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GCSE Maths Topics

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1. Numbers and Relations

1.1

1.2

Comparing and ordering numbers

1.3

Rounding numbers

2. Adding and Subtracting Integers

2.1

Introduction to integer addition

2.2

Adding integers

2.3

Introduction to integer subtraction

2.4

Subtracting integers

2.5

Application of integer operations

3. Multiplying and Dividing Integers

3.1

Understanding integer multiplication

3.2

Multiplying integers

3.3

Understanding integer division

3.4

Dividing integers

3.5

Applications of integer operations

4. Operations with decimals

4.1

Adding and subtracting decimals

4.2

Multiplying decimals

4.3

Dividing decimals

4.4

Order of operations (BIDMAS)

5. Adding and Subtracting Fractions

5.1

Using models to add and subtract fractions

5.2

Adding fractions with like denominators

5.3

Subtracting fractions with like denominators

5.4

Adding and subtracting fractions with unlike denominators

5.5

Adding and subtracting mixed numbers

6. Multiplying and Dividing Fractions

6.1

Multiplying fractions and whole numbers

6.2

Dividing fractions with whole numbers

6.3

Multiplying proper fractions

6.4

Multiplying improper fractions and mixed numbers

6.5

Dividing fractions and mixed numbers

6.6

Applications of fraction operations

7. Percents

7.1

Representing percents

7.2

Percents, fractions, and decimals

7.3

Percent of a number

7.4

Adding and multiplying percents

7.5

Taxes, discounts, tips and more

7.6

Simple interest

8. Ratios, Rates, and Proportions

8.1

8.2

8.3

9. Pythagorean Theorem

9.1

Pythagorean theorem

9.2

Estimating square roots

9.3

Using the pythagorean relationship

9.4

Applications of pythagorean theorem

10. Scale Factors and Similarity

10.1

Enlargements and reductions with scale factors

10.2

10.3

Similar triangles

10.4

Similar polygons

11. Solving Linear Equations

11.1

Solving linear equations using multiplication and division

11.2

Solving two-step linear equations: ax + b = c, x/a + b = c

11.3

Solving linear equations using distributive property: a(x + b) = c

11.4

Solving linear equations with variables on both sides

11.5

Solving literal equations

12. Measuring Systems

12.1

12.2

Imperial systems

12.3

Conversions between metric and imperial systems

12.4

Conversions involve squares and cubic

12.5

Upper and lower bound

13. Number System

13.1

Understanding the number systems

13.2

Prime factorization

13.3

Greatest Common Factors (GCF)

13.4

Least Common Multiple (LCM)

13.5

Rational vs. Irrational numbers

13.6

Converting repeating decimals to fractions

14. Surds

14.1

Operations with surds

14.2

Conversion between entire surds and mixed surds

14.3

Adding and subtracting surds

14.4

Multiplying surds

14.5

Solving surd equations

14.6

Rationalize the denominator

15. Algebraic Expressions

15.1

Equivalent algebraic expressions

15.2

Adding and subtracting algebraic expressions

15.3

Multiplying monomial by monomial

15.4

Multiplying monomial by binomial

15.5

Multiplying binomial by binomial

15.6

Multiplying polynomial by polynomial

15.7

Applications of polynomials

16. Linear Functions

16.1

Distance formula:

d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

16.2

Midpoint formula:

M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)

16.3

Gradient equation:

m = \frac{y_2-y_1}{x_2- x_1}

16.4

Gradient intercept form: y = mx + b

16.5

General form: Ax + By + C = 0

16.6

Gradient-point form:

y - y_1 = m (x - x_1)

16.7

16.8

Graphing linear functions using table of values

16.9

Graphing linear functions using x- and y-intercepts

16.10

Graphing linear functions using various forms

16.11

Graphing linear functions using a single point and gradient

16.12

Word problems of graphing linear functions

16.13

Parallel and perpendicular lines in linear functions

16.14

Applications of linear relations

16.15

Perpendicular line equation

17. Simultaneous Equations

17.1

Determining number of solutions to linear equations

17.2

Solving simultaneous linear equations by graphing

17.3

Solving simultaneous linear equations by elimination

17.4

Solving simultaneous linear equations by substitution

17.5

Money related questions in linear equations

17.6

Unknown number related questions in linear equations

17.7

Distance and time related questions in linear equations

17.8

Rectangular shape related questions in linear equations

17.9

Simultaneous linear-quadratic equations

17.10

Simultaneous quadratic-quadratic equations

17.11

Solving 3 variable simultaneous equations by substitution

17.12

Solving 3 variable simultaneous equations by elimination

17.13

Solving 3 variable simultaneous equations with no solution, infinite solutions

17.14

Word problems relating 3 variable simultaneous equations

18. Factorising Quadratic Functions

18.1

Factorise by taking out the greatest common factor

18.2

Factorise by grouping

18.3

Factorising difference of squares: x^2 - y^2

18.4

Factorising trinomials

18.5

Factoring difference of cubes

18.6

Factoring sum of cubes

19. Quadratic Functions

19.1

Introduction to quadratic functions

19.2

Transformations of quadratic functions

19.3

Quadratic function in general form: y = ax^2 + bx + c

19.4

Quadratic function in vertex form: y = a(x-p)^2 + q

19.5

Completing the square

19.6

Converting from general to vertex form by completing the square

19.7

Shortcut: Vertex formula

19.8

Graphing quadratic functions: General form VS. Vertex form

19.9

Finding the quadratic functions for given parabolas

19.10

Applications of quadratic functions

20. Solving Quadratic Equations

20.1

Solving quadratic equations by factorising

20.2

Solving quadratic equations by completing the square

20.3

Using quadratic formula to solve quadratic equations

20.4

Nature of roots of quadratic equations: The discriminant

20.5

Solving polynomial equations by iteration

20.6

Applications of quadratic equations

21. Inequalities

21.1

Express linear inequalities graphically and algebraically

21.2

Solving one-step linear inequalities

21.3

Solving multi-step linear inequalities

21.4

Compound inequalities

21.5

Graphing linear inequalities in two variables

21.6

Solving quadratic inequalities in one variable

22. Algebraic Fractions

22.1

Simplifying algebraic fractions and restrictions

22.2

Adding and subtracting algebraic fractions

22.3

Multiplying algebraic fractions

22.4

Dividing algebraic fractions

22.5

Solving equations with algebraic fractions

22.6

Applications of equations with algebraic fractions

22.7

Simplifying complex fractions

22.8

Partial fraction decomposition

23. Reciprocal Functions

23.1

Graphing reciprocals of linear functions

23.2

Graphing reciprocals of quadratic functions

24. Functions

24.1

Function notation

24.2

Operations with functions

24.3

Adding functions

24.4

Subtracting functions

24.5

Multiplying functions

24.6

Dividing functions

24.7

Composite functions

24.8

Inequalities of combined functions

24.9

Inverse functions

24.10

One to one functions

24.11

Difference quotient: applications of functions

25. Transformations

25.1

Transformations of functions: Horizontal translations

25.2

Transformations of functions: Vertical translations

25.3

Reflection across the y-axis: y = f(-x)

25.4

Reflection across the x-axis: y = -f(x)

25.5

Transformations of functions: Horizontal stretches

25.6

Transformations of functions: Vertical stretches

25.7

Combining transformations of functions

25.8

Even and odd functions

26. Sequences

26.1

Arithmetic progressions

26.2

Geometric progressions

27. Indices and Exponential Functions

27.1

Indices: Product rule (a^x)(a^y) = a^(x+y)

27.2

Indices: Division rule (a^x / a^y) = a^(x-y)

27.3

Indices: Power rule (a^x)^y = a^(x * y)

27.4

Indices: Negative exponents

27.5

Indices: Zero exponent: a^0 = 1

27.6

Indices: Rational exponents

27.7

Combining laws of indices

27.8

27.9

Convert between radicals and rational exponents

27.10

Solving for indices

27.11

Graphing exponential functions

28. Growth and Decay

28.1

Exponential growth and decay by a factor

28.2

Exponential growth and decay by percentage

28.3

Finance: Compound interest

28.4

Finance: Future value and present value

29. Congruent Triangles

29.1

Classifying Triangles

29.2

Congruence and Congruent Triangles

29.3

Triangles Congruent by SSS Proofs

29.4

Triangles Congruent by SAS and HL Proofs

29.5

Triangles Congruent by ASA and AAS Proofs

29.6

Isosceles and Equilateral Triangles

30. Circle Theorems

30.1

Angles in a circle

30.2

Chord properties

30.3

Tangent properties

30.4

Circles and circumference

30.5

Arcs of a circle

30.6

Areas and sectors of circles

30.7

Cyclic quadrilaterals

30.8

Central and inscribed angles in circles

30.9

Equations of circles

31. Surface Area and Volume

31.1

Surface area and volume of prisms

31.2

Surface area and volume of pyramids

31.3

Surface area and volume of cylinders

31.4

Surface area and volume of cones

31.5

Surface area and volume of spheres

32. Trigonometry

32.1

Use sine ratio to calculate angles and sides (Sin =

\frac{o}{h}

32.2

Use cosine ratio to calculate angles and sides (Cos =

\frac{a}{h}

32.3

Use tangent ratio to calculate angles and sides (Tan =

\frac{o}{a}

32.4

Combination of SohCahToa questions

32.5

Solving expressions using 45-45-90 special right triangles

32.6

Solving expressions using 30-60-90 special right triangles

32.7

Word problems relating ladder in trigonometry

32.8

Word problems relating guy wire in trigonometry

32.9

Other word problems relating angles in trigonometry

33. Sine Rule and Cosine Rule

33.1

33.2

33.3

Sine rule and cosine rule word problems

34. Graphing Trigonometric Functions

34.1

34.2

Sine graph: y = sin x

34.3

Cosine graph: y = cos x

34.4

Tangent graph: y = tan x

35. Bearings

35.1

Introduction to bearings

35.2

Bearings and direction word problems

35.3

Angle of elevation and depression

36. Vectors

36.1

Introduction to vectors

36.2

Magnitude of a vector

36.3

Scalar multiplication

36.4

Equivalent vectors

36.5

Adding and subtracting vectors in component form

36.6

Word problems on vectors

37. Set Theory

37.1

37.2

Set builder notation

37.3

Intersection and union of 2 sets

37.4

Intersection and union of 3 sets

38. Probability

38.1

Determining probabilities using tree diagrams and tables

38.2

Probability of independent events

38.3

Comparing experimental and theoretical probability

38.4

Conditional probability

38.5

Probability with Venn diagrams

39. Statistics

39.1

Median and mode

39.2

39.3

Range and outliers

39.4

Application of averages

40. Data and Graphs

40.1

Reading and drawing bar graphs

40.2

Reading and drawing histograms

40.3

Reading and drawing line graphs

40.4

Box-and-whisker plots and scatter plots

40.5

Scatter plots and correlation

40.6

Frequency distribution and histograms

40.7

Frequency polygons

40.8

Reading and drawing Venn diagrams

40.9

Stem-and-leaf plots

40.10

Shapes of distributions

40Chapters

245Topics

1846Videos

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