AS and A2 Mathematics

The following content is covered.

Pure Mathematics Year 1 / AS

  • Algebraic expression
  • Quadratics
  • Equations and Inequalities
  • Graphs and Transformations
  • Straight line graphs
  • Algebraic methods
  • The binomial expansion
  • Trigonometric ratios
  • Trigonometric identities and equations
  • vectors
  • Differentiation
  • Integration
  • Exponentials and Logarithms

Statistics and Mechanics Year 1 / AS

Statistics

  • Data collection
  • Measures of location and spread
  • Representation of data
  • Correlation
  • Probability
  • Statistics distributions
  • Hypothesis testing

Mechanics

  • Modelling in Mechanics
  • Constant acceleration
  • Forces and motion
  • Variable acceleration

Pure Mathematics Year 2

  • Algebraic methods
  • Functions and graphs
  • Sequences and series
  • Binomial expansion
  • Radians
  • Trigonometric functions
  • Trigonometry and modelling
  • Parametric equations
  • Differentiation
  • Numerical methods
  • integration
  • Vectors

Statistics and Mechanics Year 2

Statistics

  • Regression, Correlation and hypothesis testing
  • Conditional probability
  • The normal distribution

Mechanics

  • Moments
  • Forces and Friction
  • Projectiles
  • Application of forces
  • Further Kinematics

Content Overview

Mathematics is a creative and highly interconnected discipline that has been developed over centuries, providing the solution to some of history’s most intriguing problems. It is essential to everyday life, critical to science, technology, and engineering, and necessary for financial literacy and most forms of employment. A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.

The national curriculum for mathematics aims to ensure that all pupils:

  • Become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasing complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
  • Reason mathematically by following a line of enquiry, conjecturing relationships, and generalisations, and developing an argument, justifications or proof using mathematical language.
  • Can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

Key Stage 1

The principal focus of mathematics teaching in Key stage 1 is to ensure that pupils develop confidence and mental fluency with whole numbers, counting and place value. This should involve working with numerals, words and the four operations including with practical resources such as concrete objects and measuring tools.

At this stage, pupils should develop their ability to recognize, describe, draw, compare and sort different shapes and use related vocabulary. Teaching should also involve a range of different measures to describe and compare different quantities such as length, mass, capacity/volume, time and money.

By the end of year 2, pupils should know the number bonds to 20 and be precise in using and understanding place value. An emphasis on practice at this stage will aid fluency.Pupils should read and spell mathematical vocabulary, at a level consistent with their increasing reading and spelling knowledge at key stage 1.

Year 2

  • Number – number and place value
  • Number – addition and subtraction
  • Number – multiplication and division
  • Number – fractions
  • Measurement
  • Geometry – properties of shapes
  • Geometry – position and direction Statistics

Year 2

  • Number – number and place value
  • Number – addition and subtraction
  • Number – multiplication and division
  • Number – fractions
  • Measurement
  • Geometry – properties of shapes
  • Geometry – position and direction Statistics

Key Stage 2 (Years 3, 4, 5 and 6)

The principal focus of mathematics teaching in Key stage 2 is to ensure that pupils become increasingly fluent with whole numbers and the four operations, including number facts and the concept of place value. This should ensure that pupils develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers while making connections between multiplication and division with fractions, decimals, percentages and ratio..
At this stage, pupils should develop their ability to solve a wider range of problems, including increasing complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation. Students are introduced to the language of algebra as a means of solving a variety of problems. Teaching in geometry and measures should consolidate and extend knowledge developed in number.
By the end of year 4, pupils should have memorized their multiplication tables up to and including 12 multiplication table and show precision and fluency in their work. By the end of year 6, pupils should be fluent in written methods of all the four operations, including long multiplication and division, and in working with fractions, decimals and percentages.Pupils should read, spell and pronounce mathematical vocabulary correctly and confidently.

The following content is covered:

Content

Year 3

  • Number – number and place value
  • Number – addition and subtraction
  • Number – multiplication and division
  • Number – fractions
  • Measurement
  • Geometry – properties of shapes
  • Statistics

Content

Year 4

  • Number – number and place value
  • Number – addition and subtraction
  • Number – multiplication and division
  • Number – fractions(including decimals)
  • Measurement
  • Geometry – properties of shapes
  • Geometry – position and direction Statistics

Content

Year 5

  • Number – number and place value
  • Number – addition and subtraction
  • Number – multiplication and division
  • Number – fractions(including decimals and percentages)
  • Measurement
  • Geometry – properties of shapes
  • Statistics

Content

Year 6

  • Number – number and place value
  • Number – addition, subtraction, multiplication and division
  • Number – fractions (including decimals and percentages)
  • Ratio and proportion, Statistics
  • Algebra, Measurement
  • Geometry – properties of shapes, position and direction

Key Stage 3 Mathematics (Years 7, 8 and 9)

The following topics are covered:

1. Number

  • Place value, estimation and Rounding
  • Properties of number
  • Ordering and comparing

2. Algebra

  • Simplifying
  • Manipulating expressions, equations and formulae
  • Solving linear equations
  • Sequences
  • Graphical representations

3. Geometry and Measures

  • Geometrical properties
  • Perimeter, area and volume
  • Transforming shapes
  • Constructions

4. Statistics

  • Statistical representations and measures
  • Statistical analysis

5. Ratio, Proportion and Rates of Change

6. Probability

Key Stage 4 Mathematics (Y10 and 11)

The following topics are covered:

1. Number

  • Geometrical properties
  • Perimeter, area and volume
  • Transforming shapes
  • Constructions

2. Algebra

  • Notation, vocabulary and manipulation
  • Solving equations and inequalities
  • Sequences
  • Graphs

4. Geometry and Measures

  • Properties and constructions
  • Mensuration and calculations
  • Vectors

5. Statistics

  • Statistical representations and measures
  • Statistical analysis

6. Ratio, Proportion and Rates of Change

7. Probability