wider reading

 

Unit 9 - Volumes of Prisms

Key questions/concepts

  • 3D shapes

  • Volume ONLY of a cuboid

  • Volume ONLY of a prism

  • Volume of a cylinder

Timeframe

  • March - April

Key vocabulary

Word/phrase Definition
Surface area The total area of all the faces of a 3D shape
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
Prism A  3D shape with a uniform cross section
Cylinder A type of prism that has a circle as its cross section
Vertex  The corner of a shape whereby three or more faces meet

 

 

 

 

 

 

Wider reading

  • The Joy of X: A Guided Tour of Mathematics from One to Infinity by Steven Strogatz

 

 

Unit 10 - Percentages and compound measures

Key questions/concepts

  • 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

Timeframe

  • March - April

Key vocabulary

Word/phrase Definition
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
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 the original amount that is added to the total

 

 

 

 

 

 

Wider reading

 

Unit 11 - Linear graphs

Key questions/concepts

  • 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

  • Real life graphs

  • Simultaneous equations graphically

Timeframe

  • April - May

Key vocabulary

Word/phrase Definition
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
Simultaneous graphs Two graphs that will intersect each other. The coordinates where they cross will be a solution to each equation
Parallel Two lines that have the same gradient and will never cross

 

 

 

 

 

 

Wider reading

 

Unit 12 - Transformations

Key questions/concepts

  • Translations

  • Reflection

  • Rotational symmetry and rotation

  • Enlargement

  • Vectors

Timeframe

  • April - May

Key vocabulary

Word/phrase Definition
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

 

 

 

 

 

 

Wider reading

  • Games and Mathematics by David Wells

 

 

Unit 13 - Probability and events

Key questions/concepts

  • Calculating probabilities

  • Probability that an outcome will not happen

  • Mutually exclusive and exhaustive outcomes

  • Experimental probability

  • Expectation

  • Choices and Outcomes

Timeframe

  • June - July

Key vocabulary

Word/phrase Definition
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

 

 

 

 

 

Wider reading

 

Unit 14 - SA of prisms

Key questions/concepts

  • SA of a cuboid

  • SA of a prism

  • SA of a cylinder

Timeframe

  • June - July

Key vocabulary

Word/phrase Definition
Surface area The total area of all the faces of a 3D shape
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
Prism A 3D shape with a uniform cross section
Cylinder A type of prism that has a circle as its cross section
Cuboid A box shape - a prism with a rectangular cross section 

 

 

 

 

 

 

Wider reading

  • Things to Make and Do in the Fourth Dimension by Matt Parker
Year 10 Higher

Unit 1 - Angles

Key questions/concepts

  • Angle facts

  • Triangles

  • Angles in a polygon

  • Regular polygons

  • Angles in parallel lines

  • Special quadrilaterals

  • Scale drawing and bearings

Timeframe

  • September - October

Key vocabulary

Word/phrase Definition
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

 

 

 

 

 

 

Wider reading

  • Chaos by James Gleick

 

Unit 2 - Powers and standard form

Key questions/concepts

  • 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

Timeframe

  • September - October

Key vocabulary

Word/phrase Definition
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

 

 

 

 

Wider reading

  • The Liar Paradox and the Towers of Hanoi: 10 Greatest Math Puzzles of All Time by Marcel Danesi

 

Unit 3 - Number and Sequences

Key questions/concepts

  • 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

Timeframe

  • September - October

Key vocabulary

Word/phrase Definition
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

 

 

 

 

 

 

Wider reading

 

Unit 4 - Fractions, ratio and proportion

Key questions/concepts

  • Quantity as frac of another

  • Add and subtract fractions

  • Multiply and divide fractions

  • Percentage increase and decrease

  • Quantity as percentage of another

Timeframe

  • November - December

Key vocabulary

Word/phrase Definition
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

 

 

 

 

 

 

Wider reading

 

Unit 5 - Transformations, constructions and loci

Key questions/concepts

  • Congruent triangles

  • Rotational symmetry and rotation

  • Transformations

  • Bisectors

  • Defining a locus

  • Loci problems

  • Plans and elevations

Timeframe

  • November - December

Key vocabulary

Word/phrase Definition
Origin The centre (0,0) often used as the centre of transformations
Locus a particular position or place where something occurs or is situated
Bisect To cut equally in half
Plan view The view from the above, also known as birds eye view
Translate To move a shapes position on a coordinate axis without changing its orientation or size

 

 

 

 

 

Wider reading

  • Euclid's Window: The Story of Geometry from Parallel Lines to Hyperspace by Leonard Mlodinow

 

Unit 6 - Ratio and proportion

Key questions/concepts

  • Ratio - simplifying and exressing as a fraction

  • Direct proportion problems

  • Best buys

  • Compound measures - rates of pay and speed distance time

  • Density and pressure

  • Compound interest and repeated percentage change

  • Reverse Percentages

Timeframe

  • November - December

Key vocabulary

Word/phrase Definition
Proportional When two or more things are linked by a common multiple or ratio
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
Principle The original amount invested into a bank account when doing repeated percentage change
Compound interest When the percentage interest is recalculated each year taking into account the new 
Simple interest When a percentage of the initial amount invested is added each year as a fixed amount

 

 

 

 

 

 

Wider reading

  • Closing the Gap: The Quest to Understand Prime Numbers by Vicky Neale

 

Unit 7 - Counting, accuracy, powers and surds

Key questions/concepts

  • 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

Timeframe

  • January - February

Key vocabulary

Word/phrase Definition
Rational numbers A number that can be written as a fraction with integer numerator and denominator
Integer Whole numbers both positive and negative
Surds A way of writing an irrational number using square roots
Irrational  A number that cannot be written as a simple fraction eg the square root of 2
Bounds The limits/range of a calculation when a number has been rounded in some way

 

 

 

 

 

Wider reading

 

Unit 8 - Right-angled triangles

Key questions/concepts

  • 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

Timeframe

  • February - March

Key vocabulary

Word/phrase Definition
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
Angle of Elevation  The angle measured between a point above the horizontal and the horizontal itself

 

 

 

 

 

 

Wider reading

 

Unit 9 - Exploring and applying probability

Key questions/concepts

  • Experimental probability

  • Mutually exclusive and exhaustive outcomes

  • Expectation

  • Probability and two-way tables

  • Probability and Venn diagrams

Timeframe

  • February - March

Key vocabulary

Word/phrase Definition
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
Union The section of the venn diagram that includes values in either section
Intercept The section in the middle of the venn diagram that are only the values that are in both sets

 

 

 

 

 

Wider reading

 

Unit 10 - Linear graphs

Key questions/concepts

  • Drawing linear graphs from points

  • Gradient of a line

  • 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

Timeframe

  • April - May

Key vocabulary

Word/phrase Definition
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
Simultaneous graphs Two graphs that will intersect each other. The coordinates where they cross will be a solution to each equation
Parallel Two lines that have the same gradient and will never cross

 

 

 

 

 

 

Wider reading

 

Unit 11 - Length, area and volume

Key questions/concepts

  • Circumference and area of a circle

  • Area of a parallelogram

  • Area of a trapezium

  • Sectors

  • Volume of a prism

  • Cylinders (Vol and SA)

  • Volume of a pyramid

  • Cones

  • Spheres

Timeframe

  • April - May

Key vocabulary

Word/phrase Definition
Circumference The length around the perimeter of a circle
Arc A fraction of the circumference - also a length with an "arch" shape
Sector A fraction of the area of a circle - pizza slice shape
Surface area The total area of all the faces of a 3D shape
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

 

 

 

 

 

 

Wider reading

  • Things to Make and Do in the Fourth Dimension by Matt Parker

 

Unit 12 - Equations and inequalities

Key questions/concepts

  • 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

Timeframe

  • June - July

Key vocabulary

Word/phrase Definition
Solve Calculate a value/s which makes the equation true
Substitution Swap out a variable for a number
Variable Often a letter used to represent an unknown number, which can be changed
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

 

 

 

 

 

Wider reading

  • The Code Book by Simon Singh

 

Unit 13 - Similarity

Key questions/concepts

  • Simlar triangles

  • Problem solving using similar triangles

  • Harder problems

  • Areas and volumes of similar shapes

  • Harder problems

Timeframe

  • June - July

Key vocabulary

Word/phrase Definition
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

 

 

 

Wider reading

  • Fermat's Last Theorem by Simon Singh

Year 11 Foundation

Unit 1 - Powers and standard form

Key questions/concepts

  • Powers

  • Rules for multiplying and dividing powers

  • Multiplying and dividing by powers of 10

  • Standard form (calc)

Timeframe

  • September

Key vocabulary

Word/phrase Definition
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

 

 

 

 

Wider reading

  • How to Solve It by George Polya

 

Unit 2 - Percentages and variation

Key questions/concepts

  • Compound interest and repeated change

  • Reverse percentage

  • Direct proportion

  • Inverse proportion

Timeframe

  • September

Key vocabulary

Word/phrase Definition
Proportional When two or more things are linked by a common multiple or ratio
Direct proportion As one quantity is increased, the other is by the common ratio eg exchanging money
Inversely proportonal  When one variable is increased, the other decreases - eg temp and time for an ice cube
Constant of proportionality The total "time" or amount of work or distance which remains unchanged 
Compound interest When the percentage interest is recalculated each year taking into account the new 

 

 

 

 

 

Wider reading

 

Unit 3 - Constructions and loci

Key questions/concepts

  • Constructing triangles

  • Bisectors

  • Defining a locus

  • Loci problems

Timeframe

  • September

Key vocabulary

Word/phrase Definition
Origin The centre (0,0) often used as the centre of transformations
Locus A particular position or place where something occurs or is situated
Bisect  To cut equally in half

 

 

 

 

Wider reading

 

Unit 4 - Representation and interpretation

Key questions/concepts

  • Sampling

  • Pie charts

  • Scatter diagrams

  • Grouped data and averages

Timeframe

  • October

Key vocabulary

Word/phrase Definition
Correlation 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
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

 

 

 

 

 

 

Wider reading

 

Unit 5 - Right angled triangles

Key questions/concepts

  • 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

  • Trigonometry and bearings

  • Trigonometry and isosceles triangles

Timeframe

  • November

Key vocabulary

Word/phrase Definition
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
Converse of Pythagoras When pythagoras's theorem can be applied to a triangle it is a right angled triangle, if it cannot then it must not be right angled

 

 

 

 

 

 

Wider reading

 

Unit 6 - Number and Sequences

Key questions/concepts

  • 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

Timeframe

  • December

Key vocabulary

Word/phrase Definition
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

 

 

 

 

 

 

Wider reading

 

Unit 7 - Congruency and similarity

Key questions/concepts

  • Congruent triangles

  • Recognising similarity

  • Finding unknown sides in similar shapes

  • Problem solving using similarity

Timeframe

  • January - February

Key vocabulary

Word/phrase Definition
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

 

 

 

 

Wider reading

  • Fermat's Last Theorem by Simon Singh

 

Unit 8 - Simultaneous equations and inequalities

Key questions/concepts

  • Elimination method for simultaneous equations

  • Substitution method for simultaneous equations

  • Elimination method for harder simultaneous equations

  • Using simultaneous equations to solve problems

  • Solving linear inequalities

Timeframe

  • January - February

Key vocabulary

Word/phrase Definition
Elimination A method of solving whereby you remove one variable by adding or subtracting simultaneous equations
Substitution  A method of solving whereby you replace a variable with an equal equation. For example substituing y = 2x into 3x - y = 12 would give 3x - 2x = 12 

 

 

 

 

Wider reading

  • Why do Buses Come in Threes? by Rob Eastaway and Jeremy Wyndham

 

Unit 9 - Combined events

Key questions/concepts

  • Combined events

  • Two-way tables

  • Probability and Venn diagrams

  • Tree diagrams

Timeframe

  • February - March

Key vocabulary

Word/phrase Definition
Union The section of the venn diagram that includes values in either section
Intercept The section in the middle of the venn diagram that are only the values that are in both sets
Compliment The opposite probability which sums to 1. eg the compliment to heads is tails
Tree diagram A diagram which represents the potential outcomes for an experiment

 

 

 

 

Wider reading

 

Unit 10 - Non linear graphs

Key questions/concepts

  • Distance time graphs

  • Plotting and solving quadratic graphs

  • Solving quadratic equations by factorisation

  • Significant points of a quadratic curve

  • Cubic and reciprocal graphs

Timeframe

  • March - April

Key vocabulary

Word/phrase Definition
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
Cubic A graph which features an x^3 term as its highest power term
Plotting To draw a quadratic curve on a coordinate axis
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

 

 

 

 

 

 

Wider reading

 

Unit 11 - Curved shapes and pyramids

Key questions/concepts

  • Sectors

  • Volume of Pyramids

  • SA of pyramids

  • Volume and SA cones

  • Spheres

Timeframe

  • March - April

Key vocabulary

Word/phrase Definition
Surface area The total area of all the faces of a 3D shape
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
Circumference The length around the perimeter of a circle
Arc A fraction of the circumference - also a length with an "arch" shape
Sector A fraction of the area of a circle - pizza slice shape

 

 

 

 

 

 

Wider reading

  • How Many Socks Make a Pair? by Rob Eastawa

Year 11 Higher

Unit 1 - Quadratic equations

Key questions/concepts

  • Plotting quadratic graphs

  • Solving quadratic equations by factorisation

  • Harder problems

  • 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

Timeframe

  • September - October

Key vocabulary

Word/phrase Definition
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
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.

 

 

 

 

 

 

 

Wider reading

  • How to Solve It by George Polya

 

Unit 2 - Samping and more complex diagrams

Key questions/concepts

  • Collecting data

  • Frequency polygons

  • Cumulative frequency graphs

  • Box plots

  • Histograms

Timeframe

  • September - October

Key vocabulary

Word/phrase Definition
Cumulative When the frequency is added through the groups
Box plot A diagram which demonstrates the median, quartiles and max and minimum values for a set of grouped data, useful for comparing
Quartiles The lower and upper quartiles are the 25% and 75% marks of a data set
IQR The difference between the upper and lower quartiles which accounts for the middle 50% of a data set

 

 

 

 

 

 

Wider reading

 

Unit 3 - Combined events

Key questions/concepts

  • Addition rules for outcomes of events

  • Combined events

  • Tree diagrams

  • Independent events

  • Conditional probability

Timeframe

  • November - December

Key vocabulary

Word/phrase Definition
Relative frequency The amount of times an expected outcome is likely to occur based on the number of trials
Independent  Two events that happen which do not influence each other
Tree diagram  Similar to a sample space, this lists out all the possible outcomes of an experiment

 

 

 

 

Wider reading

 

Unit 4 - Properties of circles

Key questions/concepts

  • Circle theorems

  • Cyclic quadrilaterals

  • Tangents and chords

  • Alternate segment theorem

Timeframe

  • November - December

Key vocabulary

Word/phrase Definition
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

 

 

 

 

 

 

Wider reading

 

Unit 5 - Variation

Key questions/concepts

  • Direct proportion

  • Inverse proportion

Timeframe

  • November - December

Key vocabulary

Word/phrase Definition
Proportional When two or more things are linked by a common multiple or ratio
Direct proportion As one quantity is increased, the other is by the common ratio eg exchanging money
Inversely proportonal  When one variable is increased, the other decreases - eg temp and time for an ice cube
Constant of proportionality The total "time" or amount of work or distance which remains unchanged 

 

 

 

 

Wider reading

  • Why do Buses Come in Threes? by Rob Eastaway and Jeremy Wyndham

 

 

Unit 6 - Triangles

Key questions/concepts

  • 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

Timeframe

  • January - February

Key vocabulary

Word/phrase Definition
Hypotenuse The side of a right angled triangle that appears opposite the right angle
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

 

 

 

 

Wider reading

 

Unit 7 - Graphs

Key questions/concepts

  • Distance-time graphs

  • 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

Timeframe

  • February - March

Key vocabulary

Word/phrase Definition
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
Reciprocal  When you divide 1 by a number or fraction eg, the reciprocal of 3 is 1/3

 

 

 

 

 

Wider reading

 

Unit 8 - Algebraic fractions and functions

Key questions/concepts

  • Algebraic fractions

  • Changing the subject of a formula

  • Functions and inverses

  • Composite functions numeric and algebraic substitution

  • Iteration

Timeframe

  • March - April

Key vocabulary

Word/phrase Definition
Subject 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
Inverse The opposite function eg y = 4x has an inverse of y/4 = x each swaps the output for the input
Iteration A process whereby a calculation gets closer and closer to an amount by cycling the previous answer back into the input of a formula
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

 

 

 

 

 

 

Wider reading

  • How Many Socks Make a Pair? by Rob Eastaway

 

Unit 9 - Vector geometry

Key questions/concepts

  • Properties of vectors

  • Vectors in geometry

Timeframe

  • March - April

Key vocabulary

Word/phrase Definition
Vector A quantity which has direction and size
Magnitude Another word for size 
Scalar A quantity with no direction only size
Collinear When two lines that are parallel share a common point

 

 

 

 

Wider reading

KS4 Level Further Maths (Top set)

Unit 1 - Algebra I

Key questions/concepts

  • Binomial expansion

  • Product rule

  • Simplifying Expressions

  • Solving linear equations

  • Surds

Timeframe

  • 12 Hours

Key vocabulary

Word/phrase Definition
Binomial An algebraic expression of the sum or the difference of two terms
Equation 2 expressions separated by an equals sign
Expression A mathematical sentence with at least 2 terms and 1 operation
Rational A number that can be written as a fraction
Surd An irrational number

 

 

 

 

 

Wider reading

 

Unit 2 - Algebra II

Key questions/concepts

  • Algebraic fractions

  • Completing the square with non-unit coefficients

  • Factorising

  • Rearranging formulae

Timeframe

  • 4 Hours

Key vocabulary

Word/phrase Definition
Coefficient A multiplier placed in front of a variable
Factorise Writing an expression as the product of its factors using brackets
Formula Combination or variables used to calculate a quantity
Inverse Reversing an operation
Subject The variable being dealt with

 

 

 

 

 

Wider reading

 

Unit 3 - Algebra III

Key questions/concepts

  • Composite functions

  • Domains and ranges

  • Function notation and inverses

  • Graphs of functions

Timeframe

  • 5 Hours

Key vocabulary

Word/phrase Definition
Composite Combination of multiple functions
Domain All possible input values
Exponential Using an exponent/index/power
Function A relation or expression involving one or more variables
Range All possible output values

 

 

 

 

 

Wider reading

 

Unit 4 - Algebra IV

Key questions/concepts

  • Algebraic proof

  • Factor theorem

  • Indices

  • Inequalities

  • Quadratic equations

  • Sequences

  • Simultaneous equations

Timeframe

  • 12 Hours

Key vocabulary

Word/phrase Definition
Factors Integer values that can be multiplied to make another integer
Inequality The relation between 2 variable or expressions that are not equal
Limit The maximum or minimum value
Quadratic An expression that has its highest index as 2
Simultaneous At the same time

 

 

 

 

 

Wider reading

 

Unit 5 - Coordinate Geometry

Key questions/concepts

  • Distance between points

  • Equation of a circle

  • Intersection of lines

  • Mid points

  • Parallel and perpendicular lines

Timeframe

  • 5 Hours

Key vocabulary

Word/phrase Definition
Intersection The point where lines meet/cross
Midpoint The middle point of a line
Parallel Lines  in the same plane that will never meet
Perpendicular Lines that meet at 90 degrees
Ratio Comparison of part to part

 

 

 

 

 

Wider reading

 

Unit 6 - Geometry I

Key questions/concepts

  • Circle theorems

  • Geometric proof

  • Trigonometry including graphs and identities

Timeframe

  • 7 Hours

Key vocabulary

Word/phrase Definition
Alternate A pair of angles with different vertices and on opposite sides of a transversal at its intersection with two other lines
Identity Exactly equal to
Sector The shape created by two radii of a circle or ellipse and the arc between them
Segment Part of a circle cut off by a line or plane intersecting it
Theorem A theory that has been proved to by a chain of reasoning

 

 

 

 

 

 

Wider reading

  • Read 'Euclid's window' by Leonard Mlodinow

 

Unit 7 - Geometry II

Key questions/concepts

  • Trigonometric rules

  • Trigonometry in 3D including planes

Timeframe

  • 3 Hours

Key vocabulary

Word/phrase Definition
Dimension A measurable extent in space
Plane A flat surface on which a straight line joining any two points on it would wholly lie
Scalar A value that has magnitude but not direction
Skew Lines in 3D space that are not parallel but will not intersect
Vertex The angular point of a shape

 

 

 

 

 

Wider reading

 

Unit 8 - Calculus

Key questions/concepts

  • Differentiation - 1st and 2nd derivatives

  • Increasing and decreasing functions

  • Stationary points

  • Tangents and normals

Timeframe

  • 8 Hours

Key vocabulary

Word/phrase Definition
Derivative The rate of change of a function
Differentiate The process of finding the rate of change of a function
Normal A line that is perpendicular to a tangent
Stationary point A point on a graph with gradient of 0
Tangent A straight line that touches a curve at a single point

 

 

 

 

 

Wider reading

 

Unit 9 - Matrices

Key questions/concepts

  • Combining transformations

  • Equating elements of matrices

  • Multiplying matrices by matrices

  • Multiplying matrices by scalars

  • The identity matrix

Timeframe

  • 6 Hours

Key vocabulary

Word/phrase Definition
Conformable A matrix that’s dimensions are suitable for defining an operation
Element A part
Identity matrix A matrix with the entries on the diagonal from the top left to bottom right are 1 and the other elements are 0
Matrix A rectangular array of numbers for which operations are defined
Transformation The process of converting an expression or object into another

 

 

 

 

 

 

Wider reading

Year 12

Unit 1 - Algebra 

Key questions/concepts

  • Arguments and Proof

  • Index laws 

  • Lines and circles 

  • Surds

  • Quadraric equations 

  • Inequalities

Timeframe

  • September - October

Key vocabulary

Word/phrase Definition
Rationalise To convert fractions with surds on the denominator to fractions with integer denominators 
Axioms A statement that is known to be true which is the starting point for further proofs
Exhaustion A method of proof by evaluating all possible values and outcomes
Coefficient Is the number infront of a term in a polynomial which defines what it is multiplied by
Tangent Is a straight line that meets a curve at a single point

 

 

 

 

 

Wider reading

 

Unit 2 - Polynomials and Binomials 

Key questions/concepts

  • Expanding and factorising

  • The binomial theorem 

  • Algebraic Division

  • Curve Sketching

Timeframe

  • September - October

Key vocabulary

Word/phrase Definition
Polynomial An expression involving variables and coefficients often involwith terms linked by addtions and subtractions
Binomial An algebraic expression of the sum or the difference of two terms
Quotient The answer after we divide one term by another (dividend / divisor)
Asymptote A line whereby the distance between the a curve and this line approaches zero as either the X or Y coordinate tends to infinity
Discriminant The section below the square root on the quadratic equation which can help to identify the number of solutions for a quadratic 

 

 

 

 

 

 

 

Wider reading

 

Unit 3 - Trigonometry 

Key questions/concepts

  • The sine, Cosine and tangent graphs

  • The sine and Cosine rules

Timeframe

  • November - December

Key vocabulary

Word/phrase Definition
Periodic Graph A graph that has a regular and repeating shape over a set period or interval
Identities An equation that is always true no matter which values are substituted into it
CAST diagrams A diagram to help identify the sign of a trigonometric value based off the angle given
Quadrants The four sections of a coordinate grid separated by the X and Y axis
Trigonometric Ratio The relationships between the ratio of the sides of a right angled triangle and the subsequent angle they create

 

 

 

 

 

 

 

Unit 4 - Differentiation and Integration

Key questions/concepts

  • Differentiation from first principles

  • Differentiating ax^n and Leibniz notation 

  • Rates of change

  • Tangents and Normals

  • Turning Points

  • Integration

  • Area under a curve

Timeframe

  • November - December

Key vocabulary

Word/phrase Definition
Differentiation  The process of finding the derivative of a function 
Derivative The rate of change of a function - ie how quickly it increases or decreases over time
Constant A number with no variable part 
Turning point The point when a graph's gradient is equal to zero, as it passes from positive to negative or vice versa
Normal A line which is perpendicular to the tangent of a curve

 

 

 

 

 

Wider reading

 

Unit 5 - Exponentials and Logs

Key questions/concepts

  • The laws of logs

  • Exponential Functions

  • Exponential Processes

  • Curve Fitting

Timeframe

  • December

Key vocabulary

Word/phrase Definition
Logarithm An alternative way of expressing large/small numbers without the use of powers
Exponent A quantity representing the power which a number is to be raised to
Base The number that gets multiplied when using an exponent
Natural Log Denoted often as Ln (x) and is the inverse of e^x
Proportional A relationship that shares a common ratio eg "x is always 4 times bigger than y"

 

 

 

 

 

 

Unit 6 - Collecting, representing & interpreting data

Key questions/concepts

  • Sampling

  • Central tendancy & Spread

  • Single Variable Data

  • Bivariate Data

Timeframe

  • January - February

Key vocabulary

Word/phrase Definition
Parameter A number which describes the whole population eg the mean
Statistic A single number taken from a sample - you can take multiple statistics to make estimates for a parameter
Variance  How spread out the data is from the mean
Standard Deviation The square root of variance used to show the average spread of data from the mean value
Bivariate Data Data comparing two variables or two sets of data

 

 

 

 

 

 

Wider reading

 

Unit 7 - Probability and DRV

Key questions/concepts

  • Probability

  • Binomial Distribution

Timeframe

  • January - February

Key vocabulary

Word/phrase Definition
Probability distribution Function Function which gives all the probabilities of all possible outcomes of an experiment
Discrete random Variable Is a possible outcome in your experiment which can occur randomly
Random Whereby all outcomes are equally likely to occur and is down to chance alone
Mutually Exclusive events Two or more events that cannot occur at the same time eg, pulling a single card from a regular deck which is both an Ace and a queen
Complimentary events Two events whose probabilities are the complete opposite and create an exhaustive list. Eg, rolling and even and rolling an odd on a six sided dice. Used often with the word "not" eg, P (even) = 1/2     P(not even) = 1/2 

 

 

 

 

 

 

 

Wider reading

 

Unit 8 - Hypothesis Testing 1

Key questions/concepts

  • Formulating a test

  • The Critical Region

Timeframe

  • February - March

Key vocabulary

Word/phrase Definition
Null hypothesis The state that is assumed to be true eg the probability of flipping a coin and getting heads is 0.5
Significance level Often given as a decimal, this is the percentage chance of a result occuring due to chance alone, which can help provide evidence to support or reject the null hypothesis
Critical regions The region which lies above or below the significance level on a probability distribution curve 
Two tailed test Whereby the significance level is split and has a minimum and a maximum critical region
Alternative Hypothesis The compliment to the null hypothesis- it is used to establish whether or not a statement is true or just down to chance alone

 

 

 

 

 

 

Wider reading

 

Unit 9 - Vectors

Key questions/concepts

  • Definitions and Properties

  • Components of a Vector

Timeframe

  • February - March

Key vocabulary

Word/phrase Definition
Magnitude The size of the vector eg, how far it travels in a particular direction
Collinear When two vectors have the same direction (run parallel) but also share a common point
Resultant vector When two or more vectors are combined, the overall direction and magnitude from the starting position is known as the resultant
Component Vector A vector that has been separated into its horizontal and vertical counterparts, often used as "i's and j's" for horizontal and vertical
Position Vector Much like a coordinate, it states where an object is in space and can be used to determine its new position when a vector has been applied

 

 

 

 

 

 

 

Wider reading

 

Unit 10 - Units & Kinematics

Key questions/concepts

  • Standard Units & Basic Dimension

  • Motion in a Straight Line

  • Equations of motion for constant acceleration

  • Motion with variable acceleration

Timeframe

  • March - April

Key vocabulary

Word/phrase Definition
Displacement The distance from an objects starting position to its final position in a given timeframe. Not the total distance travelled
Acceleration A vector quantity which is the rate of change of velocity - the speed at which velocity changes
Velocity A vector quantity measuring speed in a given direction 
Variable acceleration Acceleration that is dependant on a variable which is often time
Instantaneously  Instantly at once. For example, a ball thrown vertically will be instantaneously at rest at its maximum height before accelerating back towards the ground

 

 

 

 

 

 

 

Wider reading

 

Unit 11 - Forces and Newton's Laws

Key questions/concepts

  • Forces 1

  • Dynamics 1

  • Motion under Gravity

  • Systems of Forces

Timeframe

  • April - May

Key vocabulary

Word/phrase Definition
Resolve To find the overall force in a given direction taking into account opposing forces
Tension  When an object is being pulled from  its ends eg, when a weight is hung from a string, the string is under tension
Thrust When an object is pushing another/is being compressed eg, when a vertical rod is balancing a weight, the rod is under tension as the weight is compressing the rod
Reaction Force A force that acts against another applied force when two surfaces are in contant. Eg, the weight of a book on the table will have an equal reaction force from the table it is sat on to stop it falling through the table
Inextensible Does not stretch. Often strings are considered as inextensible so that forces remain constant when there are changes in the system which would cause the string to stretch, eg, two hanging weights on a pulley suddenly being dropped

 

 

 

 

 

 

 

 

 

Wider reading

Year 13

Unit 1 - Algebra 2

Key questions/concepts

  • Further mathematical proof

  • Functions

  • Parametric Equations

  • Algebraic Fractions

  • Partial Fractions

Timeframe

  • June - July

Key vocabulary

Word/phrase Definition
Contradiction A method of proof whereby you select a counter argument that directly opposes the initial statement and prove it is false
Domain A set of values you have selected as your inputs in a function (x- axis)
Range The spread of outputs of a function seen on the y-axis
Modulus The modulus of a number is the positive version of that number, for example x = -3 then |x| = 3
Parametric Equations When two functions (often in terms x and y)are linked through a third variable/parameter for example time

 

 

 

 

 

 

Wider reading

 

Unit 2 - Sequences

Key questions/concepts

  • The Binmoial Series

  • Introduction to sequences

  • Arithmetic Sequences

  • Geometric Sequence

Timeframe

  • June - July

Key vocabulary

Word/phrase Definition
Validity The range of values whereby a sequence or expansion makes sense. Outside of this range the sequence is invalid
Periodic A sequence that consists of repeated terms, for example the sine graph 
Converging When terms get closer and closer to a particular value
Arithmetic Sequences A sequence with a term to term rule of addition of a constant
Geometric Sequences A sequence connected by multiplying each previous term by a fixed value to generate the next

 

 

 

 

 

 

Wider reading

 

Unit 3 - Trigonometry Identities

Key questions/concepts

  • Radians

  • Reciprocal & Inverse Trig functions

  • Compound Angles

  • Equivalent forms for acos θ + bsin θ

Timeframe

  • September - October

Key vocabulary

Word/phrase Definition
Radians 1 Radian is the angle made by the measure of one radius length around the arc. A full circle has an angle of 2pi radians
Inverse functions A function that reverses the stages of another swapping input and output
Reciprocal functions A reciprocal is found by dividing 1 by the original function eg, y = x would have a reciprocal of y = 1/x
Compound angle An angle made by adding or subtracting two or more angles that meet at a common vertex
Double angle formulae An formulae derived from the compound angle formulae whereby the angle in question is the same and therefore becomes double the size eg A + A = 2A

 

 

 

 

 

 

 

Unit 4 - Differentiation 2

Key questions/concepts

  • 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

Timeframe

  • October - November

Key vocabulary

Word/phrase Definition
Convex  A 'V' shape created by a function whereby it is decreasing then begins to increase 
Concave An 'n' shape created by a function whereby the function is increasing and then begins to decrease
Point of inflection When a functions changes concavity, from increasing to decreasing or vice versa
Implicit Function When a function of a particular variable is only implied to be a function of another variable eg, 2y - 2x = 4. Y is a function of x however it is not explicit in this case
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

 

 

 

 

 

 

Wider reading

 

Unit 5 - Integration & Differential Equations

Key questions/concepts

  • Standard Integrals

  • Integration by Substitution

  • Integration by Parts

  • Integrating Rational Functions

  • Differential Equations

Timeframe

  • November - December

Key vocabulary

Word/phrase Definition
Definite integral When integrating to find the area between two fixed points/ limits
Integration by parts A method of integrating functions involving products. Eg y =2x sinx
Rational fraction An algebraic fraction which has both rational numerator and denominators which are polynomials
Differential Equations An equation which expresses a relationship between functions and their derivatives
Decomposing  Breaking down a fraction 

 

 

 

 

 

 

Unit 6 - Numerical Methods

Key questions/concepts

  • Simple Root Finding

  • Iterative Root Finding

  • Newton-Raphson Root Finding

  • Numerical Integration

Timeframe

  • December

Key vocabulary

Word/phrase Definition
Iteration  A formula that converges to a fixed value
Converge  When a function gets closer and closer to a value
Underestimate When the value calculated is below the actual known value
Root A solution to a polynomial whereby it intercepts the x axis

 

 

 

 

Wider reading

 

Unit 7 - Probability and CRV

Key questions/concepts

  • Conditional Probability

  • Modelling with Probability

  • Normal Distribution

  • Using the Normal distribution as an approx to the binomial

Timeframe

  • January - February

Key vocabulary

Word/phrase Definition
Conditional Probability Definitions
Normal distribution When the distribution is symmetrical and forms a bell shape when graphed
Binomial An algebraic expression of the sum or the difference of two terms

 

 

 

 

Wider reading

 

Unit 8 - Hypothesis Testing 2

Key questions/concepts

  • Testing Correlation

  • Testing a Normal Distribution

Timeframe

  • January - February

Key vocabulary

Word/phrase Definition
Null hypothesis The state that is assumed to be true eg the probability of flipping a coin and getting heads is 0.5
Significance level Often given as a decimal, this is the percentage chance of a result occuring due to chance alone, which can help provide evidence to support or reject the null hypothesis
Critical regions The region which lies above or below the significance level on a probability distribution curve
Two tailed test Whereby the significance level is split and has a minimum and a maximum critical region
Alternative Hypothesis The compliment to the null hypothesis- it is used to establish whether or not a statement is true or just down to chance alone

 

 

 

 

 

 

Wider reading

 

Unit 9 - Motion in 2D

Key questions/concepts

  • 2D motion with constant acceleration

  • 2D motion with variable acceleration

  • Motion under gravity 2

  • Motion under forces

Timeframe

  • March - April

Key vocabulary

Word/phrase Definition
Projectile  When an object is thrown, its tragectory is often a parabola
Resultant The overal forces for a system will result in a direction and force known as the resultant
Variable acceleration Acceleration that is dependant on a variable which is often time

 

 

 

 

Wider reading

 

Unit 10 - Forces 2

Key questions/concepts

  • Vectors in 3D

  • Statics

  • Dynamics 2

  • Moments

Timeframe

  • March - April

Key vocabulary

Word/phrase Definition
Component Vector A vector that has been separated into its horizontal and vertical counterparts, often used as "i's and j's" for horizontal and vertical
Magnitude The size of the vector eg, how far it travels in a particular direction
Moment The turning effect that occurs when a weight is places on a platform that can pivot. Eg A person on  a see-saw
Resultant vector When two or more vectors are combined, the overall direction and magnitude from the starting position is known as the resultant

 

 

 

 

 

 

Wider reading

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