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Mathematics

Mathematics Staff
Mr S Clayton (Head of Team) sclayton@conyers.org.uk Mr J Downs jdowns@conyers.org.uk
Mr K Anderson kanderson@conyers.org.uk Mrs K Gray kgray@conyers.org.uk
Miss L Allanson lallanson@conyers.org.uk Mrs S Perks sperks@conyers.org.uk
Mrs A Beer abeer@conyers.org.uk Mr A Robinson arobinson@conyers.org.uk
Mr A Braithwaite abraithwaite@conyers.org.uk Mr M Taylor mtaylor@conyers.org.uk
Mr P Dixon pdixon@conyers.org.uk Mrs J Wareing jwareing@conyers.org.uk
Mrs C Blakemoore cblakemoore@conyers.org.uk Mrs J White jwhite@conyers.org.uk
  • Key Stage 4
  • A Level Mathematics
  • A Level Further Mathematics
  • Year 10 Assessment
  • Year 11 Assessment

GCSE Maths

Introduction

Mathematics is not just about ‘working out calculations’, although that is an important aspect. Employers and colleges/universities want you to have GCSE Mathematics because it shows that you can think logically, see your way through a problem and deal with abstraction. It also shows that you can remember key facts and apply them to new situations/questions. These are important skills for almost any future career or course of study.

Skills

  • Apply mathematical knowledge and understanding to solve problems
  • Think and communicate mathematically – precisely, logically and creatively
  • Apply mathematical concepts to situations arising in their own lives
  • Acquire the skills needed to use technology such as calculators and computers effectively
  • Acquire a firm foundation for further study

Course structure

All students will follow an updated GCSE Mathematics course, with a strong emphasis on ‘functional’ skills. There will be regular end of topic reviews and termly internal assessments. The GCSE Mathematics course is linear, with an examination at the end of the course in Year 11.

Assessment

There is no coursework. There are two tiers, Foundation and Higher, and students will follow the course best suited to their ability. Assessment is via three papers, one non-calculator and two calculator, taken at the end of the course.

Exam Board: Edexcel

What is Mathematics?

Mathematics at A Level builds on the algebra and trigonometry you will have seen at GCSE, and then rapidly introduces new concepts such as calculus and logarithms. It is an essential or preferred subject for many degree courses, including Accounting, Architecture, Chemistry, Computing, Engineering, Natural Sciences and Physics. In addition to the 5 A*-C grades necessary to join Conyers Sixth Form, we would strongly recommend that you achieve at least a Grade 6 in Mathematics. A Level Mathematics is very challenging and demanding; therefore students with a genuine interest and enjoyment of the subject will find it easier to succeed and will enjoy the course. Due to the demanding nature of the course, students opting to take A Level Maths will be given summer work to complete which will help prepare them for a pre-course test in the first week of term. Students who do not pass this test will be placed on a support plan if following a discussion between the student, Mr Clayton and Mr Webster, it is decided they are to remain on the course.

Why study it?

Examining the jobs market and comparing earnings with subjects studied, it finds that Mathematics is the only A-level subject that adds to earnings – up to 10 per cent – even when the employer is unaware of the person’s qualifications. Graduates who have studied Mathematics earn more than those who have not, even when the job has nothing to do with Maths. Institute of Education University of London

The structure of the course

A Level Mathematics is a linear 2 year course. It will be assessed by 3 exams at the end of the 2 year course. The content of A level Mathematics is in the process of changing and providers including ourselves are waiting on final specifications to be approved. However, we do know the majority of the course still covers Core topics but all students will also have to study some Statistics and Mechanics in both years of the course.

Content – some of the topics covered:

Core

Algebra and functions; differentiation; integration; transformation of graphs; coordinate geometry; sequences and series; trigonometry; exponentials and logarithms; numerical methods for solving equations; vectors.

Statistics

Familiarity with a data set; Probability; sampling; data presentation and interpretation; binomial distribution; normal distribution; hypothesis testing.

Mechanics

Kinematics; forces and Newton’s laws; moments; projectiles.

What next?

Studying A Level Maths can be extremely valuable if you wish to pursue a career in the following:

  • Software development and computer games design
  • Engineering
  • Pharmaceutical and medical sciences
  • Financial services

Exam Board: Edexcel

What is Further Maths?

The Further Maths course results in two A-level qualifications: Maths, and Further Maths. Fifteen hours of teaching will be offered each two week cycle rather than the usual twenty hours normally allocated for two A-level courses. The course goes beyond the syllabus of the Maths A Level, to include topics seen at University such as complex numbers, matrices and mathematical proof. We would strongly recommend that you achieve at least a Grade 7 in GCSE mathematics if you wish to follow this course. Students must also be prepared to put in a great deal of independent study as this is a very challenging course and the fact you have fewer timetabled lessons will mean you won’t have as much direct contact with your teachers as you do for some other subjects.

Why study it?

Further Maths should be taken by anyone interested in taking a Mathematics based degree at university, such as Maths, Physics or Engineering. Although courses may not state Further Maths as an entry requirement, having this additional A Level can be a huge competitive advantage when applying.

The structure of the course

A Level Mathematics and Further Mathematics are linear 2 year courses. Both courses will be assessed separately by exams at the end of the 2 year course. As this results in 2 A level qualifications you will study the same content as A level Mathematics plus extra Further Mathematics topics. Some of the Further Mathematics topics are brand new; some extend upon the knowledge gained in A level Mathematics topics.

Content – some of the topics covered in Mathematics:

Core Algebra and functions; differentiation; integration; transformation of graphs; coordinate geometry; sequences and series; trigonometry; exponentials and logarithms; numerical methods for solving equations; vectors. Statistics Familiarity with a data set; Probability; sampling; data presentation and interpretation; binomial distribution; normal distribution; hypothesis testing. Mechanics Kinematics; forces and Newton’s laws; moments; projectiles.

Some of the topics covered in Further Mathematics:

Proof; complex numbers; matrices; further algebra and functions; further calculus; further vectors; polar coordinates; hyperbolic functions; differential equations…… Plus others to be confirmed.

What next?

Studying A-Level Further Maths can be extremely valuable if you wish to pursue a career in the following:

  • Scientific research
  • Computer science
  • Mathematical and statistical modelling
  • Engineering

Year 10 Assessment

Term 1

Assessment Focus and Purpose Key Concepts/Skills Assessed Preparation/Key Areas to Revise
Unit 1: Checking, approximating and estimating Key Vocabulary

  • Approximate, Round
  • Decimal place
  • Estimate
  • Order of magnitude
  • Accurate, Accuracy
  • Significant figure
  • round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures)
  • estimate answers; check calculations using approximation and estimation, including answers obtained using technology
  • recognise and use relationships between operations, including inverse operations (e.g. cancellation to simplify calculations and expressions)
MathsWatch clip numbers: 1, 2, 3, 21, 31, 32, 90, 91, 92 MyMaths lessons: Decimal places, Significant figures, Estimating calculations1
Unit 2: Calculating fractions, decimals and percentages Key Vocabulary

  • Mixed number
  • Equivalent fraction
  • Simplify, cancel, lowest terms
  • Proper fraction, improper fraction, top-heavy fraction, vulgar fraction
  • Percent, percentage
  • Multiplier
  • Increase, decrease
  • (Simple) interest
  • Exact
  • apply the four operations, including formal written methods, to simple fractions (proper and improper), and mixed numbers
  • solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison
  • interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively
  • compare two quantities using percentages
  • interpret fractions and percentages as operators
  • work with percentages greater than 100%
  • solve problems involving percentage change, including original value problems, and simple interest including in financial mathematics
  • calculate exactly with fractions
MathsWatch clip numbers: 24, 25, 26, 40, 70, 71a, 71b, 72, 73, 74, 84, 85, 86, 87, 88, 89, 108, 109, 110, 111, 164 MyMaths lessons: Adding subtracting fractions, Multiplying fractions, Dividing fractions, Percentages of amounts 4, Percentage change 1, Reverse percentages, Change as a Percentage
Unit 3: Measuring space Key Vocabulary

  • Length, distance
  • Mass, weight
  • Volume, Capacity
  • Metre, centimetre, millimetre
  • Tonne, kilogram, gram, milligram
  • Litre, millilitre
  • Hour, minute, second
  • Inch, foot, yard
  • Pound, ounce
  • Pint, gallon
  • use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.)
  • use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate
  • change freely between related standard units (e.g. time, length, area, volume/capacity, mass) in numerical contexts
  • measure line segments and angles in geometric figures
MathsWatch clip numbers: 46a, 46b, 22a, 22b, 112 MyMaths lessons:

Time calculations, Units of length, Units of mass, Units of capacity, Metric conversion, Converting measures

Unit 4: Investigating properties of shapes Key Vocabulary

  • Hypotenuse
  • Pythagoras’ theorem
  • Similar
  • Opposite
  • Adjacent
  • Trigonometry
  • Ratio
  • Sine
  • Cosine
  • Tangent
  • Angle of elevation
  • angle of depression
  • know the formulae for: Pythagoras’ theorem, a² + b² = c², and apply it to find lengths in right-angled triangles in two dimensional and three dimensional figures
  • make links to similarity (including trigonometric ratios) and scale factors
  • know the exact values of sin(θ) and cos(θ) for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan(θ) for θ = 0°, 30°, 45° and 60°
  • know the trigonometric ratios, sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, tan(θ) = opposite/adjacent
  • apply it to find angles and lengths in right-angled triangles in two dimensional figures
MathsWatch clip numbers: 75, 81, 124, 150a, 150b, 150c, 124, 168, 173, 217 MyMaths lessons:

Pythagoras’ theorem, Pythagoras 3D, Trig missing angles, Trig missing sides

Assessment 1 (Units 1-4)
Unit 5: Numbers and the number system Key Vocabulary

  • Prime
  • Prime factor
  • Prime factorisation
  • Product
  • Venn diagram
  • Highest common factor
  • Lowest common multiple

 

  • Know the meaning of a prime number
  • Recall prime numbers up to 50
  • Write a number as a product of its prime factors
  • Use a Venn diagram to sort information
  • Solve worded problems using HCF and LCM
  • Use prime factorisations to find the highest common factor of two numbers
  • Use prime factorisations to find the lowest common multiple of two numbers
MathsWatch clip numbers: 28, 78, 79, 80 MyMaths lessons: Factors and Primes, Highest common factor, Lowest common multiple

Term 2

Assessment Focus and Purpose Key Concepts/Skills Assessed Preparation/Key Areas to Revise
Unit 6: Calculating Key Vocabulary

  • Power, Root, Index, Indices
  • Standard form
  • Inequality, Truncate, Round
  • Minimum bound,
  • Maximum bound
  • Interval
  • Decimal place,
  • Significant figure
  • Limit
  • Know the meaning of powers & roots
  • Calculate with positive and negative powers
  • estimate powers and roots of any given positive number
  • interpret a number written in standard form
  • enter a calculation written in standard form into a calculator
  • calculate with roots, and with integer and fractional indices
  • apply and interpret limits of accuracy, including upper and lower bounds
  • calculate with standard form A × 10n, where 1 ≤ A < 10 and n is an integer
MathsWatch clip numbers: 29, 81, 82, 83, 91, 131, 132, 154, 155, 188, 206 MyMaths lessons: Indices 1, Indices 2, Indices 3, Standard form large, Standard form small, Standard form calcs
Unit 7: Algebraic proficiency: tinkering Key Vocabulary

  • Equivalent
  • Equation, Expression
  • Expand, Factorise
  • Linear, Quadratic
  • Algebraic Fraction
  • Difference of two squares
  • Binomial
  • use and interpret algebraic notation, including: a²b in place of a × a × b, coefficients written as fractions rather than as decimals
  • understand and use the concepts and vocabulary of factors
  • simplify and manipulate algebraic expressions by taking out common factors and simplifying expressions simplify and manipulate algebraic expressions involving algebraic fractions
  • manipulate algebraic expressions by expanding products of more than two binomials
  • simplify and manipulate algebraic expressions (including those involving surds) by expanding products of two binomials and factorising quadratic expressions of the form x² + bx + c, including the difference of two squares
  • manipulate algebraic expressions by factorising quadratic expressions of the form ax² + bx + c
MathsWatch clip numbers: 33, 34, 35, 93, 94, 134a, 134b, 157, 158, 192, 210a MyMaths lessons: Simplifying , Single brackets, Brackets, Factorising Linear, Factorising quadratics 1, Factorising quadratics 2
Unit 8: Mathematical movement Key Vocabulary

  • Scale Factor
  • Similar
  • Axis, axes, x-axis, y-axis
  • Origin
  • Quadrant
  • Transformation
  • Reflection, Rotation
  • Translation
  • Vector Object
  • Image
  • Congruent, Congruence

 

  • understand and use lines parallel to the axes, y = x and y = -x
  • solve geometrical problems on coordinate axes
  • identify, describe and construct congruent and similar shapes including on coordinate axes, by considering rotation, reflection, enlargement (including fractional scale factors) and translation
  • make links between similarity and scale factors
  • describe the changes and invariance achieved by combinations of rotations, reflections, enlargements and translations
MathsWatch clip numbers: 8, 11, 12a, 12b, 48, 49, 50, 148, 182 MyMaths lessons: Translating shapes, Reflecting shapes, Rotating shapes, Enlarging shapes, All transformations, Similar triangles
Unit 9: Solving equations and inequalities Key Vocabulary

  • Algebraically
  • Graph Equation
  • Solve
  • Simultaneous equations
  • Point of intersection
  • Substitution, Elimination
  • Solution set, Interval
  • Iteration

 

   

Term 3

Assessment Focus and Purpose Key Concepts/Skills Assessed Preparation/Key Areas to Revise
Unit 10: Analysing statistics Key Vocabulary

  • Categorical data, Discrete data, Continuous data, Grouped data
  • Axis, axes
  • Population, Sample
  • Cumulative frequency
  • Box plot, box-and-whisker diagram
  • Central tendency
  • Mean, median, mode
  • Spread, dispersion, consistency
  • Range, Interquartile range
  • Skewness
  • infer properties of populations or distributions from a sample, whilst knowing the limitations of sampling
  • construct and interpret diagrams for grouped discrete data and continuous data, i.e. cumulative frequency graphs, and know their appropriate use
  • interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate graphical representation involving discrete, continuous and grouped data, including box plots
  • interpret, analyse and compare the distributions of data sets from univariate empirical distributions through appropriate measures of central tendency including quartiles and inter-quartile range
MathsWatch clip numbers: 62, 63, 129, 130a, 130b, 152, 176, 186, 187 MyMaths lessons: Sampling, Questionnaires, Frequency Polygons, Scatter graphs, Line of best fit, Cumulative frequency 1, Box and whisker plots
Unit 11: Proportional reasoning Key Vocabulary

  • Ratio
  • Proportion(al)
  • Multiplier
  • Speed
  • Unitary method
  • Compound unit
  • Direct proportion
  • Inverse proportion
  • Multiplier
  • change freely between compound units (e.g. density, pressure) in numerical and algebraic contexts
  • use compound units such as density and pressure
  • interpret equations that describe direct and inverse proportion
  • recognise and interpret graphs that illustrate direct and inverse proportion
  • understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y
MathsWatch clip numbers: 38, 39, 41, 42, 105, 106, 142, 143, 199 MyMaths lessons: Speed, Density, Converting compound measures, Direct proportion, Inverse proportion

Term 4

Assessment Focus and Purpose Key Concepts/Skills Assessed Preparation/Key Areas to Revise
Unit 12: Calculating space Key Vocabulary

  • Circle, Pi
  • Radius, diameter, chord, circumference
  • (Right) prism, Cylinder
  • Cross-section
  • Polygon, polygonal
  • identify and apply circle definitions and properties, including:  tangent, arc, sector and segment
  • calculate arc lengths, angles and areas of sectors of circles
  • calculate exactly with multiples of π
MathsWatch clip numbers: 53, 54, 55, 56, 117, 149, 167 MyMaths lessons: Circumference of a circle, Area of a circle, Arcs and sectors
Assessment 2 (Units 1-11)
Unit 13: Pattern searching Key Vocabulary

  • Term
  • nth term
  • Generate
  • Quadratic
  • First (second) difference
  • Geometric Progression
  • generate terms of a sequence from either a term-to-term or a position-to-term rule
  • deduce expressions to calculate the nth term of linear sequences and quadratic sequences
  • recognise and use simple geometric progressions (rn where n is an integer, and r is a rational number > 0)
  • recognise and use Fibonacci type and quadratic sequences
MathsWatch clip numbers: 37, 102, 103, 104, 163, 213 MyMaths lessons: Geometric sequences 1, Arithmetic sequences, Quadratic sequences, Recognising sequences
Unit 14: Solving equations and inequalities Key Vocabulary

  • (Linear) inequality
  • Variable
  • Manipulate
  • Solve
  • Solution set
  • Integer
  • Set notation
  • Region
  • understand and use the concepts and vocabulary of  inequalities
  • solve linear inequalities in one variable
  • represent the solution set to an inequality on a number line solve linear inequalities in two variables
  • represent the solution set to an inequality using set notation and on a graph
MathsWatch clip numbers: 138, 139, 198 MyMaths lessons: Inequalities and intervals, Inequations, Shading inequalities

Term 5

Assessment Focus and Purpose Key Concepts/Skills Assessed Preparation/Key Areas to Revise
Unit 15: Calculating space Key Vocabulary

  • Sphere, Pyramid, Cone
  • Perpendicular-height
  • Surface area, Volume
  • Congruent, congruence
  • Similarity, similar shapes, similar figures
  • Enlarge, enlargement
  • Scale factor

 

  • calculate surface area and volume of spheres, pyramids, cones and composite solids
  • apply the concepts of congruence and similarity, including the relationships between length, areas and volumes in similar figures
MathsWatch clip numbers: 114a, 114b, 115, 119, 144, 167, 170, 171, 172, 200 MyMaths lessons:

Nets, Surface area, Volume of prisms, Volume of cylinders, Volume of cones and spheres, Area scale factor, Volume scale factor

Unit 16: Investigating angles and conjecturing Key Vocabulary

  • Radius, radii
  • Tangent
  • Chord
  • Conjecture
  • Derive
  • Prove, proof
  • Counter example
  • Congruent, congruence

 

  • understand and use alternate and corresponding angles on parallel lines
  • use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)
  • apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras’ Theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs
  • apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results
MathsWatch clip numbers: 120, 121, 122, 123, 166, 183, 184 MyMaths lessons: Angles in parallel lines, Circle theorems, Congruent triangles
End of Year Assessment
Unit 17: Algebraic proficiency: visualising Key Vocabulary

  • Function, equation
  • Sketch, plot
  • Linear, non-linear
  • Quadratic, cubic, reciprocal
  • Parabola, Asymptote
  • Gradient, y-intercept, x-intercept, root
  • Rate of change
  • Acceleration, deceleration
  • Parallel, Perpendicular
  • Radius, Tangent

 

  • identify and interpret gradients and intercepts of linear functions graphically
  • recognise, sketch and interpret graphs of linear functions and quadratic functions
  • use the form y = mx + c  to identify parallel and perpendicular lines
  • find the equation of the line through two given points, or through one point with a given gradient
  • recognise and use the equation of a circle with centre at the origin
  • find the equation of a tangent to a circle at a given point
MathsWatch clip numbers: 96, 97, 98, 99, 159a, 159b, 160, 161, 194, 197, 208 MyMaths lessons: Plotting graphs 1 & 2 – lines, y = mx + c, Equations of a line 2, Plotting graphs 3 – quadratics, Equations of circles
Unit 18: Exploring fractions, decimals and percentages Key Vocabulary

  • Fraction, Mixed number
  • Percentage change, percentage increase, percentage increase
  • Compound interest,
  • Simple interest
  • Terminating decimal, Recurring decimal
  • (Exponential) growth, decay
  • change recurring decimals into their corresponding fractions and vice versa
  • solve problems involving percentage change, including original value problems, and simple interest including in financial mathematics
  • set up, solve and interpret the answers in growth and decay problems, including compound interest
MathsWatch clip numbers: 76, 108, 109, 110, 111, 164, 177 MyMaths lessons: Percentage change 1 & 2, Compound interest, Depreciation, Recurring decimals 1 & 2

Term 6

Assessment Focus and Purpose Key Concepts/Skills Assessed Preparation/Key Areas to Revise
Unit 19: Understanding risk Key Vocabulary

  • Outcome, equally likely outcomes
  • Event, independent event, dependent event
  • Tree diagrams
  • Theoretical probability, experimental probability
  • Random
  • Bias, unbiased, fair
  • Enumerate
  • Set
  • Conditional probability
  • Venn diagram
  • calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions
  • enumerate sets and combinations of sets systematically, using tree diagrams
  • understand that empirical unbiased samples tend towards theoretical probability distributions, with increasing sample size
  • apply systematic listing strategies including use of the product rule for counting
MathsWatch clip numbers: 59, 60, 61, 125, 126, 127a, 127b, 151, 175, 185, 205 MyMaths lessons: Venn diagrams 1, Venn diagrams 2, Probability revision, The OR rule, Independent probability, Dependent events
Unit 20: Solving equations and inequalities Key Vocabulary

  • (Quadratic) equation
  • Factorise
  • Rearrange
  • Variable
  • Unknown
  • Manipulate
  • Solve
  • Deduce
  • x-intercept
  • Root
  • solve quadratic equations algebraically by factorising
  • solve quadratic equations (including those that require rearrangement) algebraically by factorising
  • find approximate solutions to quadratic equations using a graph
  • deduce roots of quadratic functions algebraically
MathsWatch clip numbers: 157, 192 MyMaths lessons: Quadratic equations 1, Quadratic equations 2, Solving with graphs
Unit 21: Mathematical movement Key Vocabulary

  • Vector
  • Scalar
  • Constant
  • Magnitude
  • apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors
MathsWatch clip numbers: 174, 219 MyMaths lessons: Vectors 1
     

Year 11 Assessment

Students also sit 6 practise exams throughout the year. 1 hour long. Sat in the classroom. Full papers. Corrections and completion of papers are done as ongoing homeworks

Term 2

Trial Exams Term 4 Mock Exams Term 5 and 6 External exams