GCSE Maths

In this course, students are prepared for AQA GCSE Mathematics (8300). The following ten units are studied sequentially across Years 10 and 11. This GCSE has a Foundation tier (grades 1 – 5) and a Higher tier (grades 4 – 9). Where the key skills listed below are shown in bold, they relate only to the Higher tier.

Unit Content

Year 10 Unit 1

Similarity

This unit builds on and extends students' experience of enlargement and similarity, and teaches them to solve problems with similar triangles and trigonometry.

Key skills developed:

  • How to find scale factors
  • How to compare lengths, areas and volumes
  • How to interpret and use fractional and negative scale factors
  • How to apply Pythagoras’ Theorem and trigonometric ratios to find angles and lengths in right-angled triangles
  • How to apply the sine and cosine rule
  • How to calculate the area, sides or angles of any triangle

Assessment: Students undertake self-assessment and receive verbal feedback from the teacher every lesson. Summative assessment takes place at the end of the unit. In addition, students complete twice-yearly summative assessments which assess their retention of several units.

Year 10 Unit 2

Developing algebra

Students learn about equations and inequalities at KS3, and this unit provides them with a context in which to revisit and reinforce standard techniques and to deepen their understanding. Students are taught to solve simultaneous equations using both algebraic and graphical methods.

Key skills developed:

  • How to simplify algebraic expressions
  • How to manipulate quadratic expressions
  • How to sketch and interpret graphs of linear functions
  • How to factorise quadratic expressions
  • How to solve quadratic equations
  • How to solve linear inequalities in one or two variables
  • How to solve quadratic inequalites in one variable
  • How to represent solutions on a number line
  • How to use set notation on a graph

Assessment: Students undertake self-assessment and receive verbal feedback from the teacher every lesson. Summative assessment takes place at the end of the unit. In addition, students complete twice-yearly summative assessments which assess their retention of several units.

Year 10 Unit 3

Geometry

This unit provides a formal introduction to bearings, arcs, sectors and spheres while revisiting other materials and making links across the mathematics curriculum.

Key skills developed:

  • How to use and interpret bearings
  • How to reason deductively in geometry, number and algebra
  • How to use geometrical constructions
  • How to identify and apply circle definitions and properties
  • How to calculate arc lengths, angles and areas of sectors of circles
  • How to calculate  surface areas and volumes of spheres, pyramids, cones and composite solids
  • How to apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results
  • How to describe translations as 2D vectors
  • How to apply addition and subtraction to vectors, how to multiply vectors by a scalar, and how to work with diagrammatic and column representations of vectors
  • How to use vectors to construct geometric arguments and proofs

Assessment: Students undertake self-assessment and receive verbal feedback from the teacher every lesson. Summative assessment takes place at the end of the unit. In addition, students complete twice-yearly summative assessments which assess their retention of several units.

Year 10 Unit 4


Proportions and proportional change

This unit builds on KS3 learning about ratio, fractions, percentages and probability.

Key skills developed:

  • How to use ratio notation
  • How to divide a given quantity into two parts
  • How to use compound units such as speed, unit pricing and density to solve problems
  • How to compare lengths, areas and volumes using ratio notation
  • How to apply the concepts of congruence and similarity
  • How to express one quantity as a percentage of another
  • How to compare two quantities using percentages
  • How to solve problems involving percentage change
  • How to use a probability model to predict the outcomes of future experiments
  • How to calculate the probability of independent and dependent combined events
  • How to calculate and interpret conditional probabilities through representation using expected frequencies with two-way tables, tree diagrams and Venn diagrams

Assessment: Students undertake self-assessment and receive verbal feedback from the teacher every lesson. Summative assessment takes place at the end of the unit. In addition, students complete twice-yearly summative assessments which assess their retention of several units.

Year 10 Unit 5

Delving into data

This unit develops students' understanding of collection, representation and the use of summary statistics to describe data.

Key skills developed:

  • How to use, describe, interpret and compare observed distributions of a single variable
  • How to construct and interpret appropriate tables, charts, and diagrams
  • How to interpret and construct tables and line graphs for time series data
  • How to construct and interpret histograms and cumulative frequency graphs
  • How to interpret and analyse box plots
  • How to interpret, analyse and compare the distributions of data sets and examine the spread of data including quartiles and interquartile range

Assessment: Students undertake self-assessment and receive verbal feedback from the teacher every lesson. Summative assessment takes place at the end of the unit. In addition, students complete twice-yearly summative assessments which assess their retention of several units.

Year 10 Unit 6

Using Number

This unit develops students' understanding of prime factorisation and associated number content such as HCF and LCM. Students’ knowledge of sequences is extended to include surds and how to find the formula for a quadratic sequence.

Key skills developed:

  • How to find factors, multiples, primes, HCF and LCM
  • How to describe and continue sequences
  • How to deduce expressions to calculate the nth term of linear and quadratic sequences
  • How to recognise and use sequences of square and cube numbers
  • How to calculate exactly with fractions, decimals and surds
  • How to manipulate surds, including being able to rationalise
  • How to apply and interpret limits of accuracy when rounding or truncating including upper and lower bounds

Assessment: Students undertake self-assessment and receive verbal feedback from the teacher every lesson. Summative assessment takes place at the end of the unit. In addition, students complete twice-yearly summative assessments which assess their retention of several units.

Year 10 Unit 7

Algebra

This unit teaches students to expand, factorise and solve both linear and quadratic equations. Students’ knowledge of how to change the subject of a formula is revised and extended to include more complex formula.

Key skills developed:

  • How to know the difference between an equation and an identity
  • How to manipulate and simplify algebraic expressions including the difference of two squares
  • How to expand expressions including binomials
  • How to solve quadratic equations by factorisation
  • How to factorise expressions in the form ax2 + bx + c
  • How to use the quadratic formula to solve equations
  • How to complete the square and use this to find a turning point of a quadratic graph
  • How to change the subject of a formula, including those where the subject appears more than once
  • How to find approximate solutions to equations numerically using iteration

Assessment: Students undertake self-assessment and receive verbal feedback from the teacher every lesson. Summative assessment takes place at the end of the unit. In addition, students complete twice-yearly summative assessments which assess their retention of several units.

Year 11 Unit 1

Graphs

This unit develops and deepens students' knowledge of graphs. Students extend their knowledge of linear and non-linear graphs and revise their understanding of conversion graphs.

Key skills developed:

  • How to plot and interpret graphs
  • How to interpret the gradient of straight-line graphs
  • How to use the equation y = mx + c to identify parallel and perpendicular lines
  • How to find approximate solutions to two simulataneous equations using a graph
  • How to recognise, sketch and interpret quadratic, cubic and reciprocal functions
  • How to identify and interpret roots and intercepts of quadratic functions
  • How to recognise and use the equation of a circle
  • How to interpret the gradient at a point on a curve
  • How to calculate or estimate gradients of graphs and areas under graphs

Assessment: Students undertake self-assessment and receive verbal feedback from the teacher every lesson. Summative assessment takes place at the end of the unit. In addition, students complete twice-yearly summative assessments which assess their retention of several units.

Year 11 Unit 2

Algebra

This unit teaches students to expand, factorise and solve equations, and introduces iterations to students taking Higher tier papers. Additionally, the unit introduces the concept of formal function notation.

Key skills developed:

  • How to know the difference between an equation and an identity
  • How to manipulate and simplify algebraic expressions including the difference of two squares
  • How to factorise expressions in the form ax2 + bx + c
  • How to solve two simulataneous equations
  • How to solve linear inequalities in one variable
  • How to find approximate solutions to equations numerically using iteration
  • How to interpret simple expressions as functions
  • How to find inverse functions
  • How to find composite functions

Assessment: Students undertake self-assessment and receive verbal feedback from the teacher every lesson. Summative assessment takes place at the end of the unit. In addition, students complete twice-yearly summative assessments which assess their retention of several units.

Year 11 Unit 3

Reasoning

Students develop their multiplicative reasoning in a variety of contexts. They consolidate their knowledge of angle facts and develop their algebraic reasoning looking at complex situations.

Key skills developed:

  • How to compare lengths, areas and volumes
  • How to understand that X is inversely proportional to Y
  • How to describe direct and inverse proportion
  • How to apply and prove standard circle theorems
  • How to interpret and use bearings
  • How to apply addition and subtraction to vectors
  • How to make and test conjectures
  • How to deduce expressions to calculate the nth term of linear and quadratic sequences

Assessment: Students undertake self-assessment and receive verbal feedback from the teacher every lesson. Summative assessment takes place at the end of the unit. In addition, students complete twice-yearly summative assessments which assess their retention of several units.

Year 11 Unit 4

Revision and communication

Students revise and deepen their learning from KS3 and KS4, exploring all transformations and constructions. Students also study organisation information, with Higher tier students extending this to include the product rule for counting.

Key skills developed:

  • How to describe translations as 2D vectors
  • How to reason deductively in geometry, number and algebra, including using geometrical constructions
  • How to interpret and use fractional and negative scale factors
  • How to sketch translations and reflections of the graph of a given function
  • How to explore what can and cannot be inferred in statistical and probabilistic settings, and to express arguments formally
  • How to calculate the probability of independent and dependent combined events
  • How to calculate and interpret conditional probabilities through tree diagrams and Venn diagrams
  • How to apply systematic listing strategies including use of the product rule for counting
  • How to construct and interpret plans and elevations of 3D shapes

Assessment: Students undertake self-assessment and receive verbal feedback from the teacher every lesson. Summative assessment takes place at the end of the unit. In addition, students complete twice-yearly summative assessments which assess their retention of several units.