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.
Engage in practical and experimental activities in order to appreciate principles of probability. There is no coursework
unit overview  autumn 1  mechanics
Unit 8: Quantities and units in mechanics 

Skills 

Knowledge 
By the end of the unit, students should:

Rationale 
Having a firm knowledge of the quantities and units used in mechanics is a necessary part of mechanics as a whole. It allows us to judge if the result gained from a calculation is expected, reasonable or even possible. The interactions between the base units that create more complicated units and variables deepen our understanding of the physical processes in place and how they are interconnected. 
unit overview  autumn 1  pure
Units 1  4: Algebra and Functions 

Skills 
Completing the square.
including polynomials, y = ^{a} and y = ^{a} (including their vertical and horizontal asymptotes) s s2
o y = af(x), y = f(x) + a, y = f(x + a), y = f(ax) . 
Knowledge 
By the end of the unit, students should:

unit overview  autumn 1  statistics
Unit 1: Statistical sampling 

Skills 
Select or critique sampling techniques in the context of solving a statistical problem, including understanding that different samples can lead to different conclusions about the population. 
Knowledge 
By the end of the unit, students should:

Rationale 
Statistical sampling can be a valuable tool to collect and evaluate information about a large population, or universe, when it would otherwise be impractical (or impossible) to collect that information from the entire population. When done properly, statistical samples enable reasonable inferences to be drawn about the population based on information about the sample. Additionally, one will have an objective measure of the possible variation between samples and of the sample's relationship to the population. However, because “statistics by their very nature present an incomplete and potentially misleading description of the population,” to be reliable and useful, a sample must be designed, executed and analysed using appropriate statistical analysis techniques. Reference https://www.dhg.com/article/445dcaasuseofstatisticalsamplingunderstandingand survivingthehazards6 
unit overview  autumn 2  mechanics
Unit 9: Kinematics 1 (constant acceleration) 

Skills 

Knowledge 
By the end of the unit, students should:

Rationale 
Kinematics is the field of mechanics that deals with moving objects. As such, any object that moves can be modelled (at least partially) using a kinematics equation. Kinematics is therefore a core part of mechanics as a whole, and to the entire field of physics. Kinematics is also a logical and consistent framework while helps to develop problem solving and modelling skills. Kinematics has direct application to engineering and sport, along with many other fields. For example, is sport kinematics can be used to calculate trajectories of balls and to analyse the movement of players in order to identify areas of improvement. In engineering, kinematics is used in designing and testing cars, bikes, and other forms of transport. It is also necessary to calculate the required forces needed to accelerate and decelerate an object. 
unit overview  autumn 2  pure
Unit 13: Integration 

Skills 

Knowledge 
By the end of the unit, students should:

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. 
unit overview  autumn 2  statistics
Units 2 and 3: Data presentation and interpretation 

Skills 

Knowledge 

Rationale 
Learning about data presentation and interpretation has many uses. For example, it is used for all kinds of questions where statistical inference is appropriate, among them hypothesis testing and experimentation of all kinds, machine learning algorithms. It is useful when trying to come up with a prediction for some time series data like financial predictions, weather predictions. In manufacturing plants it is used for quality control / screening. Reference: https://www.quora.com/Howisstandarddeviationusedintherealworld 
unit overview  spring 1  mechanics
Unit 10: Forces and Motion 

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 of material. 
unit overview  spring 1  pure
Unit 11: Vectors (2D) 

Skills 

Knowledge 
By the end of the subunit, 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  statistics
Unit 6: Statistical distributions 

Skills 

Knowledge 

Rationale 
Every time you try to describe a large set of observations with a single indicator you run the risk of distorting the original data or losing important detail. For example, the batting average does not tell you whether the batter is hitting home runs or singles. It does not tell whether she's been in a slump or on a streak. The GPA does not tell you whether the student was in difficult courses or easy ones, or whether they were courses in their major field or in other disciplines. Even given these limitations, descriptive statistics provide a powerful summary that may enable comparisons across people or other units. Reference 
unit overview  spring 2  mechanics
Unit 11: Kinematics 2 (variable acceleration) 

Skills 

Knowledge 
By the end of the unit, students should:

Rationale 
Kinematics is the field of mechanics that deals with moving objects. As such, any object that moves can be modelled (at least partially) using a kinematics equation. Kinematics is therefore a core part of mechanics as a whole, and to the entire field of physics. Kinematics is also a logical and consistent framework while helps to develop problem solving and modelling skills. Kinematics has direct application to engineering and sport, along with many other fields. For example, is sport kinematics can be used to calculate trajectories of balls and to analyse the movement of players in order to identify areas of improvement. In engineering, kinematics is used in designing and testing cars, bikes, and other forms of transport. It is also necessary to calculate the required forces needed to accelerate and decelerate an object. 
unit overview  spring 2  pure
Units 7 and 8: Further algebra 

Skills 

Knowledge 
By the end of the unit, students should:
n;

Rationale 
Algebra is the basis of all higher mathematics. It allows for mathematics to be done with variables in place of numerical values, and so allows for solving and the expression of relationships with regard to these variables. In addition, it is often quicker for more complicated numerical problems to be solved algebraically instead. Algebra has many applications over a wide range of fields. For instance, it is utilized in finance, chemistry, physics and environmental science. In particular, proof develops strong reasoning skills. This improves critical thinking and causes the learner to more readily critically analyse situations. This has wide applications to almost any field of study or work that a learner may wish to pursue. Algebra also develops modelling, logic, and rationalisation skills. These can be widely applied to other areas that do not have a direct application of algebra. 
unit overview  spring 2  statistics
Unit 7: Statistical hypothesis testing 

Skills 

Knowledge 
By the end of the subunit, students should:

Rationale 
There are many real world applications of hypothesis testing and some of these are;
Reference: https://en.wikipedia.org/wiki/Statistical_hypothesis_testing#Use_and_importance 
unit overview  summer 1  pure
Units 7 and 8: Further algebra 

Skills 

Knowledge 
By the end of the unit, students should:
n;

Rationale 
Algebra is the basis of all higher mathematics. It allows for mathematics to be done with variables in place of numerical values, and so allows for solving and the expression of relationships with regard to these variables. In addition, it is often quicker for more complicated numerical problems to be solved algebraically instead. Algebra has many applications over a wide range of fields. For instance, it is utilised in finance, chemistry, physics and environmental science. In particular, proof develops strong reasoning skills. This improves critical thinking and causes the learner to more readily critically analyse situations. This has wide applications to almost any field of study or work that a learner may wish to pursue. Algebra also develops modelling, logic, and rationalisation skills. These can be widely applied to other areas that do not have a direct application of algebra. 
knowledge organisers
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.