Program of Study Maths

Mathematics - Our Vision Mathematics is essential for everyday life and understanding the world around us. It is not just about equations, numbers and calculations it is about deepening our understanding. At The Crypt we aim to empower our students by looking beyond the curriculum, to link mathematical concepts to practical and real world examples.

As a department we create a generation of problem solvers and logical thinkers that can think creatively to tackle problems. In Key Stage 3 we follow a scheme of work which focuses on a strong mastery approach and we aim to develop both the mental and written mathematical skills.

We aim to give a strong basis to move onto GCSE with topics on number, algebra, ratio and proportion, geometry and statistics. During year 11, some students have the opportunity to study AQA Certificate level 2 Further Maths GCSE and enhance their knowledge even further. Advanced mathematics is growing in popularity and is relevant to many careers. This is reflected by our popularity at KS5 with students taking Mathematics and Further Mathematics with students studying pure maths, statistics and mechanics.

Year 7

Term 1 Number

Numbers & Calculation Fractions Factors, Multiples & primes Decimals & Estimation Baseline Assessment

Term 2 Proportion

Probability Ratio, Decimal & % Ratio and Proportion

Term 3 Shape

Angles and Parallel Lines Shape and Construction Perimeter and Area

Problem Solving Investigation Non-Calculator assessment

Term 4 Sequences and Graphs

Term 5 Finding the Unknown

Term 6 Statistics & Transformations

Algebra Manipulation Sequences Coordinates & Graphs

Solving Equations & Inequalities Pythagoras

Averages Statistical Diagrams Transformations

Problem Solving Investigation

Year End Points       

Calculator assessment

Non-Calculator assessment

Calculator assessment

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1|Page

Use positive integer powers and associated real roots Apply the four operations with decimal numbers Write a quantity as a fraction or percentage of another Use multiplicative reasoning to interpret percentage change Add, subtract, multiply and divide with fractions and mixed numbers Check calculations using approximation, estimation or inverse operations Simplify and manipulate expressions by collecting like terms Simplify and manipulate expressions by multiplying a single term over a bracket Substitute numbers into formulae Solve linear equations with unknowns on both sides Find and use the nth term for a linear sequence Understand and use lines parallel to the axes, y = x and y = -x and plot and interpret graphs of linear functions Calculate surface area of cubes and cuboids Use ruler and compass methods to construct the perpendicular bisector of a line segment and to bisect an angle Understand and use geometric notation for labelling angles, lengths, equal lengths and parallel lines Apply Pythagoras’ theorem in two dimensions Apply the formulae for circumference and area of a circle Calculate theoretical probabilities for single events

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2|Page

Calculate averages from a list of data Draw a scatter graph and describe correlation Rotate, reflect, enlarge and translate a shape

Year

Term 1

Term 2

Term 3

Term 4

Term 5

Term 6

Year End Points

8

Number

Algebraic Thinking

Shape

Proportion

Investigating Data

Mensuration

Factors, Multiples & primes Numbers and Calculation Fractions Laws of Indices & Standard Form

Expressions & formula Equations & Inequalities

Angles & Polygons Transformations Pythagoras

Introduction to Trigonometry Exploring Percentages Proportional Reasoning

Collecting Data Averages Representing Data

Area, Perimeter and Volume

 Find the HCF and LCM from the product of prime numbers  Convert numbers into standard form and vice versa  Apply the multiplication, division and power laws of indices  Convert between terminating decimals and fractions  Change the subject of a formula when two steps are required  Manipulate algebraic expressions by expanding the product of two binomials  Factorise an expression by taking out common factors  Solve linear equations with unknowns on both sides and brackets  Use set notation on a Venn Diagram and use simple probability trees  Use angle rules to in a multistep problem explaining their method  missing angles in a polygon and know exterior angles add to 360  Rotate, reflect, enlarge (with a centre) and translate (using a vector) a shape  Understand Pythagoras and use in multistep problems and in context and use SOHCAHTOA on right angled triangles  Find a relevant multiplier when solving problems involving proportion, solve problems involving percentage change, including original value problems  Understand the link between compound interest to finance  Understand the importance of accurate data collection and interpret a frequency table  Draw and use a line of best fit on a scatter graph  Draw and use a cumulative frequency diagram  Find the volume and surface are of a prism  Know the difference between an arithmetic and geometric sequence  Recognise and plot a linear graph. Identify its gradient and intercept

Problem Solving Investigation

Probability Venn Diagrams and Tree Diagrams Non-Calculator assessment

3|Page

Problem Solving Investigation

Graphical Algebra Calculator assessment

Non-Calculator assessment

Sequences Graphs Calculator assessment

Year

Term 1

Term 2

Term 3

Term 4

Term 5

Term 6

9

Number

Manipulating Algebra

Shape

Proportion

Investigating Data

Probability



Factors, Multiples & primes Calculation, Checking and Rounding Indices

Problem Solving Investigation

Problem solve with area and perimeter Sectors Working in 3D Bearings

Ratio and Proportion Pythagoras and Trigonometry Exploring Percentages

Averages, Range and IQR Representing Data

Probability

 

4|Page

Linear and quadratic expressions Linear fractional

Year End Points

  

Problem solve using the HCF and LCM from the product of prime numbers Use upper and lower p Apply the negative and fractional laws of indices to simple cases Calculate in standard form Simplify a surd and simplify a simple expression with surds Solve linear equations with unknowns on

Year

Term 1

Term 2

Term 3

Term 4

Term 5

Term 6

Year End Points

10

Number and Movement

Equations and Graphs

Maths of Real Life

Trigonometry and Transforming Graphs

Construction

Probability

Exact Values – Fractions and Surds Transformations Congruency and Similarity in 2D and 3D

Solving Quadratic Equations Simultaneous Equations Linear Graphs & Coordinate Geometry

Statistical Diagrams Real Life Graphs

Trigonometry in 3D Sine and Cosine Rule Area of a Triangle Sectors and Segments Graph Transformations Trigonometric Graphs

Bisectors Loci

Product rule for counting Set Notation Venn Diagrams Tree Diagrams

Year 10 Mock Exams Non-Calculator and Calculator Paper

Vectors and Geometric Proof

 Convert between recurring decimals and fractions  Simplify Surds and rationalise a denominator  Understand similarity and apply it to length, area and volume.  Know what is meant by congruency SSS, SAS, ASA and RHS  Describe transformations using the correct mathematical language and describe the invariance achieved by combinations of transformations  Solve Loci Problems  Factorise expressions including quadratics  Solve quadratic equations  Solve quadratics by using the quadratic formula  Finding equation of line given two points  Find equations of perpendicular and parallel lines  Solve linear simultaneous equations algebraically and graphically  Draw and interpret cumulative frequency diagrams including quartiles  Draw, interpret and compare boxplots  Draw and interpret histograms  Know gradients are rates of change and apply this  Gradients and areas underneath velocity time graphs  Use formula for speed, density and pressure  Use Pythagoras and SOHCAHTOA for right angled triangles in 2D and 3D  Apply sine and cosine rule  Recognise quadratic, cubic, reciprocal and exponential graphs  Apply graph transformations given using function notation  Apply product rule for counting  Understand set notation  Find probabilities form Venn Diagrams and tree diagrams  Understand Vectors and use them for geometric Proof

Higher TierSoW GCSE Mathematics

Problem Solving Investigation

5|Page

Non-Calculator Assessment

Compound Measures

Year 10 Assessment Week Calculator Assessment

Vectors

Term 1

Term 2

Term 3

Term 4

Term 5

Term 6

Year End Points

10

Proportion and Movement

Equations and Graphs

Maths of Real Life

Trigonometry

Graphs

Probability

Exact Values – Fractions and Surds Transformations Congruency and Similarity in 2D and 3D Construction and Loci

Solving Quadratic Equations Simultaneous Equations Linear Graphs & Coordinate Geometry Quadratic, Cubic and Other Graphs

Collecting Data Statistical Diagrams Real Life Graphs Compound Measures

Trigonometry in 3D Sine and Cosine Rule Area of a Triangle Sectors and segments Proportion Graph Transformations Trigonometric Graphs

Quadratic Sequences

Product rule for counting Set Notation Venn Diagrams Tree Diagrams

 Convert between recurring decimals and fractions  Simplify Surds and rationalise a denominator  Understand similarity and apply it to length, area and volume.  Know what is meant by congruency SSS, SAS, ASA and RHS  Describe transformations using the correct mathematical language and describe the invariance achieved by combinations of transformations  Solve Loci Problems  Factorise expressions including quadratics  Solve quadratic equations  Solve quadratics by using the quadratic formula  Finding equation of line given two points  Find equations of perpendicular and parallel lines  Solve linear simultaneous equations algebraically and graphically  Draw and interpret cumulative frequency diagrams including quartiles  Draw, interpret and compare boxplots  Draw and interpret histograms  Know gradients are rates of change and apply this  Gradients and areas underneath velocity time graphs  Use formula for speed, density and pressure  Use Pythagoras and SOHCAHTOA for right angled triangles in 2D and 3D  Apply sine and cosine rule  Recognise quadratic, cubic, reciprocal and exponential graphs  Apply graph transformations given using function notation  Use Pythagoras and SOHCAHTOA for right angled triangles in 2D and 3D  Apply sine and cosine rule  Recognise quadratic, cubic, reciprocal and exponential graphs  Apply graph transformations given using function notation  Create equations for direct and inverse proportion  Create the nth term for a quadratic sequence  Apply product rule for counting  Understand set notation  Find probabilities form Venn Diagrams and

& AQA Level 2 Further MathsSoW GCSE Mathematics

Year

6|Page

Vectors Vectors and Geometric Proof

Problem Solving Investigation Non-Calculator Assessment Year 10 Assessment Week Calculator Assessment

Year 10 Mock Exams Non-Calculator and Calculator Paper

tree diagrams  Understand Vectors and use them for geometric Proof

Term 1

Term 2

Term 3

Term 4

Term 5

11

Further Algebra

Further Algebra

Proportion

Surds & Coordinate Geometry

Revision

Expanding 3 brackets Completing the Square Sketching Graphs Quadratic Inequalities Quadratic & Linear Simultaneous Functions

Review and Extend

Direct and Inverse Proportion Algebraic Fractions Iteration Quadratic Sequences

Rationalising the denominator complex surds Coordinate Geometry Circles

SoW GCSE Mathematics

Year

Circles and Proof

Term 6 GCSE EXAMS

Revision

Circle Theorems Circle Theorem Proof Algebraic Proof

Non-Calculator assessment Mock Exams

Term 1

Term 2

Term 3

Term 4

Term 5

Term 6

11

Further Algebra

Proof and Geometry

Further Maths

Further Maths

Revision

GCSE EXAMS

SoW GCSE Mathematics

Expanding 3 brackets Completing the Square Sketching Graphs Quadratic Inequalities Quadratic & Linear Simultaneous Functions Circle Theorems Circle Theorem Proof

Review and Extend

Differentiation Trigonometry Polynomials and Factor Theorem

Binomial Expansion Simultaneous Equations with 3 variables Matrices Coordinate Geometry

7|Page

Algebraic Proof Algebraic Fractions Coordinate Geometry Circles Iteration

• Simplify surds, including rationalising the

denominator of a surd expression • Manipulate quadratic expressions by completing the square • Deduce roots and turning points of quadratic functions • Understand the concept of an instantaneous rate of change • Sketch translations and reflections of given functions • Solve quadratic inequalities in one variable • Solve a simultaneous equation where one variable is linear and the other is quadratic • Find compound and inverse functions • Solve problems involving direct and inverse proportion • Know, apply and prove the circle theorems • Use algebra with proofs • Simplify and use the four operations with algebraic fractions • Use and apply iteration formulae • Find the nth term rule of a quadratic sequence • Find the equation of a tangent to a circle

Calculator Assessment

Year

Circles and Proof

Year End Points

Year End Points • Manipulate quadratic expressions by completing the square • Deduce roots and turning points of quadratic functions • Understand the concept of an instantaneous rate of change • Sketch translations and reflections of given functions • Solve quadratic inequalities in one variable • Solve a simultaneous equation where one variable is linear and the other is quadratic • Find compound and inverse functions • Solve problems involving direct and inverse proportion • Know, apply and prove the circle theorems • Use algebra with proofs • Simplify and use the four operations with algebraic fractions • Use and apply iteration formulae • Find the nth term rule of a quadratic sequence • Find the equation of a tangent to a circle

Maths& AQA Level 2 Further

Algebraic Proof

• Differentiate and find stationary points • Use a CAST diagram and solve trigonometric equations 2 2 • Use the identities and

Mock Exams

Non-Calculator assessment

sin x tan x= cos x

sin x+cos x =1

• Use the factor theorem and algebraic long division to factorise cubics n • Binomial expand

(ax +b)

Year

Term 1

Term 2

Term 3

Term 4

Term 5

Term 6

12

PURE MATHS

PURE MATHS

PURE MATHS

PURE MATHS

PURE MATHS

PURE MATHS

LEAD TEACHER 1 (6 Lessons per fortnight Pure & Statistics)

• Solve simultaneous equations with 3 variables • Calculate with matrices

TEACHER 1 Quadratics  Quadratic Functions  Simultaneous Equations  Inequalities

TEACHER 1 Trigonometry  Sine and Cosine Rule  Trigonometric graphs  Solving equations through CAST diagrams  Trigonometric Identities

TEACHER 1 Calculus - Differentiation  Maxima and minima  Optimisation Problems

TEACHER 2 Factor Theorem and Cubics  Factor theorem  Algebraic Long division  Solving Cubics

Calculus – Integration  Introduction to integration

Calculus – Differentiation  From first principles  Differentiation  Liebnitz notation  Linear coordinate geometry  Tangents and Normals TEACHER 2 Indices and Surds  Index laws  Manipulating surds  Rationalising a denominator Curve Sketching  Sketching Cubic, quartic and reciprocal grams  Curve sketching graph transformations

STATISTICS T1

Describing Data  Histogram  Means and Standard deviations  Comparing Distributions  Bivariate Data

MECHANICS T2

Motion in a straight line  Displacement time

Logarithms and Exponentials  Laws of logarithms  Solving logarithmic equations  Solving exponential equations  Logarithmic graphs

TEACHER 1 Functions (A level)  Function notation  Range and domains  Composite functions  Inverse Functions TEACHER 2 Algebraic Fractions (A level)  Simplifying  Four operations

Proof  By exhaustion  Algebraic  Disprove by counter example

Sampling and Definitions  Sampling Methods  Key definitions  Large Data Set

Forces and Units  Standard units and basic dimensions  Force units and balanced forces  Resultant forces

8|Page

Binomial Expansion  With n as an integer

TEACHER 1 Coordinate Geometry  Equation of a circle  Coordinate geometry problems

MECHANICS T2 Vectors  Notation  Magnitude  Unit vectors  Angles with an axis

STATISTICS T1

STATISTICS T1

Probability  Notation  Tree diagrams  Venn diagrams  Independence and Mutually exclusive

Discrete Probability  Discrete random variables  Binomial Distribution

MECHANICS T2 Variable Acceleration  Calculating displacement, velocity and acceleration using calculus Dynamics  Use of F=ma Connected Particles

Hypothesis Testing  Binomial hypothesis testing p-value and critical regions

MECHANICS T2 Connected Particles  Lifts  Pulleys

TEACHER 1 Binomial Expansion (A level)  n is negative or fractional Partial Fractions (A level)  Standard partial fractions  Repeated roots  Improper fractions TEACHER 2 Algebraic Fractions (A level)  Simplifying  Four operations

Year End Points Construct and present mathematical arguments through appropriate use of diagrams; sketching graphs; logical deduction and precise statements Understand and use mathematical language and syntax as set out in the content.

Understand and use language and symbols associated with set theory, as set out in the appendices. Apply to solutions of inequalities and probability.

Comprehend and critique mathematical arguments, proofs and justifications of methods and formulae, including those relating to applications of mathematics.

Recognise the underlying mathematical structure in a situation and simplify and abstract appropriately to enable problems to be solved.

Construct extended arguments to solve problems presented in an unstructured form, including problems in context.

Interpret and communicate solutions in the context of the original problem.

Evaluate, including by making reasoned estimates, the accuracy or limitations of solutions.

Understand the concept of a mathematical problem solving cycle, including specifying the problem, collecting information, processing and representing information and interpreting results, which may identify the need to repeat the cycle Understand, interpret and extract information from diagrams and construct mathematical diagrams to solve problems, including in mechanics.

Translate a situation in context into a mathematical model, making simplifying assumptions.

Use a mathematical model with suitable inputs to engage with and explore situations (for a given model or a model constructed or selected by the student).

Interpret the outputs of a mathematical model in the

TEACHER 2 (3 lesson per fortnight Pure & Mechanics)

 Cars pulling trailers

graphs  Velocity time graphs

context of the original situation (for a given model or a model constructed or selected by the student).

Constant Acceleration  SUVAT Proof  SUVAT equations

Understand that a mathematical model can be refined by considering its outputs and simplifying assumptions; evaluate whether the model is appropriate.

Understand and use modelling assumptions

Initial Assessment

9|Page

Midterm Exam

Year 12 Assessment Week

Statistics & Mechanics assessment

Year 12 Mock Exams

Year

Term 1

Term 2

Term 3

Term 4

Term 5

Term 6

12

PURE MATHS

PURE MATHS

PURE MATHS

PURE MATHS

PURE MATHS

PURE MATHS

TEACHER 2 (3 lesson per fortnight Pure & Statistics)LEAD TEACHER 1 (6 Lessons per fortnight Pure & Mechanics)

TEACHER 1 Quadratics  Quadratic Functions  Simultaneous Equations  Inequalities

TEACHER 1 Trigonometry  Sine and Cosine Rule  Trigonometric graphs  Solving equations through CAST diagrams  Trigonometric Identities

TEACHER 1 Calculus - Differentiation  Maxima and minima  Optimisation Problems

TEACHER 2 Factor Theorem and Cubics  Factor theorem  Algebraic Long division  Solving Cubics

Calculus – Integration  Introduction to integration

Calculus – Differentiation  From first principles  Differentiation  Liebnitz notation  Linear coordinate geometry  Tangents and Normals TEACHER 2 Indices and Surds  Index laws  Manipulating surds  Rationalising a denominator Curve Sketching  Sketching Cubic, quartic and reciprocal grams  Curve sketching graph transformations

Binomial Expansion  With n as an integer

TEACHER 1 Coordinate Geometry  Equation of a circle  Coordinate geometry problems Logarithms and Exponentials  Laws of logarithms  Solving logarithmic equations  Solving exponential equations  Logarithmic graphs

MECHANICS T1

MECHANICS T1 Vectors  Notation  Magnitude  Unit vectors  Angles with an axis

Motion in a straight line  Displacement time graphs  Velocity time graphs

Describing Data  Histogram  Means and Standard deviations  Comparing Distributions  Bivariate Data

Initial Assessment

10 | P a g e

Midterm Exam

TEACHER 1 Binomial Expansion (A level)  n is negative or fractional Partial Fractions (A level)  Standard partial fractions  Repeated roots  Improper fractions TEACHER 2 Algebraic Fractions (A level)  Simplifying  Four operations

STATISTICS T2 Probability  Notation  Tree diagrams  Venn diagrams  Independence and Mutually exclusive

Year 12 Assessment Week

STATISTICS T2 Discrete Probability  Discrete random variables  Binomial Distribution

Understand and use mathematical language and syntax as set out in the content.

Understand and use language and symbols associated with set theory, as set out in the appendices. Apply to solutions of inequalities and probability.

Comprehend and critique mathematical arguments, proofs and justifications of methods and formulae, including those relating to applications of mathematics.

Recognise the underlying mathematical structure in a situation and simplify and abstract appropriately to enable problems to be solved.

Construct extended arguments to solve problems presented in an unstructured form, including problems in context.

MECHANICS T1

Interpret and communicate solutions in the context of the original problem.

Variable Acceleration  Calculating displacement, velocity and acceleration using calculus

Evaluate, including by making reasoned estimates, the accuracy or limitations of solutions.

Dynamics  Use of F=ma

Understand the concept of a mathematical problem solving cycle, including specifying the problem, collecting information, processing and representing information and interpreting results, which may identify the need to repeat the cycle

Connected Particles  Cars pulling trailers  Lifts  Pulleys

Constant Acceleration  SUVAT Proof  SUVAT equations

STATISTICS T2

TEACHER 2 Algebraic Fractions (A level)  Simplifying  Four operations

Proof  By exhaustion  Algebraic  Disprove by counter example

Forces and Units  Standard units and basic dimensions  Force units and balanced forces  Resultant forces

Sampling and Definitions  Sampling Methods  Key definitions  Large Data Set

TEACHER 1 Functions (A level)  Function notation  Range and domains  Composite functions  Inverse Functions

Year End Points Construct and present mathematical arguments through appropriate use of diagrams; sketching graphs; logical deduction and precise statements

Understand, interpret and extract information from diagrams and construct mathematical diagrams to solve problems, including in mechanics.

STATISTICS T2

Translate a situation in context into a mathematical model, making simplifying assumptions.

Hypothesis Testing  Binomial hypothesis testing p-value and critical regions

Use a mathematical model with suitable inputs to engage with and explore situations (for a given model or a model constructed or selected by the student).

Interpret the outputs of a mathematical model in the context of the original situation (for a given model or a model constructed or selected by the student).

Statistics & Mechanics assessment

Year 12 Mock Exams

Understand that a mathematical model can be refined by considering its outputs and simplifying assumptions; evaluate whether the model is appropriate.

Understand and use modelling assumptions

Term 1

Term 2

Term 3

Term 4

Term 5

Term 6

13

PURE MATHS

PURE MATHS

PURE MATHS

PURE MATHS

PURE MATHS

PURE MATHS

TEACHER 2 (3 lesson per fortnight Pure & Mechanics)LEAD TEACHER 1 (6 Lessons per fortnight Pure & Statistics)

Year

TEACHER 1 Trigonometry

 Introduction to radians  Arc length and area  Reciprocal trigonometric functions  Inverse trigonometric functions  Identities  R Formula  Small angle approximations  Differentiation of trig from first principles

TEACHER 2 Sequences and Series  Recurrance relationships  Arithmetic Sequences  Geometric Sequences

TEACHER 1 Calculus Differentiation

 Chain, product and quotient  Derivations of inverses  Shapes of functions

TEACHER 2 Numerical Methods

 Iteration  Newton Rapheson  Trapezium Rule

STATISTICS T1 Conditional Probability

 Applied to tree diagrams and Venn diagrams

Normal Distribution

 Finding probabilities  Working backwards  Z values and finding mean and standard deviation

MECHANICS T2

MECHANICS T2

Moments  Multiple pivots and

Vectors in 3D

TEACHER 1 Calculus Integration

 Area between two curves  Integration by cover up  Rational functions  Partial fractions  Trigonometric identities  By parts  Substitution  Standard Results

TEACHER 1 Parametric Equations 2

 Differentiating parametrics  Integrating parametrics

 Differentiating parametrics  Integrating parametrics

TEACHER 2 Graph Sketching  Modulus graphs  Solving modulus equations

Recognise the underlying mathematical structure in a situation and simplify and abstract appropriately to enable problems to be solved.

STATISTICS T1 Approximating Distributions

 Approximating Binomial with a normal distribution  Normal distribution hypothesis testing

STATISTICS T1 Hypothesis Testing

 Normal hypothesis testing p-value  Correlation hypothesis testing p-value

Construct extended arguments to solve problems presented in an unstructured form, including problems in context.

Interpret and communicate solutions in the context of the original problem.

Understand that many mathematical problems cannot be solved analytically, but numerical methods permit solution to a required level of accuracy.

Evaluate, including by making reasoned estimates, the accuracy or limitations of solutions, including those obtained using numerical methods.

Calculus Differentiation

 Implicit differentiation  Normals, tangents and turning points

MECHANICS T2

Proof  Proof by contradiction

Projectiles 

MECHANICS T2 Statics

Year 13 Mock Exams

Understand the concept of a mathematical problem solving cycle, including specifying the problem, collecting information, processing and representing information and interpreting results, which may identify the need to repeat the cycle Understand, interpret and extract information from diagrams and construct mathematical diagrams to solve problems, including in mechanics.

 At an angle  Coefficient of friction

Translate a situation in context into a mathematical model, making simplifying assumptions.

Dynamic

Use a mathematical model with suitable inputs to engage with and explore situations (for a given model or a model constructed or selected by the student).

Interpret the outputs of a mathematical model in the context of the original situation (for a given model or a model constructed or selected by the student).

 At an angle  Coefficient of friction

 Calculating displacement, velocity and acceleration using calculus

Year 13 Assessment Week

Understand and use language and symbols associated with set theory, as set out in the appendices. Apply to solutions of inequalities and probability Understand and use the definition of a function; domain and range of functions.

Parametric Equations 1

 The graphs of parametric equations  Parametric to cartesian

Understand and use mathematical language and syntax as set out in the content.

Comprehend and critique mathematical arguments, proofs and justifications of methods and formulae, including those relating to applications of mathematics.

Variable Acceleration

11 | P a g e

TEACHER 2 Revision of Mechanics

Solving Differential Equations

suspensions

Year 13 transitional Exam

TEACHER 1 Revision of Pure and Statistics

Year End Points Construct and present mathematical arguments through appropriate use of diagrams; sketching graphs; logical deduction; precise statements involving correct use of symbols and connecting language

Statistics & Mechanics Assessment

Understand that a mathematical model can be refined by considering its outputs and simplifying assumptions; evaluate whether the model is appropriate.

Understand and use modelling assumptions

12 | P a g e

Year

Term 1

Term 2

Term 3

Term 4

Term 5

Term 6

13

PURE MATHS

PURE MATHS

PURE MATHS

PURE MATHS

PURE MATHS

PURE MATHS

TEACHER 2 (3 lesson per fortnight Pure & Statistics)LEAD TEACHER 1 (6 Lessons per fortnight Pure & Mechanics)

TEACHER 1 Trigonometry

 Introduction to radians  Arc length and area  Reciprocal trigonometric functions  Inverse trigonometric functions  Identities  R Formula  Small angle approximations  Differentiation of trig from first principles

TEACHER 2 Sequences and Series  Recurrance relationships  Arithmetic Sequences  Geometric Sequences

TEACHER 1 Calculus Differentiation

 Chain, product and quotient  Derivations of inverses  Shapes of functions

TEACHER 2 Numerical Methods

 Iteration  Newton Rapheson  Trapezium Rule

Mechanics T1

Moments  Multiple pivots and suspensions

Variable Acceleration

 Calculating displacement, velocity and acceleration using calculus

Vectors in 3D Statistics T2 Conditional Probability

 Applied to tree diagrams and Venn diagrams

Year 13 transitional Exam

Statistics T2 Normal Distribution

 Finding probabilities  Working backwards  Z values and finding mean and standard deviation

Year 13 Assessment Week

TEACHER 1 Calculus Integration

 Area between two curves  Integration by cover up  Rational functions  Partial fractions  Trigonometric identities  By parts  Substitution  Standard Results

TEACHER 1 Parametric Equations 2

TEACHER 1 Revision of Pure and Mechanics

 Differentiating parametrics  Integrating parametrics

TEACHER 2 Revision of Statistics

Solving Differential Equations

 Differentiating parametrics  Integrating parametrics

Recognise the underlying mathematical structure in a situation and simplify and abstract appropriately to enable problems to be solved.

Mechanics T1 Projectiles 

Mechanics T1 Statics

 At an angle  Coefficient of friction

Dynamic

 At an angle  Coefficient of friction

 Modulus graphs  Solving modulus equations

Calculus Differentiation

Proof  Proof by contradiction

Understand and use language and symbols associated with set theory, as set out in the appendices. Apply to solutions of inequalities and probability

Comprehend and critique mathematical arguments, proofs and justifications of methods and formulae, including those relating to applications of mathematics.

TEACHER 2 Graph Sketching

 Implicit differentiation  Normals, tangents and turning points

Understand and use mathematical language and syntax as set out in the content.

Understand and use the definition of a function; domain and range of functions.

Parametric Equations 1

 The graphs of parametric equations  Parametric to cartesian

Year End Points Construct and present mathematical arguments through appropriate use of diagrams; sketching graphs; logical deduction; precise statements involving correct use of symbols and connecting language

Statistics T2 Approximating Distributions

 Approximating Binomial with a normal distribution  Normal distribution hypothesis testing

Year 13 Mock Exams

Statistics T2 Hypothesis Testing  Normal hypothesis testing p-value Correlation hypothesis testing p-value

Statistics & Mechanics assessment

Construct extended arguments to solve problems presented in an unstructured form, including problems in context.

Interpret and communicate solutions in the context of the original problem.

Understand that many mathematical problems cannot be solved analytically, but numerical methods permit solution to a required level of accuracy.

Evaluate, including by making reasoned estimates, the accuracy or limitations of solutions, including those obtained using numerical methods.

Understand the concept of a mathematical problem solving cycle, including specifying the problem, collecting information, processing and representing information and interpreting results, which may identify the need to repeat the cycle Understand, interpret and extract information from diagrams and construct mathematical diagrams to solve problems, including in mechanics.

Translate a situation in context into a mathematical model, making simplifying assumptions.

Use a mathematical model with suitable inputs to engage with and explore situations (for a given model or a model constructed or selected by the student).

Interpret the outputs of a mathematical model in the context of the original situation (for a given model or a model constructed or selected by the student).

Understand that a mathematical model can be refined by considering its outputs and simplifying assumptions; evaluate whether the model is appropriate.

Understand and use modelling assumptions

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