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Revision notes
KS3
Maths
Maths: KS3
Finding the Input of a Function

Finding the Input of a Function

Maths: KS3, topic 2.6.1

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Previous topic2.5.1 Changing the Subject Next topic2.7.1 Solving Linear Equations (One Step)

Maths: KS3 contents

1 Number
- 1.1 Place Value & Ordering
  1.1.1 Ordering Integers
  1.1.2 Ordering Decimals
  1.1.3 Equal Symbols
  1.1.4 Place Value
- 1.2 Numerical Operations
  1.2.1 Adding Integers
  1.2.2 Subtracting Integers
  1.2.3 Multiplying Integers
  1.2.4 Dividing Integers
  1.2.5 Dividing with a Remainder
  1.2.6 Adding & Subtracting Decimals
  1.2.7 Multiplying Decimals
  1.2.8 Dividing Decimals
  1.2.9 Adding & Subtracting Negative Numbers
  1.2.10 Multiplying & Dividing Negative Numbers
  1.2.11 Multiplying by Powers of Ten
  1.2.12 Dividing by Powers of Ten
- 1.3 Fractions
  1.3.1 Writing Fractions
  1.3.2 Simplifying Fractions
  1.3.3 Equivalent Fractions
  1.3.4 Constructing Fractions
  1.3.5 Ordering Fractions
  1.3.6 Recurring Decimal Notation
  1.3.7 Mixed Numbers & Improper Fractions
- 1.4 Numerical Operations (Fractions)
  1.4.1 Adding & Subtracting Fractions
  1.4.2 Add & Subtract Mixed Numbers & Improper Fractions
  1.4.3 Multiplying Fractions
  1.4.4 Multiplying Mixed Numbers
  1.4.5 Reciprocals
  1.4.6 Dividing Fractions
  1.4.7 Dividing Mixed Numbers
- 1.5 Roots & Powers
  1.5.1 Roots
  1.5.2 Integer Powers
  1.5.3 Estimating Powers & Roots
  1.5.4 Laws of Indicies (Multiplication)
- 1.6 Structure of Calculations
  1.6.1 Order of Operations (BIDMAS)
- 1.7 Numerical Skills
  1.7.1 Using a Calculator - Powers, Roots & Fractions
- 1.8 Factors & Multiples
  1.8.1 Divisibility Rules
  1.8.2 Finding Multiples
  1.8.3 Finding Factors
  1.8.4 Finding Prime Numbers
- 1.9 Systematic Listing
  1.9.1 Systematic Listing
- 1.10 Standard Form
  1.10.1 Reading Standard Form
  1.10.2 Converting to Standard Form (Positive Powers)
  1.10.3 Converting to Standard Form (Negative Powers)
  1.10.4 Converting Form Standard Form (Positive Powers)
  1.10.5 Converting From Standard Form (Negative Powers)
  1.10.6 Adding & Subtracting Standard Form
  1.10.7 Standard Form on a Calculator
- 1.11 Fractions, Decimals & Percentages
  1.11.1 Converting Fractions, Decimals & Percentages
  1.11.2 Numbers as Percentages
  1.11.3 Fractions of Amounts
- 1.12 Percentage Change
  1.12.1 Percentages of Amounts (Calculator)
  1.12.2 Percentages of Amounts (No Calculator)
  1.12.3 Percentage Change
- 1.13 Rounding & Estimation
  1.13.1 Rounding Integers
  1.13.2 Estimating Calculations
  1.13.3 Rounding Decimals
  1.13.4 Rounding With Significant Figures
- 1.14 Bounds & Accuracy
  1.14.1 Finding Error Intervals
2 Algebra
- 2.1 Algebraic Notation
  2.1.1 Function Machines
  2.1.2 Using Algebraic Notation
- 2.2 Substitution & Simplification
  2.2.1 Substituting into Expressions with Operations
  2.2.2 Substituting into Algebraic Expressions
  2.2.3 Substituting into Real-Life Expressions
  2.2.4 Simplifying Expressions by Collecting Like Terms
- 2.3 Brackets
  2.3.1 Expanding Single Brackets
  2.3.2 Expanding & Simplifying with Single Brackets
  2.3.3 Expanding Double Brackets
  2.3.4 Factorising Into One Bracket
- 2.4 Algebraic Fractions
  2.4.1 Operations with Algebraic Fractions
- 2.5 Rearranging
  2.5.1 Changing the Subject
- 2.6 Functions
  2.6.1 Finding the Input of a Function
- 2.7 Solving Linear Equations
  2.7.1 Solving Linear Equations (One Step)
  2.7.2 Solving Linear Equations (Multi-Step)
  2.7.3 Solving Linear Equations (Unknown Both Sides)
  2.7.4 Solving Equations (Unknown in Denominator)
  2.7.5 Forming & Solving Linear Equations
- 2.8 Inequalities
  2.8.1 Representing Inequalities on a Number Line
  2.8.2 Solving Linear Inequalities
  2.8.3 Linear Inequalities with Unknowns on Both Sides
- 2.9 Simultaneous Equations
  2.9.1 Solving Simultaneous Equations Graphically
  2.9.2 Solving Simultaneous Equations by Elimination
- 2.10 Sequences
  2.10.1 Term-to-Term Rules (Patterns)
  2.10.2 Term-to-Term Rules (Numerical)
  2.10.3 Substituting into a Given Rule
  2.10.4 Position-to-Term Rules
  2.10.5 Finding the Nth Term (Linear Sequences)
  2.10.6 Simple Geometric Progressions
- 2.11 Coordinates
  2.11.1 Midpoints of Line Segments
- 2.12 Linear Graphs
  2.12.1 Equations of Straight Lines
  2.12.2 Finding Line Equation from Point & Gradient
  2.12.3 Finding Line Equations from Two Points
  2.12.4 Parallel Line Equations
- 2.13 Quadratic Graphs
  2.13.1 Interpreting Quadratics
3 Ratio, Proportion & Rates of Change
- 3.1 Unit Conversion
  3.1.1 Using Clocks
  3.1.2 Calculating with Time
  3.1.3 Using Timetables
  3.1.4 Using Calendars
  3.1.5 Converting Units of Length
  3.1.6 Converting Units of Mass
  3.1.7 Converting Units of Capacity
  3.1.8 Metric Conversions
  3.1.9 Converting Units of Area & Volume
- 3.2 Compound Units
  3.2.1 Estimating & Measuring
  3.2.2 Calculating Speed
  3.2.3 Best Buy & Unit Pricing
  3.2.4 Density, Mass & Volume
- 3.3 Ratio Fundamentals
  3.3.1 Ratio Notation & Simplification
  3.3.2 Ratios as Fractions and Linear Equations
  3.3.3 Sharing in a Ratio
  3.3.4 Proportion Problems
- 3.4 Advanced Ratio and Scale
  3.4.1 Map Scales & Real Distances
- 3.5 Proportion
  3.5.1 Currency Conversion
  3.5.2 Direct Proportion
  3.5.3 Inverse Proportion
- 3.6 Algebraic Proportion
  3.6.1 Direct Proportion
  3.6.2 Inverse Proportion
4 Geometry & Measures
- 4.1 Area & Perimeter
  4.1.1 Perimeter of Simple Shapes
  4.1.2 Perimeter of Compound Shapes
  4.1.3 Area of Triangles
  4.1.4 Area of Rectangles & Parallelograms
  4.1.5 Area of Trapezia
  4.1.6 Area of Compound Shapes
  4.1.7 Area of Compound Shapes with Triangles
- 4.2 Properties of Shapes
  4.2.1 Naming & Classifying Triangles
  4.2.2 Naming & Classifying Quadrilaterals
  4.2.3 Properties of Lines
  4.2.4 Shortest Distance from a Point to a Line
  4.2.5 Properties of 3D Shapes
- 4.3 Angles
  4.3.1 Classification of Angles
  4.3.2 Angles on a Line & Around a Point
  4.3.3 Combining Angle Facts in Triangles
  4.3.4 Angles on Parallel Lines
  4.3.5 Interior & Exterior Angles in Polygons
- 4.4 Trigonometry
  4.4.1 Pythagoras' Theorem
  4.4.2 Sides in Right-Angles Triangles
  4.4.3 Angles in Right-Angled Triangles
- 4.5 Similarity & Congruence
  4.5.1 Congruent Shapes
  4.5.2 Length Scale Factors in Similar Shapes
- 4.6 Circle Geometry
  4.6.1 Identifying Parts of a Circle
  4.6.2 Calculating Circumference
  4.6.3 Calculating Area of a Circle
  4.6.4 Calculating Arc Lengths
  4.6.5 Calculating Area of Sectors
- 4.7 3D Representations
  4.7.1 Nets of 3D Shapes
- 4.8 Surface Area
  4.8.1 Surface Area of Cubes & Cuboids
  4.8.2 Surface Area of Prisms
  4.8.3 Surface Area of Cylinders
- 4.9 Volume
  4.9.1 Volume of Prisms
  4.9.2 Volume of Cylinders
- 4.10 Transformations
  4.10.1 Translation using Vectors
  4.10.2 Rotations
  4.10.3 Enlargements & Positive Scale Factors
- 4.11 Scale Drawings
  4.11.1 Scale Drawings
- 4.12 Bearings
  4.12.1 Bearings
5 Probability
- 5.1 Single Events
  5.1.1 Writing Probabilities as Fractions
  5.1.2 Mutually Exclusive Events
  5.1.3 Expected Results
- 5.2 Combined Events
  5.2.1 Reading Venn Diagrams
  5.2.2 Venn Diagrams (Set Notation)
  5.2.3 Independent & Mutually Exclusive Events
- 5.3 Experimental Probability
  5.3.1 Relative Frequency & Convergence
6 Statistics
- 6.1 Averages & Range
  6.1.1 Range
  6.1.2 Median
  6.1.3 Mode
  6.1.4 Mean
  6.1.5 Interpreting Two-Way Tables
- 6.2 Scatter Graphs
  6.2.1 Lines of Best Fit
- 6.3 Collecting & Presenting Data
  6.3.1 Types of Data

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