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GCE O-Level Maths Topics

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Numbers and Relations
Place value
Comparing and ordering numbers
Rounding numbers
video
Number Theory
Divisibility Rules
Determining Common Factors
Determining Common Multiples
Introduction to exponents
video
Adding and Subtracting Integers
Introduction to integer addition
Adding integers
Introduction to integer subtraction
Subtracting integers
Application of integer operations
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Multiplying and Dividing Integers
Understanding integer multiplication
Multiplying integers
Understanding integer division
Dividing integers
Applications of integer operations
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Operations with decimals
Adding and subtracting decimals
Multiplying decimals
Dividing decimals
Order of operations (BEDMAS)
video
Adding and Subtracting Fractions
Using models to add and subtract fractions
Adding fractions with like denominators
Subtracting fractions with like denominators
Adding and subtracting fractions with unlike denominators
Adding and subtracting mixed numbers
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Multiplying and Dividing Fractions
Multiplying fractions and whole numbers
Dividing fractions with whole numbers
Multiplying proper fractions
Multiplying improper fractions and mixed numbers
Dividing fractions and mixed numbers
Applications of fraction operations
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Ratios, Rates, and Proportions
Ratios
Rates
Proportions
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Percents
Representing percents
Percents, fractions, and decimals
Percent of a number
Adding and multiplying percents
Taxes, discounts, tips and more
Simple interest
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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
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Linear Inequalities
Express linear inequalities graphically and algebraically
Solving one-step linear inequalities
Solving multi-step linear inequalities
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Measuring Systems
Metric systems
Imperial systems
Conversions between metric and imperial systems
Conversions involve squares and cubic
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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
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Surds
Square and square roots
Cubic and cube roots
Evaluating and simplifying radicals
Converting radicals to mixed radicals
Converting radicals to entire radicals
Adding and subtracting surds
Multiplying and dividing surds
Rationalize the denominator
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Direct and Inverse Proportion
Direct variation
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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
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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
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
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: (a - b)(a + b) = (a^2 - b^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
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Solving Quadratic Equations
Solving quadratic equations by factorising
Solving quadratic equations by completing the square
Using quadratic formula to solve quadratic equations
The discriminant: Nature of roots of quadratic equations
Applications of quadratic equations
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Algeraic 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
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
video
Exponential Functions
Solving exponential equations using laws of indices
Graphing exponential functions
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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
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Matrices
Notation of matrices
Adding and subtracting matrices
Multiplying a matrix by a scalar
Multiplying a matrix by another matrix
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Geometry and Measurement
Parallel and perpendicular line segments
Perpendicular bisectors
Angle bisectors
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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
Classifying Triangles
Congruence and Congruent Triangles
Triangles Congruent by SSS Proofs
Triangles Congruent by SAS and HL Proofs
Triangles Congruent by ASA and AAS Proofs
Isosceles and Equilateral Triangles
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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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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
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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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Trigonometry
Use sine ratio to calculate angles and sides (Sin = oh \frac{o}{h}ho​ )
Use cosine ratio to calculate angles and sides (Cos = ah \frac{a}{h}ha​ )
Use tangent ratio to calculate angles and sides (Tan = oa \frac{o}{a}ao​ )
Combination of SohCahToa questions
Solving expressions using 45-45-90 special right triangles
Solving expressions using 30-60-90 special right triangles
Word problems relating ladder in trigonometry
Word problems relating guy wire in trigonometry
Other word problems relating angles in trigonometry
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Angle Measure in Radian
Converting between degrees and radians
Radian measure and arc length
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Sine Rule and Cosine Rule
Sine rule
Cosine rule
Sine rule and cosine rule word problems
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Bearings
Introduction to bearings
Bearings and direction word problems
Angle of elevation and depression
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Set Theory
Set notation
Set builder notation
Intersection and union of 2 sets
Intersection and union of 3 sets
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Data and Graphs
Reading and drawing bar graphs
Reading and drawing histograms
Reading and drawing line graphs
Box-and-whisker plots and scatter plots
Reading and drawing stem-and-leaf diagrams
Reading and drawing Venn diagrams
Frequency tables and dot diagrams
Pie charts
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Representing Data
Advantages and disadvantages of different graphs
Misleading graphs
Critiquing data presentation
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Statistics
Median and mode
Mean
Range and outliers
Application of averages
Standard deviation and variance
Z-score, quartiles, and percentiles
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Probability
Determining probabilities using tree diagrams and tables
Probability of independent events
Frequency distribution and histograms
Addition rule for "OR"
Multiplication rule for "AND"

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