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GCE O-Level A Maths Topics

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1. Solving Linear Equations

1.1

Solving linear equations using multiplication and division

1.2

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

1.3

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

1.4

Solving linear equations with variables on both sides

1.5

Solving literal equations

2. Linear Inequalities

2.1

Express linear inequalities graphically and algebraically

2.2

Solving one-step linear inequalities

2.3

Solving multi-step linear inequalities

3. Measuring Systems

3.1

3.2

Imperial systems

3.3

Conversions between metric and imperial systems

3.4

Conversions involve squares and cubic

4. Number Systems

4.1

Understanding the number systems

4.2

Prime factorisation

4.3

Highest common factors (HCF)

4.4

Least Common Multiple (LCM)

4.5

Rational vs. Irrational numbers

4.6

Converting repeating decimals to fractions

5. Direct and Inverse Proportion

5.1

Direct variation

6. Algebraic Expressions

6.1

Equivalent algebraic expressions

6.2

Adding and subtracting algebraic expressions

6.3

Multiplying monomial by monomial

6.4

Multiplying monomial by binomial

6.5

Multiplying binomial by binomial

6.6

Multiplying polynomial by polynomial

6.7

Applications of polynomials

7. Surds

7.1

Square and square roots

7.2

Cubic and cube roots

7.3

Operations with surds

7.4

Conversion between entire radicals and mixed radicals

7.5

Adding and subtracting surds

7.6

Multiplying surds

7.7

Rationalize the denominator

7.8

Solving equations with surds

8. Linear Functions

8.1

Distance formula:

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

8.2

Midpoint formula:

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

8.3

Gradient equation:

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

8.4

Gradient intercept form: y = mx + b

8.5

General form: Ax + By + C = 0

8.6

Gradient-point form:

y - y_1 = m (x - x_1)

8.7

8.8

Graphing linear functions using table of values

8.9

Graphing linear functions using x- and y-intercepts

8.10

Graphing from slope-intercept form y=mx+b

8.11

Graphing linear functions using a single point and gradient

8.12

Word problems of graphing linear functions

8.13

Applications of linear relations

9. Factorising Quadratic Functions

9.1

Factorise by taking out the greatest common factor

9.2

Factorise by grouping

9.3

Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

9.4

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

9.5

Factorising trinomials

9.6

Solving polynomials with unknown coefficients

9.7

Solving polynomials with unknown constant terms

10. Quadratic Functions

10.1

Introduction to quadratic functions

10.2

Transformations of quadratic functions

10.3

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

10.4

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

10.5

Completing the square

10.6

Converting from general to vertex form by completing the square

10.7

Shortcut: Vertex formula

10.8

Graphing quadratic functions: General form VS. Vertex form

10.9

Finding the quadratic functions for given parabolas

10.10

Applications of quadratic functions

11. Quadratic Equations and Inequalities

11.1

Solving quadratic equations by factoring

11.2

Solving quadratic equations by completing the square

11.3

Using quadratic formula to solve quadratic equations

11.4

Nature of roots of quadratic equations: The discriminant

11.5

Applications of quadratic equations

11.6

Solving quadratic inequalities

12. Algebraic Fractions

12.1

Simplifying algebraic fractions and restrictions

12.2

Adding and subtracting algebraic fractions

12.3

Multiplying algebraic fractions

12.4

Dividing algebraic fractions

12.5

Solving equations with algebraic fractions

12.6

Applications of equations with algebraic fractions

12.7

Simplifying complex fractions

12.8

Partial fraction decomposition

13. Simultaneous Equations

13.1

Determining number of solutions to linear equations

13.2

Solving simultaneous linear equations by graphing

13.3

Solving simultaneous linear equations by elimination

13.4

Solving simultaneous linear equations by substitution

13.5

Money related questions in linear equations

13.6

Unknown number related questions in linear equations

13.7

Distance and time related questions in linear equations

13.8

Rectangular shape related questions in linear equations

13.9

Simultaneous linear equations

13.10

Simultaneous linear-quadratic equations

13.11

Simultaneous quadratic-quadratic equations

14. Inequalities in Two Variables

14.1

Graphing linear inequalities in two variables

14.2

Graphing systems of linear inequalities

14.3

Graphing quadratic inequalities in two variables

14.4

Graphing systems of quadratic inequalities

14.5

Applications of inequalities

14.6

What is linear programming?

14.7

Linear programming word problems

15. Laws of Indices

15.1

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

15.2

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

15.3

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

15.4

Negative indices

15.5

Zero index: a^0 = 1

15.6

Rational indices

15.7

16. Polynomial Functions

16.1

Polynomial long division

16.2

Polynomial synthetic division

16.3

Remainder theorem

16.4

17. Binomial expansions

17.1

Factorial notation

17.2

Binomial theorem

18. Exponential Functions

18.1

Solving exponential equations using laws of indices

18.2

Graphing exponential functions

18.3

Graphing transformations of exponential functions

18.4

Finding an exponential function given its graph

19. Logarithms

19.1

What is a logarithm?

19.2

Converting from logarithmic form to exponential form

19.3

Evaluating logarithms without a calculator

19.4

Common logarithms

19.5

Natural log: ln

19.6

Evaluating logarithms using change-of-base formula

19.7

Converting from exponential form to logarithmic form

19.8

Solving exponential equations with logarithms

19.9

Product rule of logarithms

19.10

Quotient rule of logarithms

19.11

Combining product rule and quotient rule in logarithms

19.12

Evaluating logarithms using logarithm rules

19.13

Solving logarithmic equations

19.14

Graphing logarithmic functions

19.15

Finding a logarithmic function given its graph

20. Modulus Functions

20.1

Modulus functions

20.2

Solving modulus equations

21. Vectors

21.1

Introduction to vectors

21.2

Magnitude of a vector

21.3

Direction angle of a vector

21.4

Scalar multiplication

21.5

Adding and subtracting vectors in component form

21.6

Operations on vectors in magnitude and direction form

21.7

Word problems on vectors

22. Matrices

22.1

Notation of matrices

22.2

Adding and subtracting matrices

22.3

Multiplying a matrix by a scalar

22.4

Multiplying a matrix by another matrix

23. Trigonometric Ratios and Angle Measure

23.1

Angle in standard position

23.2

Coterminal angles

23.3

Reference angle

23.4

Find the exact value of trigonometric ratios

23.5

ASTC rule in trigonometry (All Students Take Calculus)

23.6

23.7

Converting between degrees and radians

23.8

Trigonometric ratios of angles in radians

23.9

Radian measure and arc length

24. Sine Rule and Cosine Rule

24.1

24.2

24.3

Sine rule and cosine rule word problems

25. Bearings

25.1

Introduction to bearings

25.2

Bearings and direction word problems

25.3

Angle of elevation and depression

26. Graphing Trigonometric Functions

26.1

Sine graph: y = sin x

26.2

Cosine graph: y = cos x

26.3

Tangent graph: y = tan x

26.4

Cotangent graph: y = cot x

26.5

Secant graph: y = sec x

26.6

Cosecant graph: y = csc x

26.7

Graphing transformations of trigonometric functions

26.8

Determining trigonometric functions given their graphs

27. Applications of Trigonometric Functions

27.1

Ferris wheel trig problems

27.2

Tides and water depth trig problems

27.3

Spring (simple harmonic motion) trig problems

28. Trigonometric Identities

28.1

Quotient identities and reciprocal identities

28.2

Pythagorean identities

28.3

Sum and difference identities

28.4

Cofunction identities

28.5

Double-angle identities

29. Solving Trigonometric Equations

29.1

Solving first degree trigonometric equations

29.2

Determining non-permissible values for trig expressions

29.3

Solving second degree trigonometric equations

29.4

Solving trigonometric equations involving multiple angles

29.5

Solving trigonometric equations using pythagorean identities

29.6

Solving trigonometric equations using sum and difference identities

29.7

Solving trigonometric equations using double-angle identities

30. Inverse Trigonometric Functions

30.1

Finding inverse trigonometric function from its graph

30.2

Evaluating inverse trigonometric functions

30.3

Finding inverse reciprocal trigonometric function from its graph

30.4

Inverse reciprocal trigonometric function: finding the exact value

31. Angles, Lines, and Transversals

31.1

Pairs of lines and angles

31.2

Parallel lines and transversals

31.3

Parallel line proofs

31.4

Perpendicular line proofs

32. Scale Factors and Similarity

32.1

Enlargements and reductions with scale factors

32.2

32.3

Similar triangles

32.4

Similar polygons

33. Congruent Triangles

33.1

Congruence and congruent triangles

33.2

Triangles congruent by SSS proofs

33.3

Triangles congruent by SAS and HL proofs

33.4

Triangles congruent by ASA and AAS proofs

34. Circles

34.1

Angles in a circle

34.2

Chord properties

34.3

Tangent properties

34.4

Circle and circumference

34.5

Arcs of a circle

34.6

Areas and sectors of circles

34.7

Inscribed quadrilaterals in circles

34.8

Central and inscribed angles in circles

35. Surface Area and Volume

35.1

Surface area and volume of prisms

35.2

Surface area and volume of pyramids

35.3

Surface area and volume of cylinders

35.4

Surface area and volume of cones

35.5

Surface area and volume of spheres

36. Conics

36.1

Conics - Parabola

36.2

Conics - Circle

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. Data and Graphs

38.1

Reading and drawing bar graphs

38.2

Reading and drawing histograms

38.3

Reading and drawing line graphs

38.4

Box-and-whisker plots and scatter plots

38.5

Stem-and-leaf plots

38.6

Reading and drawing Venn diagrams

38.7

Frequency tables and dot diagrams

38.8

39. Statistics

39.1

Median and mode

39.2

39.3

Range and outliers

39.4

Application of averages

39.5

Standard deviation, and variance

39.6

Z-score, quartiles, and percentiles

40. Probability

40.1

Determining probabilities using tree diagrams and tables

40.2

Probability of independent events

40.3

Frequency distribution and histograms

40.4

Addition rule for "OR"

40.5

Multiplication rule for "AND"

41. Differentiation

41.1

41.2

Slope and equation of tangent line

41.3

41.4

Derivative of trigonometric functions

41.5

Derivative of exponential functions

41.6

41.7

41.8

Derivative of logarithmic functions

41.9

Higher order derivatives

41.10

Rectilinear Motion: Derivative

41.11

Critical number & maximum and minimum values

42. Integration

42.1

Antiderivatives

42.2

Definite integral

42.3

Integration by parts

42.4

Trigonometric substitution

42.5

Integration of rational functions by partial fractions

42.6

Areas between curves

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