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GCE O-Level A Maths Topics

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video
Solving Linear Equations
Solving linear equations using multiplication and division
Solving two-step linear equations: ax + b = c, x/a + b = c
Solving linear equations using distributive property: a(x + b) = c
Solving linear equations with variables on both sides
Solving literal equations
video
Linear Inequalities
Express linear inequalities graphically and algebraically
Solving one-step linear inequalities
Solving multi-step linear inequalities
video
Measuring Systems
Metric systems
Imperial systems
Conversions between metric and imperial systems
Conversions involve squares and cubic
video
Number Systems
Understanding the number systems
Prime factorisation
Highest common factors (HCF)
Least Common Multiple (LCM)
Rational vs. Irrational numbers
Converting repeating decimals to fractions
video
Direct and Inverse Proportion
Direct variation
video
Algebraic Expressions
Equivalent algebraic expressions
Adding and subtracting algebraic expressions
Multiplying monomial by monomial
Multiplying monomial by binomial
Multiplying binomial by binomial
Multiplying polynomial by polynomial
Applications of polynomials
video
Surds
Square and square roots
Cubic and cube roots
Operations with surds
Conversion between entire radicals and mixed radicals
Adding and subtracting surds
Multiplying surds
Rationalize the denominator
Solving equations with surds
video
Linear Functions
Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}d=(x2​−x1​)2+(y2​−y1​)2​
Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)M=(2x1​+x2​​,2y1​+y2​​)
Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}m=x2​−x1​y2​−y1​​
Gradient intercept form: y = mx + b
General form: Ax + By + C = 0
Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)y−y1​=m(x−x1​)
Rate of change
Graphing linear functions using table of values
Graphing linear functions using x- and y-intercepts
Graphing from slope-intercept form y=mx+b
Graphing linear functions using a single point and gradient
Word problems of graphing linear functions
Applications of linear relations
video
Factorising Quadratic Functions
Factorise by taking out the greatest common factor
Factorise by grouping
Factorising perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2
Factorising difference of squares: x^2 - y^2
Factorising trinomials
Solving polynomials with unknown coefficients
Solving polynomials with unknown constant terms
video
Quadratic Functions
Introduction to quadratic functions
Transformations of quadratic functions
Quadratic function in general form: y = ax^2 + bx + c
Quadratic function in vertex form: y = a(x-p)^2 + q
Completing the square
Converting from general to vertex form by completing the square
Shortcut: Vertex formula
Graphing quadratic functions: General form VS. Vertex form
Finding the quadratic functions for given parabolas
Applications of quadratic functions
video
Quadratic Equations and Inequalities
Solving quadratic equations by factoring
Solving quadratic equations by completing the square
Using quadratic formula to solve quadratic equations
Nature of roots of quadratic equations: The discriminant
Applications of quadratic equations
Solving quadratic inequalities
video
Algebraic Fractions
Simplifying algebraic fractions and restrictions
Adding and subtracting algebraic fractions
Multiplying algebraic fractions
Dividing algebraic fractions
Solving equations with algebraic fractions
Applications of equations with algebraic fractions
Simplifying complex fractions
Partial fraction decomposition
video
Simultaneous Equations
Determining number of solutions to linear equations
Solving simultaneous linear equations by graphing
Solving simultaneous linear equations by elimination
Solving simultaneous linear equations by substitution
Money related questions in linear equations
Unknown number related questions in linear equations
Distance and time related questions in linear equations
Rectangular shape related questions in linear equations
Simultaneous linear equations
Simultaneous linear-quadratic equations
Simultaneous quadratic-quadratic equations
video
Inequalities in Two Variables
Graphing linear inequalities in two variables
Graphing systems of linear inequalities
Graphing quadratic inequalities in two variables
Graphing systems of quadratic inequalities
Applications of inequalities
What is linear programming?
Linear programming word problems
video
Laws of Indices
Indices: Product rule (a^x)(a^y) = a^(x+y)
Indices: Division rule (a^x / a^y) = a^(x-y)
Indices: Power rule (a^x)^y = a^(x * y)
Negative indices
Zero index: a^0 = 1
Rational indices
Standard form
video
Polynomial Functions
Polynomial long division
Polynomial synthetic division
Remainder theorem
Factor theorem
video
Binomial expansions
Factorial notation
Binomial theorem
video
Exponential Functions
Solving exponential equations using laws of indices
Graphing exponential functions
Graphing transformations of exponential functions
Finding an exponential function given its graph
video
Logarithms
What is a logarithm?
Converting from logarithmic form to exponential form
Evaluating logarithms without a calculator
Common logarithms
Natural log: ln
Evaluating logarithms using change-of-base formula
Converting from exponential form to logarithmic form
Solving exponential equations with logarithms
Product rule of logarithms
Quotient rule of logarithms
Combining product rule and quotient rule in logarithms
Evaluating logarithms using logarithm rules
Solving logarithmic equations
Graphing logarithmic functions
Finding a logarithmic function given its graph
video
Modulus Functions
Modulus functions
Solving modulus equations
video
Vectors
Introduction to vectors
Magnitude of a vector
Direction angle of a vector
Scalar multiplication
Adding and subtracting vectors in component form
Operations on vectors in magnitude and direction form
Word problems on vectors
video
Matrices
Notation of matrices
Adding and subtracting matrices
Multiplying a matrix by a scalar
Multiplying a matrix by another matrix
video
Trigonometric Ratios and Angle Measure
Angle in standard position
Coterminal angles
Reference angle
Find the exact value of trigonometric ratios
ASTC rule in trigonometry (All Students Take Calculus)
Unit circle
Converting between degrees and radians
Trigonometric ratios of angles in radians
Radian measure and arc length
video
Sine Rule and Cosine Rule
Sine rule
Cosine rule
Sine rule and cosine rule word problems
video
Bearings
Introduction to bearings
Bearings and direction word problems
Angle of elevation and depression
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Graphing Trigonometric Functions
Sine graph: y = sin x
Cosine graph: y = cos x
Tangent graph: y = tan x
Cotangent graph: y = cot x
Secant graph: y = sec x
Cosecant graph: y = csc x
Graphing transformations of trigonometric functions
Determining trigonometric functions given their graphs
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Applications of Trigonometric Functions
Ferris wheel trig problems
Tides and water depth trig problems
Spring (simple harmonic motion) trig problems
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Trigonometric Identities
Quotient identities and reciprocal identities
Pythagorean identities
Sum and difference identities
Cofunction identities
Double-angle identities
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Solving Trigonometric Equations
Solving first degree trigonometric equations
Determining non-permissible values for trig expressions
Solving second degree trigonometric equations
Solving trigonometric equations involving multiple angles
Solving trigonometric equations using pythagorean identities
Solving trigonometric equations using sum and difference identities
Solving trigonometric equations using double-angle identities
video
Inverse Trigonometric Functions
Finding inverse trigonometric function from its graph
Evaluating inverse trigonometric functions
Finding inverse reciprocal trigonometric function from its graph
Inverse reciprocal trigonometric function: finding the exact value
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Angles, Lines, and Transversals
Pairs of lines and angles
Parallel lines and transversals
Parallel line proofs
Perpendicular line proofs
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Scale Factors and Similarity
Enlargements and reductions with scale factors
Scale diagrams
Similar triangles
Similar polygons
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Congruent Triangles
Congruence and congruent triangles
Triangles congruent by SSS proofs
Triangles congruent by SAS and HL proofs
Triangles congruent by ASA and AAS proofs
video
Circles
Angles in a circle
Chord properties
Tangent properties
Circle and circumference
Arcs of a circle
Areas and sectors of circles
Inscribed quadrilaterals in circles
Central and inscribed angles in circles
video
Surface Area and Volume
Surface area and volume of prisms
Surface area and volume of pyramids
Surface area and volume of cylinders
Surface area and volume of cones
Surface area and volume of spheres
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Conics
Conics - Parabola
Conics - Circle
video
Set Theory
Set notation
Set builder notation
Intersection and union of 2 sets
Intersection and union of 3 sets
video
Data and Graphs
Reading and drawing bar graphs
Reading and drawing histograms
Reading and drawing line graphs
Box-and-whisker plots and scatter plots
Stem-and-leaf plots
Reading and drawing Venn diagrams
Frequency tables and dot diagrams
Pie charts
video
Statistics
Median and mode
Mean
Range and outliers
Application of averages
Standard deviation, and variance
Z-score, quartiles, and percentiles
video
Probability
Determining probabilities using tree diagrams and tables
Probability of independent events
Frequency distribution and histograms
Addition rule for "OR"
Multiplication rule for "AND"
video
Differentiation
Power rule
Slope and equation of tangent line
Chain rule
Derivative of trigonometric functions
Derivative of exponential functions
Product rule
Quotient rule
Derivative of logarithmic functions
Higher order derivatives
Rectilinear Motion: Derivative
Critical number & maximum and minimum values
video
Integration
Antiderivatives
Definite integral
Integration by parts
Trigonometric substitution
Integration of rational functions by partial fractions
Areas between curves

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