# Maths - Year 13

### Term 1: Y13 Pure Mathematics Proof, Sequences and Series, Functions and modelling, Algebraic fractions, Partial fractions, Binomial Theorem.

1. Proof and algebraic fractions

• Proof by contradiction

• Algebraic fractions

• Partial fractions

• Algebraic division

2. Functions and graphs

• The modulus function

• Functions and mappings

• Composite functions

• Inverse functions

• y = |f(x)| and y = f(|x|)

• Combining transformations

• Solving modulus problems

3. Sequences and Series

• Arithmetic sequences

• Arithmetic series

• Geometric sequences

• Geometric series

• Sum to infinity

• Sigma notation

• Recurrence relations

• Modelling with series

4. Binomial Expansion

• Expanding (1 + x)n

• Expanding (a + bx)n

• Using partial fractions

1. Internal topic assessment of 50 minutes duration on each area studied.

A Unit Test on the topics studied during the term.

Assessment at the end of the year is through two 2 hour exams in Pure Maths, worth 66% of the total.

###### https://nrich.maths.org/10321

This is a link to some useful maths notation Please refer also to Edexcel AL Maths Specification (https://qualifications.pearson.com/) Appendix 2 for a full list of notation required for Maths and Further Maths AS and AL

• Spiritual
• Moral
• Social
• Cultural
###### Develop the individual:

Develop an awareness of the relevance of mathematics to other fields of study, to the world of work and to society in general. Take increasing responsibility for their own learning and the evaluation of their own mathematical development.

###### Create a supportive community:

Use mathematics as an effective means of communication. Be able to discuss approaches to problem solving, working collaboratively to support each other.

### Term 2: Y13 Pure Mathematics Radians, Numerical methods, Integration (1), Trigonometric functions, Trigonometry and modelling, Parametric equations, Differentiation.

5. Trigonometry (Trig 1)

• Arc length

• Areas of sectors and segments

• Exact values and approximations

• Solving trigonometric equations

6. Trigonometric functions (Trig 2)

• Secant, cosecant and cotangent

• Graphs of sec x, cosec x and cot x Using sec x, cosec x and cot x

• Trigonometric identities

• Inverse trigonometric functions

7. Trigonometry and modelling (Trig 3)

• Using the addition formulae

• Double angle formulae

• Solving trigonometric equations

• Simplifying a cos x ± b sin x

• Proving trigonometric identities

• Modelling with trigonometric functions6. Parametric Equations

8. Parametric equations

• Using trigonometric identities

• Curve sketching

• Points of intersection

• Modelling with parametric equations

9. Differentiation

• Differentiating sin x and cos x

• Differentiating exponentials and logarithms

• The chain rule

• The product rule

• The quotient rule

• Differentiating trigonometric functions

• Parametric

1. Internal topic assessment of 50 minutes duration on each area studied. Unit test on the topics studied during the term.

Assessment of this area is within two 2 hour papers at the end of Year 13, worth 66% of the total for the A level.

###### https://nrich.maths.org/10321

This is a link to some useful maths notation Please refer also to Edexcel AL Maths Specification (https://qualifications.pearson.com/) Appendix 2 for a full list of notation required for Maths and Further Maths AS and AL

• Spiritual
• Moral
• Social
• Cultural
###### Develop the individual:

Develop an awareness of the relevance of mathematics to other fields of study, to the world of work and to society in general. Take increasing responsibility for their own learning and the evaluation of their own mathematical development.

###### Create a supportive community:

Use mathematics as an effective means of communication. Be able to discuss approaches to problem solving, working collaboratively to support each other.

### Term 3: Y13 Pure Mathematics Integration,Vectors in 3D

10. Numerical methods

• Locating roots

• Iteration

• The Newton-Raphson method

• Applications to modelling

11. Integration

• Integrating standard functions

• Integrating f(ax + b)

• Using trigonometric identities

• Reverse chain rule

• Integration by substitution

• Integration by parts

• Partial fractions

• Finding areas

• The trapezium rule

• Solving differential equations

• Modelling with differential equations

12. Vectors

• 3D Coordinates

• Vectors in 3D

• Solving geometric problems

• Application to mechanics

1. Internal topic assessment of 50 minutes duration on each area studied.

Assessment at the end of Year 13, two 2 hour exams in Pure Maths, worth 66% of the A level.

###### https://nrich.maths.org/10321

This is a link to some useful maths notation Please refer also to Edexcel AL Maths Specification (https://qualifications.pearson.com/) Appendix 2 for a full list of notation required for Maths and Further Maths AS and AL

• Spiritual
• Moral
• Social
• Cultural
###### Develop the individual:

Develop an awareness of the relevance of mathematics to other fields of study, to the world of work and to society in general. Take increasing responsibility for their own learning and the evaluation of their own mathematical development.

###### Create a supportive community:

Use mathematics as an effective means of communication. Be able to discuss approaches to problem solving, working collaboratively to support each other.

### Term 4: Y13 Applied Mathematics - Statistics Regression and Correlation, Probability, The Normal Distribution.

1. Regression and correlation

• Change of variable

• Exponential modelling

• Measuring correlation

• Hypothesis testing for 0 correlation

2. Conditional probability

• Set notation

• Conditional probability

• Venn diagrams

• Probability formulae

• Tree diagrams

3. The normal distribution

• The normal distribution

• Finding probabilities for normal distributions

• The inverse normal distribution function

• The standard normal distribution

• Finding μ and σ

• Approximating a binomial distribution

• Hypothesis testing with the normal distribution

1. Internal topic assessment of 50 minutes duration on each area studied.

Assessment at the end of Year 13, one two hour exam in Applied Mathematics of which half the content is Statistics.

###### https://nrich.maths.org/10321

This is a link to some useful maths notation Please refer also to Edexcel AL Maths Specification (https://qualifications.pearson.com/) Appendix 2 for a full list of notation required for Maths and Further Maths AS and AL

• Spiritual
• Moral
• Social
• Cultural
###### Develop the individual:

Develop an awareness of the relevance of mathematics to other fields of study, to the world of work and to society in general. Take increasing responsibility for their own learning and the evaluation of their own mathematical development.

###### Create a supportive community:

Use mathematics as an effective means of communication. Be able to discuss approaches to problem solving, working collaboratively to support each other.

### Term 4: Y13 Applied Mathematics - Mechanics Moments, Forces, Applications of kinematics, Applications of forces, Further kinematics

1. Moments

• Resultant moments

• Equilibrium

• Centres of mass

• Tilting

2. Forces and friction

• Resolving forces

• Inclined planes

• Friction

3. Projectiles

• Horizontal projection

• Horizontal and vertical components

• Projection at any angle

• Projectile motion formulae

4. Applications of forces

• Static particles

• Modelling with statics

• Friction and static particles

• Static rigid bodies

• Dynamics and inclined planes

• Connected particles

5. Further kinematics

• Vectors in kinematics

• Vector methods with projectiles

• Variable acceleration in one dimension

• Differentiating vectors

• Integrating vectors

1. Topic tests of 50 minutes duration.

Assessment at the end of the course in a 2 hour exam where half the questions are on Mechanics. Edexcel specification.

###### https://nrich.maths.org/10321

This is a link to some useful maths notation Please refer also to Edexcel AL Maths Specification (https://qualifications.pearson.com/) Appendix 2 for a full list of notation required for Maths and Further Maths AS and AL

• Spiritual
• Moral
• Social
• Cultural
###### Develop the individual:

Develop an awareness of the relevance of mathematics to other fields of study, to the world of work and to society in general. Take increasing responsibility for their own learning and the evaluation of their own mathematical development.

###### Create a supportive community:

Use mathematics as an effective means of communication. Be able to discuss approaches to problem solving, working collaboratively to support each other.

### Term 5: Revision

A Level revision and preparation

1. A Level examinations
• Spiritual
• Moral
• Social
• Cultural