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GCE N(A)-Level A Maths topics

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1Linear Inequalities

1.1Express linear inequalities graphically and algebraically (free lessons)
1.2Solving one-step linear inequalities (free lessons)
1.3Solving multi-step linear inequalities (free lessons)

2Algebraic Expressions

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

3Linear Functions

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

4Simultaneous Equations

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

5Factorisation

5.1Factorise by taking out the greatest common factor (free lessons)
5.2Factorise by grouping
5.3Factorising perfect square trinomials: (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2 or (a−b)2=a2−2ab+b2(a - b)^2 = a^2 - 2ab + b^2 (free lessons)
5.4Factorising difference of squares: x2−y2x^2 - y^2
5.5Factorise trinomials
5.6Solving polynomials with unknown coefficients
5.7Solving polynomials with unknown constant terms
5.8Factorising difference of cubes: a3−b3a^3-b^3
5.9Factorising sum of cubes: a3+b3a^3+b^3

6Quadratic Functions

6.1Introduction to quadratic functions (free lessons)
6.2Transformations of quadratic functions
6.3Quadratic function in general form: y=ax2+bx+cy = ax^2 + bx+c
6.4Quadratic function in vertex form: y=a(x−p)2+qy = a(x-p)^2 + q
6.5Completing the square (free lessons)
6.6Converting from general to vertex form by completing the square
6.7Shortcut: Vertex formula (free lessons)
6.8Graphing quadratic functions: General form VS. Vertex form
6.9Finding the quadratic functions for given parabolas (free lessons)
6.10Applications of quadratic functions

7Quadratic Equations and Inequalities

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

8Surds

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

9Solving Simultaneous Equations

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

10Laws of Indices

10.1Indices: Product rule (ax)(ay)=a(x+y) (a^x)(a^y)=a^{(x+y)} (free lessons)
10.2Indices: Division rule axay=a(x−y){a^x \over a^y}=a^{(x-y)}
10.3Indices: Power rule (ax)y=a(x⋅y) (a^x)^y = a^{(x\cdot y)} (free lessons)
10.4Negative indices
10.5Zero index: a0=1 a^0 = 1
10.6Rational indices
10.7Standard form

11Algebraic Fractions

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

12Exponential Functions

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

13Binomial expansions

13.1Factorial notation
13.2Binomial theorem

14Geometry and Measurement

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

15Congruent Triangles

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

16Angles, Lines, and Transversals

16.1Pairs of lines and angles
16.2Parallel lines and transversals
16.3Parallel line proofs
16.4Perpendicular line proofs (free lessons)

17Circles

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

18Surface Area and Volume

18.1Surface area and volume of prisms (free lessons)
18.2Surface area and volume of pyramids
18.3Surface area and volume of cylinders
18.4Surface area and volume of cones (free lessons)
18.5Surface area and volume of spheres

19Conics

19.1Conics - Parabola
19.2Conics - Circle

20Trigonometric Ratios and Angle Measure

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

21Sine Rule and Cosine Rule

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

22Bearings

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

23Graphing Trigonometric Functions

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

24Applications of Trigonometric Functions

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

25Trigonometric Identities

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

26Solving Trigonometric Equations

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

27Inverse Trigonometric Functions

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

28Data and Graphs

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

29Representing Data

29.1Advantages and disadvantages of different graphs (free lessons)
29.2Misleading graphs
29.3Critiquing data presentation

30Statistics

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

31Probability

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

32Differentiation

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

33Integration

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