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9-1 GCSE Mathematics by Mind Map: 9-1 GCSE Mathematics
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9-1 GCSE Mathematics

Algebra

Notation, Vocabulary and Manipulation

Expanding Brackets, Expanding Single Brackets, Expanding Two or More Brackets, Powerpoint, Expanding Cubics Revision Booklet, MyMaths link- Factorising linear, MyMaths link- Factorising Quadratics 1, MyMaths link- Factorising Quadratics 2

Factorising into Brackets, Factoring Single Brackets and longer Expressions, Factorising- Grouping, Factorising - Difference of 2 Squares, Factorising Quadratics - By Inspection, Factorising Quadratics- Splitting the middle term, Powerpoint, Past paper questions and answers, 9-1 Style Questions and Answers, Spec point- simplify and manipulate algebraic expressions by: ● collecting like terms ● multiplying a single term over a bracket ● taking out common factors ● expanding products of two binomials ● factorising quadratic expressions of the form x2 + bx + c, including the difference of two squares;

Expressions and Formulae, Collecting Like terms, Powerpoint, MyMaths link- Simplifying 1, MyMaths link- Simplifying 2, Spec point- Use and interpret algebraic manipulation, including: • ab in place of a × b • 3y in place of y + y + y and 3 × y • a2 in place of a × a, a3 in place of a × a × a, a2b in place of a × a × b • coefficients written as fractions rather than as decimals • brackets Substitute numerical values into formulae and expressions, including scientific formulae Understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factors

Rearranging Formulae, Changing the Subject, Powerpoint, Past Paper Questions and Answers, 9-1 Style Questions and Answers, MyMaths link- Rearranging 1, MyMaths link- Rearranging 2, Spec Point- understand and use standard mathematical formulae; rearrange formulae to change the subject

Algebraic Fractions, Simplifying Algebraic Fractions, Multiplying and Dividing Algebraic Fractions, Adding and Subtracting Algebraic Fractions 1, Adding and Subtracting Fractions 2, Powerpoint, Exam Style Practise Questions- Adding, Exam Style Practise Questions- Dividing, Exam Style Practise Questions- Multiplying, Exam Stlye Practise Questions- Simplifying, 9-1 Style Questions and Answers, MyMaths link- Adding Algebraic Fractions, MyMaths link- Simplifying Algebraic Fractions, MyMaths link- Multiplying/Dividing Algebraic Fractions

*New Topic* Functions, Composite Functions, Inverse Functions, Powerpoint, Exam Stlye Practise Questions and Answers, Revision Booklet, MyMaths link- Function Notation, MyMaths link- Composite and Inverse Functions, Spec point- where appropriate, interpret simple expressions as functions with inputs and outputs; interpret the reverse process as the ‘inverse function’; interpret the succession of two functions as a ‘composite function’ (the use of formal function notation is expected)

Solving Equations

Linear, Video Help-Solving Linear Equations (Brackets) (There are many videos on all different types of solving equation questions if you open the video up in Youtube), Video Help- Solving Linear Equations (Fractions), Powerpoint with questions, Past Paper Questions, Spec point- solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation); find approximate solutions using a graph, MyMaths link- Brackets, MyMaths link- Level 8 with equations with fractions

Quadratic, Solving Quadratics by Completing the Square, Solving Quadratics by using the Formula, Solving Quadratics by Factorising, Quadratic Formula Song, Powerpoint- Solving Quadratics, Powerpoint- Sketching Quadratics, Past Paper Questions and Answers- Fomula, Past Paper Questions and Answers- Factorising, Past Paper Questions and Answers- Completing the Square, Spec point- identify and interpret roots, intercepts, turning points of quadratic functions graphically; deduce roots algebraically by factorising, completing the square and using the fomula, MyMaths link- Solving Quadratics with Fractions, MyMaths link- Solving Quadratics by Factorising, MyMaths link- Solving quadratics by plotting the graph, Revision Booklet- Deducing Turning Points of Quadratics

Simultaneous Equations, Solving Simultaneous Equations-Elimination Method, Solving Simultaneous Equations- Substitution Method, Quadratic Simultaneous Equations, Powerpoint- Linear, Powerpoint- Quadratic, Past Paper Linear Questions and Answers, Exam Style Practise Questions- Quadratic, 9-1 Style Questions and Answers, Spec point- Solve two simultaneous equations in two variables (linear/linear algebraically; find approximate solutions using a graph . Translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or two simultaneous equations), solve the equation(s) and interpret the solution, MyMaths link- Linear, MyMaths link- Solving Graphically, MyMaths link- Quadratic

Forming and Solving Equations, Forming and Solving Equations PPQ, 9-1 Style Questions and Answers

Graphs

Curved Graphs, Powerpoint- Quadratic, Cubics, Reciprocals, Exponentials and Circles, Past Paper Questions on Drawing Quadratics, Spec point- recognise, sketch and interpret graphs of linear functions, quadratic functions, simple cubic functions, the reciprocal function.

Straight Lines, y=mx+c, Perpindicular lines, Powerpoint- Includes Perpindicular Lines, Exam Style Questions and Answers, MyMaths link 1, MyMaths link 2, Spec point- plot graphs of equations that correspond to straight-line graphs in the coordinate plane; use the form y = mx + c to identify parallel lines; find the equation of the line through two given points or through one point with a given gradient A10 identify and interpret gradients and intercepts of linear functions graphically and algebraically

Circles and Tangents, Circles and Tangents, Powerpoint, Practise Exam type Questions, Exam Style Questions and Answers, 9-1 Style Questions and Answers

Kinematic Graphs, Speed and Density calculations are covered under Ratio- Compount Units, Past Paper Questions and Answers- Distance Time Graphs, Practise Questions and Answers - Velocity Time Graphs, MyMaths link, Spec point- plot and interpret graphs (including reciprocal graphs) and graphs of non-standard functions in real contexts to find approximate solutions to problems such as simple kinematic problems involving distance, speed and acceleration

*New Topic* Gradients and Areas under Graphs, *Use the booklets as a good source to look over this topic*, Powerpoint, Revision Booklet- Area under Graphs, Revision Booklet- Gradients of Graphs and Rate of Change, 9-1 Style Questions and Answers, MyMaths link- Gradients of Tangents, MyMaths link- Area under a graphs, Spec point- calculate or estimate gradients of graphs and areas under graphs (including quadratic and other non-linear graphs), and interpret results in cases such as distance-time graphs, velocity-time graphs and graphs in financial contexts (this does not include calculus)

Inequalities

Linear, Solving Inequalities, Video Help- Solving Linear Inequalities, Powerpoint with questions, Past Paper Questions with Answers, MyMaths link, Graphing Inequalities, Video Help- Graphing Inequalities, Powerpoint with questions, Past Paper Questions and Answers, MyMaths link

Quadratic, Video Help- Quadratic Inequalities Intro, Video Help- Harder Quadratic Inequalities, Powerpoint with questions, Exam Style Questions and Answers, Revision Booklet

Spec point- solve linear inequalities in one or two variable(s), and quadratic inequalities in one variable; represent the solution set on a number line, using set notation and on a graph

Sequences

Linear, Video Help- Nth Term, Powerpoint with questions, Past Paper Questions and Answers, Spec Point- generate terms of a sequence from either a term-to-term or a position-to term rule, MyMaths link

Quadratic, Video Help- Quadratic sequences, Powerpoint with questions, Exam Style Questions and Answers, Revision Booklet, Spec Point- deduce expressions to calculate the nth term of linear and quadratic sequences, MyMaths link

Special Sequences, Revision Booklet

Geometric Progressions, Revision Booklet, MyMaths link

9-1 Style Questions and Answers

Specifiication point- recognise and use sequences of triangular, square and cube numbers, simple arithmetic progressions, Fibonacci type sequences, quadratic sequences, and simple geometric progressions (rn where n is an integer, and r is a rational number > 0 or a surd)

*New Topic* Iteration

Video Help- Iterations, Video Help- Interval Bisection

Powerpoint

Practise Questions with answers

9-1 Style Questions and Answers

Revision Booklet

MyMaths link

Algebraic Proof

Algebraic Proof

Past Paper Questions and Answers

9-1 Stlye Questions and Answers

MyMaths link- Identities

MyMaths link- Proof

Number

Structure and Calculation

Surds, Intro and Simplifying Surds, Rationalising the denominator, Powerpoint, Past Paper Questions and Answers, More Exam Style Questions and Answers, 9-1 Style Questions and Answers, MyMaths link- Intro to Surds, MyMaths link- Multiplying and Rationalising

Indices, Multiplication and Division, Negative and Fractional Powers, Raising to the power and power 0, Powerpoint, Exam Style Questions and Answers- First 3 laws, Past Paper Questions and Answers- Negative and Fractional Powers, MyMaths link- First 3 laws, MyMaths link- Negative Indices, MyMaths link- Fractional Indices, MyMaths link- Changing the base

Standard Form, gcse maths standard form, Powerpoint, Past Paper Questions and Answers, 9-1 Style Questions and Answers, Spec point- calculate with and interpret standard form A × 10n, where 1 ≤ A < 10 and n is an integer, MyMaths link- Calculations, MyMaths link- Large Numbers, MyMaths link- Small Numbers

Highest Common Factor, Lowest Common Multiple and Prime Factorisation, Prime Factorisation, HCF and LCM, Powerpoint (Extra topics included: Squares, cubes, divisibility rules), Exam Style Questions and Answers, Spec point- use the concepts and vocabulary of prime numbers, factors (divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation theorem, MyMaths link- HCF, MyMaths link- LCM

Fractions, Decimals and Percentages

Fractions, Adding and Subtracting Fractions, Multiplying and Dividing Fractions, Powerpoint, Exam style questions- Multiplying and Dividing, Exam Style Questions- Adding and Subtracting, 9-1 Style Questions and Answers, Spec point- apply the four operations, including formal written methods, to integers, decimals and simple fractions (proper and improper), and mixed numbers, MyMaths link- Dividing Fractions, MyMaths link- Multiplying Fractions, MyMaths link- Adding and Subtracting Fractions

Converting Fractions Decimals and Percentages, Video Help, Powerpoint, Exam Style Questions and Answers, Spec point work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 or 3/8), MyMaths link-

Recurring Decimals into Fractions, Recurring Decimals, Powerpoint, Exam Style Questions and Answers, 9-1 Style Questions and Answers, MyMaths link- Recurring Decimals, Spec point- work interchangeably with terminating decimals and their corresponding fractions , change recurring decimals into their corresponding fractions and vice versa.

Percentage Change/Reverse, Reverse Percentages, Percentage Change, Compound Interest, Powerpoint, Percentage Revision, Exam Style Questions and Answers, 9-1 Style Questions and Answers - Percentage Change, 9-1 Style Questions and Answers - Reverse Percentages, MyMaths link- Compound Interest, MyMaths link- Reverse Percentages

Measures and Accuracy

Bounds, Bounds Intervals using Inequalities, Bounds Calculations, Powerpoint, Past Paper Questions and Answers, Revision Booklet, 9-1 Style Questions and Answers, MyMaths link- Upper and Lower Bounds, MyMaths link- Calculating with Bounds

Estimation, Rounding to SF and DP, Powerpoint, Exam Style Questions and Answers

Spec point- round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures); use inequality notation to specify simple error intervals due to truncation or rounding . Apply and interpret limits of accuracy, including upper and lower bounds

Statistics

Grouped and Continuous Data

Video Help

Powerpoint

Past Paper Questions and Answers

Exam Style Questions and Answers - Median and Quartiles

MyMaths link

Charts and Averages

Video Help- MMMR from Frequency Tables

Video Help- Pie Charts

Powerpoint

Past Paper Questions and Answers - Pie Charts and MMMR

Exam Style Questions and Answers - Estimated Mean

Spec point- interpret and construct tables, charts and diagrams, including frequency tables, bar charts, pie charts and pictograms for categorical data, vertical line charts for ungrouped discrete numerical data, appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers, quartiles and inter-quartile range)

MyMaths link

Sampling

Video Help

Powerpoint, Questions

Spec point- infer properties of populations or distributions from a sample, while knowing the limitations of sampling, apply statistics to describe a population

Past Paper Questions and Answers - Stratified Sampling

Exam Style Questions and Answers - Stratified Sampling

MyMaths link

Cumulative Frequency and Box Plots

Video Help 1, Video Help 2

Powerpoint- Frequency Polygons and Quartiles added.

Past Paper Questions and Answers

Exam Style Questions and Answers

9-1 Style Questions and Answers- Cumulative Frequency

9-1 Style Questions and Answers- Box Plots

Spec Point- ● appropriate graphical representation involving discrete, continuous and grouped data, including box plots ● appropriate measures of central tendency (median, mean, mode and modal class) and spread (range, including consideration of outliers, quartiles and inter-quartile range)

MyMaths link

Scatter Diagrams

Video Help

Powerpoint

Spec Point- use and interpret scatter graphs of bivariate data; recognise correlation and know that it does not indicate causation; draw estimated lines of best fit; make predictions; interpolate and extrapolate apparent trends while knowing the dangers of so doing

MyMaths link

Past Paper Questions

Histograms

Video Help, Histograms - Unequal Class Widths

Powerpoint

Past Paper Questions and Answers

Exam Style Questions and Answers

9-1 Style Questions and Answers

Spec Point- construct and interpret diagrams for grouped discrete data and continuous data, i.e. histograms with equal and unequal class intervals

MyMaths link

Ratio, Proportion and Rate of Change

Compound Units

Density, Speed

Conversion

Powerpoint- Units

Past Paper Questions and Answers

MyMaths link- Algebra with Compound Measures

MyMaths link- Converting Compound Measures

MyMaths link- Density

MyMaths link- Speed

Spec Point- change freely between related standard units (e.g. time, length, area, volume/capacity, mass) and compound units (e.g. speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts

Direct and Inverse Proportion

Direct and Inverse Proportion, Graphs of Direct and Inverse Proportion

Powerpoint

Exam Style Questions and Answers

Past Paper Questions and Answers

MyMaths link

Spec point- solve problems involving direct and inverse proportion, including graphical and algebraic representations

Ratio

Dividing into Ratios

Powerpoint

Past Paper Questions and Answers - Ratio

Past Paper Questions and Answers- Proportion Recipes

9-1 Style Questions and Answers

MyMaths link- Unitary Method

MyMaths link- Dividing into Ratio

Spec point- divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio; apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations)

Compound Interest- Growth and Decay

Compount Interest, Growth and Decay

9-1 Style Questions and Answers

MyMaths link- Compound Interest

Rate of Change (Covered in Algebra-Graphs)

Percentage Change (Covered in Number Section)

Geometry and Measures

Constructions and Loci

Video Help

Powerpoint with answers for worksheet

Worksheet of key questions

Exam Style Questions and Answers

Spec point- use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); use these to construct given figures and solve loci problems; know that the perpendicular distance from a point to a line is the shortest distance to the line

Vectors

Video Help

Powerpoint

Past Paper Questions and Answers

9-1 Style Questions and Answers

Spec point- apply addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors

MyMaths link- adding and subtracting vectors

MyMaths link- reading and geometric proof

Circle Theorems

Video Help- Theorems

Video Help- Proofs

Powerpoint

Past Paper Questions and Answers

Exam Style Questions- Circle Theorems Proofs

9-1 Style Questions and Answers

Spec Point- Identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment - Apply and prove the standard circle theorems concerning angles, radii, tangents and chords, and use them to prove related results

MyMaths link- Theorems

MyMaths link- Proofs

Trigonometry

Right Angled Triangles, Pythagoras, Video Help, SOHCAHTOA, Video Help- Finding a Side, Video Help- Finding an Angle, Powerpoint with questions, Exam Style Questions and Answes, 9-1 Style Questions and Answers- Trig, 9-1 Style Questions and Answers- Pythagoras, Spec Point- know the formulae for: Pythagoras’ theorem a2 + b2 = c2, and the trigonometric ratios, sin θ=opposite/hypotenuse cos θ = adjacent/hypotenuse and tan θ = opposite/adjacent ; apply them to find angles and lengths in right-angled triangles and, where possible, general triangles in two and three dimensional figures -know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan θ for θ = 0°, 30°, 45° and 60°, MyMaths link - Pythagoras, MyMaths link- SOHCAHTOA, MyMaths link- Special Angles

Non- Right Angled Triangles, SINE and COSINE Rule, Video Help- Sine Rule (Finding a length), Video Help- Cosine Rule, Video Help- Sine Rule (Finding an angle), Video Help- Cosine Rule, Area of a Triangle, Video Help, Powerpoint with questions, Exam Style Questions and Answers, 9-1 Style Questions and Answers, Spec Point, MyMaths link- Sine Rule, MyMaths link- Cosine Rule Angle, MyMaths link- Cosine Rule Sides, MyMaths link- Area of Triangle

Trigonometry Exact Values, Trig Exact Values, Exam Style Questions and Answers, 9-1 Style Questions and Answers, MyMaths link-, Spec Point- know the exact values of sin θ and cos θ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tan θ for θ = 0°, 30°, 45° and 60°. Knowledge of how to find exact values from the triangles is key.

3D Trigonometry, 3D Trig, Practise Questions and Answers, Exam Style Questions and Answers, MyMaths link- First 5 parts only

Transformations

2D Shapes, Translations, Rotations, Reflections, Englargements, Negative and Fractional Enlargements, Powerpoint, Past Paper Questions and Answers, Spec point- identify, describe and construct congruent and similar shapes, including on coordinate axes, by considering rotation, reflection, translation and enlargement (including fractional and negative scale factors), MyMaths link-

Functions, Translations, Reflections, Powerpoint, Past Paper Questions and Answers (Skip 2b 4b 5b 7c as not on spec), Exam Style Questions and Answers (Ignore questions that are e.g. 2f(x) or f(2x) )

Polygons and Angles in Parallel Lines

Angles in Parallel lines, Interior and Exterior Angles

Powerpoint

Past paper Questions and Answers

9-1 Style Questions and Answers- Parallel lines

Exam Style Questions and Answers- Polygons

MyMaths link- Angles in Parallel Lines

MyMaths link- Interior and Exterior Angles

Spec point- apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles; understand and use alternate and corresponding angles on parallel lines; derive and use the sum of angles in a triangle (e.g. to deduce and use the angle sum in any polygon, and to derive properties of regular polygons)

3D Shapes

3D Surface Area, 3D Volumes

Practise Questions and Answers

Powerpoint- Similarity and Scale Factors

Powerpoint- Volumes and Surface Areas

Exam Style Questions and Answers- Sphere

Exam Style Questions Area and Volume Scale Factor

9-1 Style Questions and Answers- Similarity and Congruence

9-1 Style Questions and Answers- Volumes

MyMaths link- Volumes of Cylinder

MyMaths link- Volumes of Prisms

MyMaths link- Volumes of Cones and Spheres

2D Shapes

Congruent Shapes, Congruent Triangle, Powerpoint, Practise Questions and Answers, MyMaths link-

Area and Permiter, Area and Perimeter, Areas of Sectors and Segments, Powerpoint, Past paper questions and answers, Past Paper Questions and Answers- Area of Sectors and Arc Lengths, 9-1 Style Questions and Answers- Area of Sectors and Arc Lengths, MyMaths link- arcs and sectors

Probability

Experimental and Theoretical Probability

Sample Space

Two way tables

Powerpoint with questions

Past Paper Questions and Answers

9-1 Style Questions and Answers

Spec Point- construct theoretical possibility spaces for single and combined experiments with equally likely outcomes and use these to calculate theoretical probabilities

MyMaths link

Tree Diagrams and Frequency Trees

Frequency Trees

Tree Diagrams

Powerpoint with questions

Spec Point- calculate the probability of independent and dependent combined events, including using tree diagrams and other representations, and know the underlying assumptions

MyMaths link - Tree Diagrams

MyMaths link- Frequency Trees

Venn Diagrams

Introduction to Venn, Example of Venn, 3 set problem

Powerpoint and answers to Practise Questions

Practise Questions

Edexcel Revision Booklet

9-1 Style Questions and Answers

MyMaths link

Combinations and Systematic Listing

Probability and Combinatorics Example 1, Probability and Combinatorics Example 2, Probability and Combinatorics Example 3

9-1 Style Questions and Answers

MyMaths link - Introducing Factorials

Spec Point- N5 apply systematic listing strategies

Specification

Useful Websites-     1) https://www.mymaths.co.uk/ Very useful for step by step lessons and interactive worksheets. Lessons are embedded into the different areas of the mindmap.                                                                                                                               2) http://www.examsolutions.net/gcse-maths/ Videos that talk you through key areas on a wide range of the GCSE Specification. Videos from this website are embedded throughout the mindmap.                                                                   3) http://mrcartermaths.com/# Differentiated questions (Bronze/Silver/Gold) that allows you to practise fluency of key skills.                                                                                                                                                                                           4) http://www.mathsgenie.co.uk/gcse.html 1-9 levels broken down into topics related to each level. Comes with revision videos and practise questions (mostly past paper questions) with solutions.                                                               5) https://corbettmaths.com/ Website that has hundreds of 5-a-days to practise a range of skills each day that target different levels- answers are with the '5 a days A*-G' only. Very useful section of topics broken down alphabetically with a huge number of fluency practise of skills.                                                                                                                       6) http://mrbartonmaths.com/students/gcse/ A great website that breaks down topics and allows users to revise, practise and understand topics. It has the GCSE takeaway section which is past paper questions and multiple choice quizzes for each topic.                                                                                                                                                                           7) http://mathsbot.com/gcseRevisionGrid  This website and this specific section generates 'higher' questions with answers instantaneously, similar to the 5-a-days but more working required to get an answer.                                                                                                                                                                                                                     The websites aren't in any order, they are free and checked thoroughly for usefulness- allowing students to enhance their skills, knowledge and understanding of the GCSE Specification. If you are not sure on how to use any of the websites then please ask Mr Barker.

GCSE Revision Section (Under Construction)

Main Revision Booklet

Key Formulas you MUST learn

Higher Topic 9-1 Checklist

Aiming for Grade Booklets

Aiming for Grade 5 and Answers

Aiming for Grade 7 and Answers

Aiming for Grade 9 and Answers

'Grade 9' Papers- note: these do not claim to be a grade 9 paper, it contains questions which need a variety of skills to solve.

Calculator Paper

Non Calc Paper

Sample Papers

Speciman Papers