Mathematics
SUBJECT overview
Mathematics can be applied in practical tasks, real life problems and within mathematics itself. The aim of the course is to develop mathematical vocabulary, improve mental calculation and use a range of methods of computation and apply these to a variety of problems.
The course of study should help you whether working individually or collaboratively to reason logically, plan strategies and improve your confidence in solving complex problems.
During Maths lessons you will learn how to:
 Use and apply maths in practical tasks, real life problems and within mathematics itself.
 Develop and use a range of methods of computation and apply these to a variety of problems.
 Develop mathematical vocabulary and improve mental calculation.
 Consider how algebra can be used to model real life situations and solve problems.
 Explore shape and space through drawing and practical work using a range of materials and a variety of different representations.
 Use statistical methods to formulate questions about data, represent data and draw conclusions.
UNIT OVERVIEW  AUTUMN 1  MECHANICS
Unit 5: Forces and Friction 

Skills 

Knowledge 
By the end of the unit, students should:

Rationale 
Newton’s laws summarise and govern the basic interactions between objects and forces. At their most fundamental level, forces tell us how different objects interact. This can be viewed on a macro scale (such as the forces between a car and the road), or on a micro scale (such as looking how the forces between atoms cause the atoms to form an object). As such, knowledge of forces and how they work has application to chemistry, physics, engineering, sport, architecture and building, and any other field the deals with one object interacting with another. For example, structural materials need to be tested to decide if they are appropriate for certain situations. As such they need to be subjected various shear and compressive/stretching forces to determine the grade or material. 
UNIT OVERVIEW  AUTUMN 1  PURE
Units 5, 6, and 7: Radians and Trigonometry 

Skills 
2 i.e. sin θ ≈ θ, cos θ ≈ 1 – ^{8} , tan θ ≈ θ where θ is in radians. 2
6 4 3 2 and exact values of tan for 0 , ^{n}, ^{n}, ^{n}, ^{n}, π and multiples thereof. 6 4 3 2
B) and tan (A ± B); understand geometrical proofs of these formulae.
R cos (θ ± α) or R sin (θ ± α) .

Knowledge 
By the end of the unit, students should:

UNIT OVERVIEW  AUTUMN 2  MECHANICS
Unit 7: Applications of forces 

Skills 
extend to situations where forces need to be resolved (restricted to 2 dimensions).
in a straight line; application to problems involving smooth pulleys and connected particles; resolving forces in 2 dimensions; equilibrium of a particle under coplanar forces.

Knowledge 
By the end of the unit, students should:

Rationale 
Newton’s laws summarise and govern the basic interactions between objects and forces. At their most fundamental level, forces tell us how different objects interact. This can be viewed on a macro scale (such as the forces between a car and the road), or on a micro scale (such as looking how the forces between atoms cause the atoms to form an object). As such, knowledge of forces and how they work has application to chemistry, physics, engineering, sport, architecture and building, and any other field the deals with one object interacting with another. For example, structural materials need to be tested to decide if they are appropriate for certain situations. As such they need to be subjected various shear and compressive/stretching forces to determine the grade of material. 
unit overview  autumn 2  pure
Subject: Units 5, 6, and 7: Radians and Trigonometry 

Skills 
2 i.e. sin θ ≈ θ, cos θ ≈ 1 – ^{8} , tan θ ≈ θ where θ is in radians. 2
6 4 3 2 and exact values of tan for 0 , ^{n}, ^{n}, ^{n}, ^{n}, π and multiples thereof. 6 4 3 2
B) and tan (A ± B); understand geometrical proofs of these formulae.
R cos (θ ± α) or R sin (θ ± α) .

Knowledge 
By the end of the unit, students should:

Subject: Unit 11: Integration 

Skills 
s differences and constant multiples. To include integration of standard functions such as sin 3x, sec2 2x, tan x, e5x, ^{1} . 2s Students are expected to be able to use trigonometric identities to integrate, for example, sin2 x, tan2 x, cos2 3x.

Knowledge 
By the end of the subunit, students should:
s ln x;
.
õ f( x)


and the general solution. 
Rationale 
Integration is the second half of calculus, with the first half being differentiation. Integration is essentially the inverse operation of differentiation, and as such is applicable and useful wherever differentiation is. At the most fundamental level, integration finds the area between the graph of the function and the variable axis. Depending on the variables involved in the function, this will tell us different information. For example, for a function of velocity over time, the integral will give us the distance travelled over a given time period. Integration is heavily used in the field of Finance, Physics, Engineering, Chemistry, and almost all other forms of science and economic fields. 
Subject: Unit 12: Vectors (3D) 

Skills 
Knowledge of column vectors and i, j and k unit vectors in three dimensions. 
Knowledge 
By the end of the unit, students should:

Rationale 
A vector is a quantity that has an intrinsic magnitude and direction. Quantities like displacement, velocity, acceleration, force, and momentum are all vectors. When vectors of the same type are applied to the same object they combine in specific ways.
Vectors are utilised in many different fields, such as navigation, computer graphics, and engineering. In Navigation, when bearings are combined with distance they create a vector. Total displacement from a series of directions can then be calculated using vector addition, as well as average speed if the time frame is available.
Vectors are used to resolve forces, and as such are a core part of structural architecture, as buildings need to be in equilibrium. Through vector addition of forces and dispersion of these forces stable structures can be designed. 
unit overview  spring 1  mechanics
Unit 2: Conditional Probability 

Skills 
P(B)

Knowledge 
By the end of the unit, students should:
P(B)

Rationale 
Probability theory is applied in everyday life in risk assessment and modelling. The insurance industry and markets use actuarial science to determine pricing and make trading decisions. Governments apply probabilistic methods in environmental regulation, entitlement analysis (Reliability theory of aging and longevity), and financial regulation. A good example of the use of probability theory in equity trading is the effect of the perceived probability of any widespread Middle East conflict on oil prices, which have ripple effects in the economy as a whole. An assessment by a commodity trader that a war is more likely can send that commodity's prices up or down, and signals other traders of that opinion. Accordingly, the probabilities are neither assessed independently nor necessarily very rationally. The theory of behavioural finance emerged to describe the effect of such groupthink on pricing, on policy, and on peace and conflict. Reference https://en.wikipedia.org/wiki/Probability#Applications 
unit overview  spring 1  pure
Unit 4: The binomial theorem 

Skills 
a 
Knowledge 
By the end of the unit, students should:
b
a 1;

Rationale 
The Binomial theorem, and therefore the binomial expansion is a naturally occurring distribution based off of a system with a fixed probability of success and only two states (success or failure). Even if the system technically has more than two states, it is a helpful tool that can simplify that system down to a success/failure cutoff point. A simple example of this is a dice, which can roll a 1, 2, 3, 4, 5, or 6. If you need to roll a minimum of a 5 for a game, then the success state is 5 or 6, and failure is 1, 2, 3, or 4. At this point the exact number does not matter – only if you “win” the roll or not. Binomial distributions have immediate applications to games of chance, but also to natural occurrences. For example, farmers or animal breeders could use a binomial expansion to calculate the probability of breeding a certain number of offspring with a desired genetic trait. 
unit overview  spring 1  statistics
Unit 2: Conditional Probability 

Skills 
P(B)

Knowledge 
By the end of the unit, students should:
P(B)

Rationale 
Probability theory is applied in everyday life in risk assessment and modelling. The insurance industry and markets use actuarial science to determine pricing and make trading decisions. Governments apply probabilistic methods in environmental regulation, entitlement analysis (Reliability theory of aging and longevity), and financial regulation. A good example of the use of probability theory in equity trading is the effect of the perceived probability of any widespread Middle East conflict on oil prices, which have ripple effects in the economy as a whole. An assessment by a commodity trader that a war is more likely can send that commodity's prices up or down, and signals other traders of that opinion. Accordingly, the probabilities are neither assessed independently nor necessarily very rationally. The theory of behavioural finance emerged to describe the effect of such groupthink on pricing, on policy, and on peace and conflict. Reference https://en.wikipedia.org/wiki/Probability#Applications 
unit overview  spring 2  pure
Unit 10: Numerical methods 

Skills 

Knowledge 
By the end of the unit, students should:

Rationale 
Numerical methods are processed based methods of find approximations of a solution to complex problems. These can be used to get an approximate answer in order to fact check longer solutions, or when automating a problem solving process. For example, in computing and computer science, numerical methods are relatively straightforward to implement as they usually focus on iterative processes. In fact, calculators and mathematical software will often use numerical methods to solve more complicated mathematical operations that would otherwise require abstract or algebraic solutions. 
unit overview  spring 2  statistics
Unit 1: Regression and correlation 

Skills 

Knowledge 
By the end of the unit, students should:

Rationale 
Linear regression is widely used in biological, behavioural and social sciences to describe possible relationships between variables. It ranks as one of the most important tools used in these disciplines. Linear regression is the predominant empirical tool in economics. For example, it is used to predict consumption spending, fixed investment spending, inventory investment, and purchases of a country's exports, spending on imports, the demand to hold liquid assets, labour demand, and labour supply. The capital asset pricing model uses linear regression as well as the concept of beta for analysing and quantifying the systematic risk of an investment. This comes directly from the beta coefficient of the linear regression model that relates the return on the investment to the return on all risky assets. Reference https://en.wikipedia.org/wiki/Linear_regression#Applications 
unit overview  summer 2  mechanics
Unit 4: Moments 

Skills 

Knowledge 
By the end of the unit, students should:

Rationale 
Moments are created when a force causes an object to rotate. The size of this moment depends on the size of the force, the angle of application and the distance that the fore was applied from the axis of rotation. Moments are a core concept to the idea of equilibrium, which is when an object is in a completely balanced state. This idea is applied to construction and architecture, where if a building gin not in equilibrium it may become unstable and collapse. Moments are also used in engineering, when a rotating wheel (on a car, for example) will have a moment applied to the axle which will cause the wheel to spin, hence accelerating the car. The size of the moment will determine how fast the car can accelerate. 
unit overview  summer 2  pure
Unit 1 (Part 1): Algebraic and partial fractions 

Skills 

Knowledge 
By the end of the unit, students should:
is a factor of a polynomial;

Rationale 
Algebraic manipulation is a key skill in any further mathematical studies, as well as fields that make frequent use of mathematical models. This includes finance, economics, engineering, and most forms of science. Algebraic and partial fractions is an important part of this algebraic manipulation toolkit. Being able to split and simplify fractions can in turn reduce complicated fractional functions into much easier to solve in implement mathematical models, which can be introduced into Full models linearly in sections rather than all at once. In the field of computer programming (or applied programming to finance or science) it is essential to be able to individually test and isolate different parts of the function. This can be achieved through partial fractions. 
unit overview  summer 2  statistics
Subject: Unit 3: The Normal distribution 

Skills 
probabilities using the Normal distribution
and the binomial distribution.
context, with appropriate reasoning, including recognising when the binomial or the Normal model may not be appropriate.
distribution with known, given or assumed variance and interpret the results in context. 
Knowledge 
By the end of the unit, students should:
distribution.

Rationale 
Measurement errors in physical experiments are often modelled by a normal distribution. This use of a normal distribution does not imply that one is assuming the measurement errors are normally distributed, rather using the normal distribution produces the most conservative predictions possible given only knowledge about the mean and variance of the errors.
Many scores are derived from the normal distribution, including percentile ranks ("percentiles" or "quantiles"), normal curve equivalents, stanines, zscores, and Tscores. Additionally, some behavioural statistical procedures assume that scores are normally distributed; for example, ttests and ANOVAs. Bell curve grading assigns relative grades based on a normal distribution of scores. Reference:
https://en.wikipedia.org/wiki/Normal_distribution#Occurrence_and_applications 
knowledge Organiser
A knowledge organiser is an important document that lists the important facts that learners should know by the end of a unit of work. It is important that learners can recall these facts easily, so that when they are answering challenging questions in their assessments and GCSE and ALevel exams, they are not wasting precious time in exams focusing on remembering simple facts, but making complex arguments, and calculations.
We encourage all pupils to use them by doing the following:
 Quiz themselves at home, using the read, write, cover, check method.
 Practise spelling key vocabulary
 Further researching people, events and processes most relevant to the unit.