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GCE N(A)-Level A Maths Topics

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1. Linear Inequalities

1.1 Express linear inequalities graphically and algebraically
1.2 Solving one-step linear inequalities
1.3 Solving multi-step linear inequalities

2. Algebraic Expressions

2.1 Equivalent algebraic expressions
2.2 Adding and subtracting algebraic expressions
2.3 Multiplying monomial by monomial
2.4 Multiplying monomial by binomial
2.5 Multiplying binomial by binomial
2.6 Multiplying polynomial by polynomial
2.7 Applications of algebraic expressions

3. Linear Functions

3.1 Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
3.2 Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
3.3 Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
3.4 Gradient intercept form: y = mx + b
3.5 General form: Ax + By + C = 0
3.6 Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)
3.7 Rate of change
3.8 Graphing linear functions using table of values
3.9 Graphing linear functions using x- and y-intercepts
3.10 Graphing from slope-intercept form y=mx+b
3.11 Graphing linear functions using a single point and gradient
3.12 Word problems of graphing linear functions
3.13 Applications of linear relations

4. Simultaneous Equations

4.1 Determining number of solutions to linear equations
4.2 Solving simultaneous linear equations by graphing
4.3 Solving simultaneous linear equations by elimination
4.4 Solving simultaneous linear equations by substitution
4.5 Money related questions in linear equations
4.6 Unknown number related questions in linear equations
4.7 Distance and time related questions in linear equations
4.8 Rectangular shape related questions in linear equations

5. Factorisation

5.1 Factorise by taking out the greatest common factor
5.2 Factorise by grouping
5.3 Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2
5.4 Factorising difference of squares: x^2 - y^2
5.5 Factorise trinomials
5.6 Solving polynomials with unknown coefficients
5.7 Solving polynomials with unknown constant terms
5.8 Factorising difference of cubes: a3−b3a^3-b^3
5.9 Factorising sum of cubes: a3+b3a^3+b^3

6. Quadratic Functions

6.1 Introduction to quadratic functions
6.2 Transformations of quadratic functions
6.3 Quadratic function in general form: y = ax^2 + bx + c
6.4 Quadratic function in vertex form: y = a(x-p)^2 + q
6.5 Completing the square
6.6 Converting from general to vertex form by completing the square
6.7 Shortcut: Vertex formula
6.8 Graphing quadratic functions: General form VS. Vertex form
6.9 Finding the quadratic functions for given parabolas
6.10 Applications of quadratic functions

7. Quadratic Equations and Inequalities

7.1 Solving quadratic equations by factoring
7.2 Solving quadratic equations by completing the square
7.3 Using quadratic formula to solve quadratic equations
7.4 Nature of roots of quadratic equations: The discriminant
7.5 Applications of quadratic equations
7.6 Solving quadratic inequalities

8. Surds

8.1 Square and square roots
8.2 Cubic and cube roots
8.3 Operations with surds
8.4 Conversion between entire radicals and mixed radicals
8.5 Adding and subtracting surds
8.6 Multiplying surds
8.7 Rationalize the denominator
8.8 Solving equations with surds

9. Solving Simultaneous Equations

9.1 System of linear equations
9.2 System of linear-quadratic equations
9.3 System of quadratic-quadratic equations
9.4 Solving 3 variable systems of equations by substitution
9.5 Solving 3 variable systems of equations by elimination
9.6 Solving 3 variable systems of equations with no solution, infinite solutions
9.7 Word problems relating 3 variable systems of equations

10. Laws of Indices

10.1 Indices: Product rule (a^x)(a^y) = a^(x+y)
10.2 Indices: Division rule (a^x / a^y) = a^(x-y)
10.3 Indices: Power rule (a^x)^y = a^(x * y)
10.4 Negative indices
10.5 Zero index: a^0 = 1
10.6 Rational indices
10.7 Standard form

11. Algebraic Fractions

11.1 Simplifying algebraic fractions and restrictions
11.2 Adding and subtracting algebraic fractions
11.3 Multiplying algebraic fractions
11.4 Dividing algebraic fractions
11.5 Solving equations with algebraic fractions
11.6 Applications of equations with algebraic fractions
11.7 Simplifying complex fractions

12. Exponential Functions

12.1 Solving exponential equations using laws of indices
12.2 Graphing exponential functions
12.3 Graphing transformations of exponential functions
12.4 Finding an exponential function given its graph

13. Binomial expansions

13.1 Factorial notation
13.2 Binomial theorem

14. Geometry and Measurement

14.1 Parallel and perpendicular line segments
14.2 Perpendicular bisectors
14.3 Angle bisectors

15. Congruent Triangles

15.1 Classifying Triangles
15.2 Congruence and Congruent Triangles
15.3 Triangles Congruent by SSS Proofs
15.4 Triangles Congruent by SAS and HL Proofs
15.5 Triangles Congruent by ASA and AAS Proofs
15.6 Isosceles and Equilateral Triangles

16. Angles, Lines, and Transversals

16.1 Pairs of lines and angles
16.2 Parallel lines and transversals
16.3 Parallel line proofs
16.4 Perpendicular line proofs

17. Circles

17.1 Angles in a circle
17.2 Chord properties
17.3 Tangent properties
17.4 Circle and circumference
17.5 Arcs of a circle
17.6 Areas and sectors of circles
17.7 Inscribed quadrilaterals in circles
17.8 Central and inscribed angles in circles

18. Surface Area and Volume

18.1 Surface area and volume of prisms
18.2 Surface area and volume of pyramids
18.3 Surface area and volume of cylinders
18.4 Surface area and volume of cones
18.5 Surface area and volume of spheres

19. Conics

19.1 Conics - Parabola
19.2 Conics - Circle

20. Trigonometric Ratios and Angle Measure

20.1 Angle in standard position
20.2 Coterminal angles
20.3 Reference angle
20.4 Find the exact value of trigonometric ratios
20.5 ASTC rule in trigonometry (All Students Take Calculus)
20.6 Unit circle
20.7 Converting between degrees and radians
20.8 Trigonometric ratios of angles in radians
20.9 Radian measure and arc length

21. Sine Rule and Cosine Rule

21.1 Sine rule
21.2 Cosine rule
21.3 Sine rule and cosine rule word problems

22. Bearings

22.1 Introduction to bearings
22.2 Bearings and direction word problems
22.3 Angle of elevation and depression

23. Graphing Trigonometric Functions

23.1 Sine graph: y = sin x
23.2 Cosine graph: y = cos x
23.3 Tangent graph: y = tan x
23.4 Cotangent graph: y = cot x
23.5 Secant graph: y = sec x
23.6 Cosecant graph: y = csc x
23.7 Graphing transformations of trigonometric functions
23.8 Determining trigonometric functions given their graphs

24. Applications of Trigonometric Functions

24.1 Ferris wheel trig problems
24.2 Tides and water depth trig problems
24.3 Spring (simple harmonic motion) trig problems

25. Trigonometric Identities

25.1 Quotient identities and reciprocal identities
25.2 Pythagorean identities
25.3 Sum and difference identities
25.4 Cofunction identities
25.5 Double-angle identities

26. Solving Trigonometric Equations

26.1 Solving first degree trigonometric equations
26.2 Determining non-permissible values for trig expressions
26.3 Solving second degree trigonometric equations
26.4 Solving trigonometric equations involving multiple angles
26.5 Solving trigonometric equations using pythagorean identities
26.6 Solving trigonometric equations using sum and difference identities
26.7 Solving trigonometric equations using double-angle identities

27. Inverse Trigonometric Functions

27.1 Finding inverse trigonometric function from its graph
27.2 Evaluating inverse trigonometric functions
27.3 Finding inverse reciprocal trigonometric function from its graph
27.4 Inverse reciprocal trigonometric function: finding the exact value

28. Data and Graphs

28.1 Reading and drawing bar graphs
28.2 Reading and drawing histograms
28.3 Reading and drawing line graphs
28.4 Box-and-whisker plots and scatter plots
28.5 Reading and drawing stem-and-leaf diagrams
28.6 Reading and drawing Venn diagrams
28.7 Frequency tables and dot diagrams
28.8 Pie charts

29. Representing Data

29.1 Advantages and disadvantages of different graphs
29.2 Misleading graphs
29.3 Critiquing data presentation

30. Statistics

30.1 Median and mode
30.2 Mean
30.3 Range and outliers
30.4 Application of averages
30.5 Standard deviation, and variance
30.6 Z-score, quartiles, and percentiles

31. Probability

31.1 Determining probabilities using tree diagrams and tables
31.2 Probability of independent events
31.3 Frequency distribution and histograms
31.4 Addition rule for "OR"
31.5 Multiplication rule for "AND"

32. Differentiation

32.1 Power rule
32.2 Slope and equation of tangent line
32.3 Chain rule
32.4 Product rule
32.5 Quotient rule
32.6 Higher order derivatives
32.7 Critical number & maximum and minimum values

33. Integration

33.1 Antiderivatives
33.2 Definite integral
33.3 Integration by parts
33.4 Integration of rational functions by partial fractions
33.5 Areas between curves

33 Chapters · 195 Topics · 1341 Videos

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We cover all N(A)-Level Additional Mathematics topics including trigonometry, calculus, algebra, coordinate geometry, logarithms, indices, and binomial theorem.

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