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Aligning with the new GCSE maths 9 - 1 specifications of all exam boards, our comprehensive lessons cover content in all six topic areas including Number; Algebra; Ratio, proportion and rates of change; Geometry and measures; Probability; and Statistics. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest gcse maths questions. Then, strengthen your understanding with tons of GCSE maths practice questions.

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  1. 1Numbers and Relations
    1. 1.1Place value
    2. 1.2Comparing and ordering numbers
    3. 1.3Rounding numbers
  2. 2Adding and Subtracting Integers
    1. 2.1Introduction to integer addition
    2. 2.2Adding integers
    3. 2.3Introduction to integer subtraction
    4. 2.4Subtracting integers
    5. 2.5Application of integer operations
  3. 3Multiplying and Dividing Integers
    1. 3.1Understanding integer multiplication
    2. 3.2Multiplying integers
    3. 3.3Understanding integer division
    4. 3.4Dividing integers
    5. 3.5Applications of integer operations
  4. 4Operations with decimals
    1. 4.1Adding and subtracting decimals
    2. 4.2Multiplying decimals
    3. 4.3Dividing decimals
    4. 4.4Order of operations (BIDMAS)
  5. 5Adding and Subtracting Fractions
    1. 5.1Using models to add and subtract fractions
    2. 5.2Adding fractions with like denominators
    3. 5.3Subtracting fractions with like denominators
    4. 5.4Adding and subtracting fractions with unlike denominators
    5. 5.5Adding and subtracting mixed numbers
  6. 6Multiplying and Dividing Fractions
    1. 6.1Multiplying fractions and whole numbers
    2. 6.2Dividing fractions with whole numbers
    3. 6.3Multiplying proper fractions
    4. 6.4Multiplying improper fractions and mixed numbers
    5. 6.5Dividing fractions and mixed numbers
    6. 6.6Applications of fraction operations
  7. 7Percents
    1. 7.1Representing percents
    2. 7.2Percents, fractions, and decimals
    3. 7.3Percent of a number
    4. 7.4Adding and multiplying percents
    5. 7.5Taxes, discounts, tips and more
    6. 7.6Simple interest
  8. 8Ratios, Rates, and Proportions
    1. 8.1Ratios
    2. 8.2Rates
    3. 8.3Proportions
  9. 9Pythagorean Theorem
    1. 9.1Pythagorean theorem
    2. 9.2Estimating square roots
    3. 9.3Using the pythagorean relationship
    4. 9.4Applications of pythagorean theorem
  10. 10Scale Factors and Similarity
    1. 10.1Enlargements and reductions with scale factors
    2. 10.2Scale diagrams
    3. 10.3Similar triangles
    4. 10.4Similar polygons
  11. 11Solving Linear Equations
    1. 11.1Solving linear equations using multiplication and division
    2. 11.2Solving two-step linear equations: ax+b=cax + b = c, xa+b=c{x \over a} + b = c
    3. 11.3Solving linear equations using distributive property: a(x+b)=ca(x + b) = c
    4. 11.4Solving linear equations with variables on both sides
    5. 11.5Solving literal equations
  12. 12Measuring Systems
    1. 12.1Metric systems
    2. 12.2Imperial systems
    3. 12.3Conversions between metric and imperial systems
    4. 12.4Conversions involve squares and cubic
    5. 12.5Upper and lower bound
  13. 13Number System
    1. 13.1Understanding the number systems
    2. 13.2Prime factorization
    3. 13.3Greatest Common Factors (GCF)
    4. 13.4Least Common Multiple (LCM)
    5. 13.5Rational vs. Irrational numbers
    6. 13.6Converting repeating decimals to fractions
  14. 14Surds
    1. 14.1Operations with surds
    2. 14.2Conversion between entire surds and mixed surds
    3. 14.3Adding and subtracting surds
    4. 14.4Multiplying surds
    5. 14.5Solving surd equations
    6. 14.6Rationalize the denominator
  15. 15Algebraic Expressions
    1. 15.1Equivalent algebraic expressions
    2. 15.2Adding and subtracting algebraic expressions
    3. 15.3Multiplying monomial by monomial
    4. 15.4Multiplying monomial by binomial
    5. 15.5Multiplying binomial by binomial
    6. 15.6Multiplying polynomial by polynomial
    7. 15.7Applications of polynomials
  16. 16Linear Functions
    1. 16.1Distance formula: d=(x2x1)2+(y2y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
    2. 16.2Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
    3. 16.3Gradient equation: m=y2y1x2x1m = \frac{y_2-y_1}{x_2- x_1}
    4. 16.4Gradient intercept form: y = mx + b
    5. 16.5General form: Ax + By + C = 0
    6. 16.6Gradient-point form: yy1=m(xx1)y - y_1 = m (x - x_1)
    7. 16.7Rate of change
    8. 16.8Graphing linear functions using table of values
    9. 16.9Graphing linear functions using x- and y-intercepts
    10. 16.10Graphing linear functions using various forms
    11. 16.11Graphing linear functions using a single point and gradient
    12. 16.12Word problems of graphing linear functions
    13. 16.13Parallel and perpendicular lines in linear functions
    14. 16.14Applications of linear relations
    15. 16.15Perpendicular line equation
  17. 17Simultaneous Equations
    1. 17.1Determining number of solutions to linear equations
    2. 17.2Solving simultaneous linear equations by graphing
    3. 17.3Solving simultaneous linear equations by elimination
    4. 17.4Solving simultaneous linear equations by substitution
    5. 17.5Money related questions in linear equations
    6. 17.6Unknown number related questions in linear equations
    7. 17.7Distance and time related questions in linear equations
    8. 17.8Rectangular shape related questions in linear equations
    9. 17.9Simultaneous linear-quadratic equations
    10. 17.10Simultaneous quadratic-quadratic equations
    11. 17.11Solving 3 variable simultaneous equations by substitution
    12. 17.12Solving 3 variable simultaneous equations by elimination
    13. 17.13Solving 3 variable simultaneous equations with no solution, infinite solutions
    14. 17.14Word problems relating 3 variable simultaneous equations
  18. 18Factorising Quadratic Functions
    1. 18.1Factorise by taking out the greatest common factor
    2. 18.2Factorise by grouping
    3. 18.3Factorising difference of squares: x2y2x^2 - y^2
    4. 18.4Factorising trinomials
    5. 18.5Factoring difference of cubes
    6. 18.6Factoring sum of cubes
  19. 19Quadratic Functions
    1. 19.1Introduction to quadratic functions
    2. 19.2Transformations of quadratic functions
    3. 19.3Quadratic function in general form: y=ax2+bx+cy = ax^2 + bx+c
    4. 19.4Quadratic function in vertex form: y=a(xp)2+qy = a(x-p)^2 + q
    5. 19.5Completing the square
    6. 19.6Converting from general to vertex form by completing the square
    7. 19.7Shortcut: Vertex formula
    8. 19.8Graphing quadratic functions: General form VS. Vertex form
    9. 19.9Finding the quadratic functions for given parabolas
    10. 19.10Applications of quadratic functions
  20. 20Solving Quadratic Equations
    1. 20.1Solving quadratic equations by factorising
    2. 20.2Solving quadratic equations by completing the square
    3. 20.3Using quadratic formula to solve quadratic equations
    4. 20.4Nature of roots of quadratic equations: The discriminant
    5. 20.5Solving polynomial equations by iteration
    6. 20.6Applications of quadratic equations
  21. 21Inequalities
    1. 21.1Express linear inequalities graphically and algebraically
    2. 21.2Solving one-step linear inequalities
    3. 21.3Solving multi-step linear inequalities
    4. 21.4Compound inequalities
    5. 21.5Graphing linear inequalities in two variables
    6. 21.6Solving quadratic inequalities in one variable
  22. 22Algebraic Fractions
    1. 22.1Simplifying algebraic fractions and restrictions
    2. 22.2Adding and subtracting algebraic fractions
    3. 22.3Multiplying algebraic fractions
    4. 22.4Dividing algebraic fractions
    5. 22.5Solving equations with algebraic fractions
    6. 22.6Applications of equations with algebraic fractions
    7. 22.7Simplifying complex fractions
    8. 22.8Partial fraction decomposition
  23. 23Reciprocal Functions
    1. 23.1Graphing reciprocals of linear functions
    2. 23.2Graphing reciprocals of quadratic functions
  24. 24Functions
    1. 24.1Function notation
    2. 24.2Operations with functions
    3. 24.3Adding functions
    4. 24.4Subtracting functions
    5. 24.5Multiplying functions
    6. 24.6Dividing functions
    7. 24.7Composite functions
    8. 24.8Inequalities of combined functions
    9. 24.9Inverse functions
    10. 24.10One to one functions
    11. 24.11Difference quotient: applications of functions
  25. 25Transformations
    1. 25.1Transformations of functions: Horizontal translations
    2. 25.2Transformations of functions: Vertical translations
    3. 25.3Reflection across the y-axis: y=f(x)y = f(-x)
    4. 25.4Reflection across the x-axis: y=f(x)y = -f(x)
    5. 25.5Transformations of functions: Horizontal stretches
    6. 25.6Transformations of functions: Vertical stretches
    7. 25.7Combining transformations of functions
    8. 25.8Even and odd functions
  26. 26Sequences
    1. 26.1Arithmetic progressions
    2. 26.2Geometric progressions
  27. 27Indices and Exponential Functions
    1. 27.1Indices: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)}
    2. 27.2Indices: Division rule axay=a(xy){a^x \over a^y}=a^{(x-y)}
    3. 27.3Indices: Power rule (ax)y=a(xy) (a^x)^y = a^{(x\cdot y)}
    4. 27.4Indices: Negative exponents
    5. 27.5Indices: Zero exponent: a0=1 a^0 = 1
    6. 27.6Indices: Rational exponents
    7. 27.7Combining laws of indices
    8. 27.8Standard form
    9. 27.9Convert between radicals and rational exponents
    10. 27.10Solving for indices
    11. 27.11Graphing exponential functions
  28. 28Growth and Decay
    1. 28.1Exponential growth and decay by a factor
    2. 28.2Exponential growth and decay by percentage
    3. 28.3Finance: Compound interest
    4. 28.4Finance: Future value and present value
  29. 29Congruent Triangles
    1. 29.1Classifying Triangles
    2. 29.2Congruence and Congruent Triangles
    3. 29.3Triangles Congruent by SSS Proofs
    4. 29.4Triangles Congruent by SAS and HL Proofs
    5. 29.5Triangles Congruent by ASA and AAS Proofs
    6. 29.6Isosceles and Equilateral Triangles
  30. 30Circle Theorems
    1. 30.1Angles in a circle
    2. 30.2Chord properties
    3. 30.3Tangent properties
    4. 30.4Circles and circumference
    5. 30.5Arcs of a circle
    6. 30.6Areas and sectors of circles
    7. 30.7Cyclic quadrilaterals
    8. 30.8Central and inscribed angles in circles
    9. 30.9Equations of circles
  31. 31Surface Area and Volume
    1. 31.1Surface area and volume of prisms
    2. 31.2Surface area and volume of pyramids
    3. 31.3Surface area and volume of cylinders
    4. 31.4Surface area and volume of cones
    5. 31.5Surface area and volume of spheres
  32. 32Trigonometry
    1. 32.1Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h} )
    2. 32.2Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h} )
    3. 32.3Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a} )
    4. 32.4Combination of SohCahToa questions
    5. 32.5Solving expressions using 45-45-90 special right triangles
    6. 32.6Solving expressions using 30-60-90 special right triangles
    7. 32.7Word problems relating ladder in trigonometry
    8. 32.8Word problems relating guy wire in trigonometry
    9. 32.9Other word problems relating angles in trigonometry
  33. 33Sine Rule and Cosine Rule
    1. 33.1Sine rule
    2. 33.2Cosine rule
    3. 33.3Sine rule and cosine rule word problems
  34. 34Graphing Trigonometric Functions
    1. 34.1Unit circle
    2. 34.2Sine graph: y = sin x
    3. 34.3Cosine graph: y = cos x
    4. 34.4Tangent graph: y = tan x
  35. 35Bearings
    1. 35.1Introduction to bearings
    2. 35.2Bearings and direction word problems
    3. 35.3Angle of elevation and depression
  36. 36Vectors
    1. 36.1Introduction to vectors
    2. 36.2Magnitude of a vector
    3. 36.3Scalar multiplication
    4. 36.4Equivalent vectors
    5. 36.5Adding and subtracting vectors in component form
    6. 36.6Word problems on vectors
  37. 37Set Theory
    1. 37.1Set notation
    2. 37.2Set builder notation
    3. 37.3Intersection and union of 2 sets
    4. 37.4Intersection and union of 3 sets
  38. 38Probability
    1. 38.1Determining probabilities using tree diagrams and tables
    2. 38.2Probability of independent events
    3. 38.3Comparing experimental and theoretical probability
    4. 38.4Conditional probability
    5. 38.5Probability with Venn diagrams
  39. 39Statistics
    1. 39.1Median and mode
    2. 39.2Mean
    3. 39.3Range and outliers
    4. 39.4Application of averages
  40. 40Data and Graphs
    1. 40.1Reading and drawing bar graphs
    2. 40.2Reading and drawing histograms
    3. 40.3Reading and drawing line graphs
    4. 40.4Box-and-whisker plots and scatter plots
    5. 40.5Scatter plots and correlation
    6. 40.6Frequency distribution and histograms
    7. 40.7Frequency polygons
    8. 40.8Reading and drawing Venn diagrams
    9. 40.9Stem-and-leaf plots
    10. 40.10Shapes of distributions

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