AQA · GCSE
Your journey to excellence inFurther Mathematics
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Understanding Fractions
1Understanding FractionsRead next2Converting Fractions to DecimalsRead next3Converting Decimals to FractionsRead next4Simplifying FractionsRead next5Adding and Subtracting FractionsRead next6Multiplying FractionsRead next7Dividing FractionsRead next8Understanding DecimalsRead next9Rounding DecimalsRead next10Adding and Subtracting DecimalsRead next11Multiplying DecimalsRead next12Dividing DecimalsRead next13Understanding PercentagesRead next14Converting Percentages to FractionsRead next15Converting Percentages to DecimalsRead next16Percentage Increase and DecreaseRead next17Solving Percentage ProblemsRead next18Understanding RatiosRead next19Simplifying RatiosRead next20Using Ratios in ProblemsRead next21Understanding ProportionRead next22Direct Proportion ProblemsRead next23Inverse Proportion ProblemsRead next24Order of Operations (BIDMAS)Read next25Applying BIDMAS in CalculationsRead next26Common Errors in BIDMASRead next27The Product Rule for CountingRead next28Worked Examples of Product RuleRead next29Simplifying SurdsRead next30Adding and Subtracting SurdsRead next31Multiplying SurdsRead next32Dividing SurdsRead next33Rationalising the DenominatorRead next34Exact Calculations Using SurdsRead next35Common Errors in Surds ManipulationRead next36Mixed Problems on SurdsRead next
Definition of a Function
1Definition of a FunctionRead next2Understanding Function NotationRead next3Domain of a FunctionRead next4Range of a FunctionRead next5Composite FunctionsRead next6Inverse FunctionsRead next7Expanding Single BracketsRead next8Expanding Double BracketsRead next9Expanding Triple BracketsRead next10Using Pascal’s Triangle in ExpansionsRead next11Factorising Simple ExpressionsRead next12Factorising Quadratic ExpressionsRead next13Factorising Higher Degree PolynomialsRead next14Manipulating Algebraic FractionsRead next15Adding and Subtracting Rational ExpressionsRead next16Multiplying and Dividing Rational ExpressionsRead next17Simplifying Complex Rational ExpressionsRead next18Rearranging Formulae to Change the SubjectRead next19Using the Factor TheoremRead next20Factorising Using the Factor TheoremRead next21Completing the Square for QuadraticsRead next22Finding Turning Points via Completing the SquareRead next23Sketching Quadratic GraphsRead next24Sketching Exponential GraphsRead next25Interpreting Graphs of FunctionsRead next26Solving Linear EquationsRead next27Solving Quadratic Equations by FactorisationRead next28Solving Quadratic Equations Using the FormulaRead next29Solving Quadratic Equations by Completing the SquareRead next30Graphical Solutions to Quadratic EquationsRead next31Solving Simultaneous Linear EquationsRead next32Solving Simultaneous Equations with One QuadraticRead next33Solving Simultaneous Equations GraphicallyRead next34Solving Linear Equations in Three VariablesRead next35Solving Linear InequalitiesRead next36Solving Quadratic InequalitiesRead next37Simplifying Expressions with Index LawsRead next38Solving Equations with Fractional IndicesRead next39Solving Equations with Negative IndicesRead next40Proving Divisibility Using Algebraic ProofRead next41Proving Identities Using Algebraic ProofRead next
Understanding Linear Sequences
1Understanding Linear SequencesRead next2Finding the nth Term of Linear SequencesRead next3Worked Examples: nth Term of Linear SequencesRead next4Identifying Patterns in Linear SequencesRead next5Using the nth Term to Find Specific TermsRead next6Solving Problems with Linear SequencesRead next7Understanding Quadratic SequencesRead next8Finding the nth Term of Quadratic SequencesRead next9Worked Examples: nth Term of Quadratic SequencesRead next10Using the nth Term for Quadratic SequencesRead next11Identifying Patterns in Quadratic SequencesRead next12Solving Problems with Quadratic SequencesRead next13Comparing Linear and Quadratic SequencesRead next14Introduction to Limiting ValuesRead next15Finding Limiting Values of SequencesRead next16Worked Examples: Limiting Values of SequencesRead next17Understanding Converging SequencesRead next18Understanding Diverging SequencesRead next19Using Limiting Values in Problem SolvingRead next20Arithmetic Sequences: Basics and FormulasRead next21Geometric Sequences: Basics and FormulasRead next22Solving Problems with Arithmetic SequencesRead next23Solving Problems with Geometric SequencesRead next24Special Sequences: Fibonacci and OthersRead next25Finding Differences Between Sequence TermsRead next26Finding Sums of Sequence TermsRead next27Worked Examples: Summing Sequence TermsRead next28Applications of Sequences in Real-Life ProblemsRead next29Common Exam Traps in Sequence QuestionsRead next30Practice Problems: Linear SequencesRead next31Practice Problems: Quadratic SequencesRead next32Practice Problems: Limiting ValuesRead next33Practice Problems: Arithmetic SequencesRead next34Practice Problems: Geometric SequencesRead next35Exam Techniques for Sequence QuestionsRead next
Definition of Gradient
1Definition of GradientRead next2Calculating Gradients of LinesRead next3Gradients of Parallel LinesRead next4Gradients of Perpendicular LinesRead next5Using Pythagoras to Find DistanceRead next6Distance Between Two Points FormulaRead next7Definition of MidpointRead next8Finding Midpoint Between Two PointsRead next9Using Ratios to Divide a Line SegmentRead next10Equation of a Straight Line: y = mx + cRead next11Equation of a Straight Line: Point-Slope FormRead next12Interpreting Gradient and Y-InterceptRead next13Drawing Straight Lines from EquationsRead next14Equation of a Circle with Centre (0, 0)Read next15Writing Circle Equation from RadiusRead next16Circle Geometry: Angle in a Semi-CircleRead next17Circle Geometry: Perpendicular Bisector of a ChordRead next18Circle Geometry: Tangent-Radius AngleRead next19Circle Geometry: Equal Length TangentsRead next20Equation of a Circle with Centre (a, b)Read next21Writing Circle Equation from Centre and RadiusRead next22Equation of Tangent to a CircleRead next23Finding Gradient of Tangent at a PointRead next24Finding Equation of Tangent to CircleRead next25Worked Examples: Gradient and DistanceRead next26Worked Examples: Midpoint and RatiosRead next27Worked Examples: Straight Line EquationsRead next28Worked Examples: Circle EquationsRead next29Exam Trap: Misinterpreting Gradient SignsRead next30Exam Trap: Forgetting Units in DistanceRead next31Exam Trap: Incorrect Circle Equation FormRead next
Definition of Gradient Function
1Definition of Gradient FunctionRead next2Rate of Change of y with Respect to xRead next3Gradient of a Function at a PointRead next4Differentiation of kx^nRead next5Simplifying Expressions Before DifferentiationRead next6Finding dy/dx for Polynomial FunctionsRead next7Equation of a Tangent to a CurveRead next8Equation of a Normal to a CurveRead next9Identifying Increasing FunctionsRead next10Identifying Decreasing FunctionsRead next11Second Derivative Notation (d²y/dx²)Read next12Rate of Change of Gradient FunctionRead next13Using Differentiation to Find MaximaRead next14Using Differentiation to Find MinimaRead next15Determining Nature of Stationary PointsRead next16Using d²y/dx² to Classify PointsRead next17Maxima and Minima in Simple ProblemsRead next18Sketching Curves with Maxima and MinimaRead next19Interpreting Curves with Stationary PointsRead next20Worked Example: Finding dy/dx Step-by-StepRead next21Worked Example: Tangent EquationRead next22Worked Example: Normal EquationRead next23Worked Example: Increasing and Decreasing FunctionsRead next24Worked Example: Maxima and Minima Using DifferentiationRead next25Exam Trap: Forgetting to Simplify Before DifferentiationRead next26Exam Trap: Misinterpreting d²y/dx² ResultsRead next27Exam Trap: Incorrect Gradient Calculation for TangentsRead next28Exam Trap: Confusing Tangents with NormalsRead next29Exam Trap: Missing Stationary Points on Curve SketchesRead next30Application: Optimisation Problems Using DifferentiationRead next31Application: Real-Life Rate of Change ProblemsRead next32Application: Curve Sketching in ContextRead next
Matrix Multiplication Basics
1Matrix Multiplication BasicsRead next2Multiplying Two 2x2 MatricesRead next3Multiplying a 2x2 Matrix by a 2x1 MatrixRead next4Scalar Multiplication of MatricesRead next5Understanding the Identity MatrixRead next6Properties of the Identity MatrixRead next7Matrix Representation of TransformationsRead next8Transformations of the Unit SquareRead next9Rotation by 90 Degrees About the OriginRead next10Rotation by 180 Degrees About the OriginRead next11Rotation by 270 Degrees About the OriginRead next12Reflection in the Line x = 0Read next13Reflection in the Line y = 0Read next14Reflection in the Line y = xRead next15Reflection in the Line y = -xRead next16Enlargements Centered at the OriginRead next17Understanding Combination of TransformationsRead next18Matrix Multiplication for Combined TransformationsRead next19Worked Examples: Combining RotationsRead next20Worked Examples: Combining ReflectionsRead next21Worked Examples: Combining EnlargementsRead next22Exam Trap: Order of Matrix MultiplicationsRead next23Inverse Transformations Using MatricesRead next24Checking Matrix Multiplication ResultsRead next25Geometric Interpretation of Matrix TransformationsRead next26Identifying Transformation Types from MatricesRead next27Zero Matrix and Its Role in TransformationsRead next28Diagonal Matrices in TransformationsRead next29Symmetry in Matrix TransformationsRead next30Using Determinants to Analyze TransformationsRead next31Effect of Determinant on Area ScalingRead next32Worked Example: Area Scaling via DeterminantsRead next33Transformations and Coordinate SystemsRead next34Exam Trap: Misinterpreting Transformation DirectionsRead next35Matrix Transformations in Problem ContextsRead next36Exam Strategy for Matrix TransformationsRead next
Understanding Perimeter of Shapes
1Understanding Perimeter of ShapesRead next2Calculating Area of RectanglesRead next3Area of Triangles and ParallelogramsRead next4Area of Trapezia Step-by-StepRead next5Surface Area of PrismsRead next6Volume of Prisms ExplainedRead next7Surface Area of CylindersRead next8Volume of Cylinders FormulaRead next9Surface Area of SpheresRead next10Volume of Spheres FormulaRead next11Surface Area of ConesRead next12Volume of Cones CalculationRead next13Volume of Pyramids FormulaRead next14Circle Theorems: Angle at the CentreRead next15Circle Theorems: Angles in Same SegmentRead next16Circle Theorems: Cyclic QuadrilateralRead next17Circle Theorems: Alternate SegmentRead next18Circle Theorems: Tangent-Radius AngleRead next19Geometric Proofs with Circle TheoremsRead next20Using Pythagoras' Theorem in 2DRead next21Recognising Pythagorean TriplesRead next22Using Pythagoras' Theorem in 3DRead next23Understanding Trigonometric RatiosRead next24Solving Right-Angled TrianglesRead next25Sine Rule in Scalene TrianglesRead next26Cosine Rule in Scalene TrianglesRead next27Area of a Triangle Using SineRead next28Applying Trigonometry in 2D ProblemsRead next29Applying Trigonometry in 3D ProblemsRead next30Angle Between Line and PlaneRead next31Angle Between Two PlanesRead next32Graphs of y = sin xRead next33Graphs of y = cos xRead next34Graphs of y = tan xRead next35Using Trigonometric DefinitionsRead next36Special Triangles: 30-60-90Read next37Special Triangles: 45-45-90Read next38Using tan θ = sin θ / cos θRead next39Using sin²θ + cos²θ = 1Read next40Solving Simple Trigonometric EquationsRead next41Common Errors in Trigonometric ProblemsRead next
The Sine Function: Definition and Basics
1The Sine Function: Definition and BasicsRead next2The Cosine Function: Definition and BasicsRead next3The Tangent Function: Definition and BasicsRead next4Sketching the Sine GraphRead next5Sketching the Cosine GraphRead next6Sketching the Tangent GraphRead next7Key Features of Sine GraphsRead next8Key Features of Cosine GraphsRead next9Key Features of Tangent GraphsRead next10Periodicity of Sine, Cosine, and TangentRead next11Amplitude and Frequency of Sine and CosineRead next12Phase Shift in Trigonometric GraphsRead next13Transformations of Sine GraphsRead next14Transformations of Cosine GraphsRead next15Transformations of Tangent GraphsRead next16Interpreting Sine Graphs in ContextRead next17Interpreting Cosine Graphs in ContextRead next18Interpreting Tangent Graphs in ContextRead next19Trigonometric Identities: sin²θ + cos²θ = 1Read next20Trigonometric Identities: tanθ = sinθ/cosθRead next21Simplifying Expressions with Trigonometric IdentitiesRead next22Proving Trigonometric IdentitiesRead next23Solving sinθ = k for θ in [0°, 360°]Read next24Solving cosθ = k for θ in [0°, 360°]Read next25Solving tanθ = k for θ in [0°, 360°]Read next26Solving Trigonometric Equations with Multiple SolutionsRead next27Using Graphs to Solve Trigonometric EquationsRead next28Common Errors in Solving Trigonometric EquationsRead next29Using sinθ, cosθ, and tanθ for Angles Beyond 360°Read next30Understanding 30°, 60°, 90° TrianglesRead next31Understanding 45°, 45°, 90° TrianglesRead next32Exact Values of Sine, Cosine, and Tangent for Special AnglesRead next33Using Trigonometric Ratios in Problem SolvingRead next34Graphical Representation of Trigonometric IdentitiesRead next35Using Trigonometric Graphs in Real-Life ApplicationsRead next36Linking Trigonometric Graphs to Circular MotionRead next37Impact of Negative Angles on Trigonometric FunctionsRead next38Finding Maximum and Minimum Values from Trigonometric GraphsRead next39Inverse Trigonometric Functions and Their GraphsRead next40Solving Trigonometric Equations with Inverse FunctionsRead next41Using Trigonometric Graphs to Model Periodic PhenomenaRead next42Relationship Between Degrees and Radians in GraphsRead next43Using Technology to Sketch Trigonometric GraphsRead next44Exam Tips for Trigonometric Graphs and EquationsRead next