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KINEMATICS

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Cambridge Mathematics IGCSE Core - Algebra

ALGEBRAIC EXPRESSIONS

Topic – Using Rules: Subtraction
Topic – Using Rules: Addition
Topic – Using Rules: Multiplication
Topic – Using Rules: Division
Topic – Using Rules: Multiply and Add
Topic – Using Rules: Multiply and Subtract
Topic – Using Rules: Add and Multiply
Topic – Using Rules: Multiply Itself
Topic – Using Rules: Missing Numbers involving Multiply and Add
Topic – Using Rules: Missing Numbers involving Multiply and Subtract
Topic – Using Rules: Missing Numbers involving Subtract and Divide

Writing and Finding Formulas

Topic – Rewriting Formula Leaving Out Multiplication Signs
Topic – Writing Formulas: Addition
Topic – Writing Formulas: Subtraction
Topic – Writing Formulas: Mixed Addition
Topic – Writing Formulas: Mixed Subtraction
Topic – Writing Formulas: Positive Coefficients and Addition
Topic – Writing Formulas: Positive Coefficients and Subtraction
Topic – Writing Formulas: Negative Coefficients and Addition
Topic – Writing Formulas: Negative Coefficients and Subtraction
Topic – Writing Formulas: Positive Coefficients
Topic – Writing Formulas: Negative Coefficients

Topic – Substitution to y = x + a Form
Topic – Substitution to y = a – x Form
Topic – Substitution to y = ax + b Form
Topic – Substitution to y = a (x + b) Form
Topic – Substitution to y = -a (x + b) Form
Topic – Substitution to y = a (x + b) + c Form
Topic – Substitution to y = a (b – x) + c Form
Topic – Substitution to ax + by Form
Topic – Substitution to Square Expressions

Problem Solving using Algebra

Topic – Problem Solving using Algebra 1
Topic – Problem Solving using Algebra 2
Topic – Problem Solving using Algebra 3

Expressions and Equations

Topic – Writing Mathematical Expressions
Topic – Writing Mathematical Expressions: True or False
Topic – Choose Matching Expressions
Topic – Match Mathematical Expressions
Topic – Writing Mathematical Expressions by Rules

Expanding Single Brackets

Video – Expanding Expressions (6:15)
Video – Expanding Single Brackets (4:27)
Video – Expansion of Single Brackets (4:58)
Video – Expansion of Single Brackets and Simplify (2:58)
Video – Expansion of two Single Brackets and Simplify (4:10)
Topic – Expand & Simplify: Coefficients Times Linear Binomial Terms
Topic – Expand & Simplify: Variables Times Linear Binomial Terms
Topic – Expand & Simplify: Coefficient Times Trinomials
Topic – Expand & Simplify: Variables Times Trinomials
Topic – Expand & Simplify: Quadratic Times Linear Binomial Terms
Topic – Expand & Simplify: Multiple Single Brackets
Topic – Expand & Simplify: Multiple Single Brackets with Variables
Topic – Expand and Simplify Linear Expressions

Expanding Pairs of Brackets

Video – Expanding and Simplifying Expressions (9:40)
Video – Expanding Formula of Binomial Algebraic Expressions (6:05)
Video – Expanding Pair of Brackets (4:19)
Video – Expanding Pair of Brackets and Additional Terms (9:52)
Video – Expanding with Trinomials (4:28)
Video – 2 by 3 Expansions (4:48)
Video – The Product of Two Linear Expressions (2:58)
Video – Expanding Pairs of Brackets (7:27)
Topic – Linear Times Linear
Topic – Linear Times Linear with Coefficients
Topic – Non-Monic Linear Times Non-Monic Linear
Topic – Non-Monic Linear Times Non-Monic Linear with Coefficients
Topic – Square of Linear Expressions
Topic – Square of Linear Expressions with Coefficients
Topic – Linear Times Quadratics
Topic – Linear Times Trinomials
Topic – Expand and Simplify Binomial Expressions
Topic – Expand and Simplify Cubic Expressions
Topic – Expand and Simplify Trinomial Expressions

Expanding Difference of Squares

Video – Expanding Difference of Squares (7:02)
Video – Expanding Difference of Two Squares (4:51)
Topic – Expand Difference of Squares: Variables & Constants
Topic – Expand Difference of Squares: Mixed Variables & Constants
Topic – Expand Difference of Squares: Constants & Variables
Topic – Expand Difference of Squares: Non-Monic Variables
Topic – Expand Difference of Squares: Multiplier
Topic – Expand Difference of Squares: Multiplier to Non-Monic Variables
Topic – Expand and Simplify the Difference of Squares

Perfect Square Expansions

Video – Basic Square Expansions (5:19)
Video – Further Square Expansions (6:37)
Video – Expanding with Squares (7:40)
Video – Expanding with Completed Squares (9:46)
Video – Expanding Perfect Squares (6:56)
Video – Basic Rules of Completing the Square (7:19)
Video – Completing the Square of Quadratic Expressions (3:52)
Topic – Expand Squares of Additions of Monic Expressions
Topic – Expand Squares of Subtractions of Monic Expressions
Topic – Expand Squares of Additions of Non-Monic Expressions
Topic – Expand Squares of Subtractions of Non-Monic Expressions
Topic – Expand Squares of Additions of Non-Monic Expressions with Coefficients
Topic – Expand Squares of Subtractions of Non-Monic Expressions with Coefficients
Topic – Expand & Simplify Squares

Algebraic Substitution

Video – Basic Substitution (11:17)
Video – Algebraic Substitution (4:20)
Video – Algebraic Substitution involving Indices (4:20)
Video – Substitutions into Surds (4:24)
Topic – Substitution to Additions & Subtractions
Topic – Substitution to Additions & Subtractions involving Multiplications
Topic – Substitution to Additions & Subtractions involving Divisions
Topic – Substitution to Additions & Subtractions involving Squares
Topic – Substitution to Additions & Subtractions involving Squares & Brackets
Topic – Substitution to Additions & Subtractions involving Squares & Binomial Terms
Topic – Substitution to Additions & Subtractions involving Cubes
Topic – Substitution to Mixed Expressions
Topic – Substitution to Square Roots

Formula Substitution

Video – Substitution into a Basic Formula (5:00)
Video – Substitution into Exponents Involving Formulae (2:20)
Video – Substitution into Rational Formulae (3:20)
Video – Substitution into Irrational Formulae (2:55)
Video – Equations Arising from Substitution 1 (4:19)
Video – Equations Arising from Substitution 2 (3:39)
Video – Evaluating Formula using Substitutions (4:49)
Topic – Formula Substitution of Linear Expressions
Topic – Formula Substitution of Approximation Values
Topic – Formula Substitution of Quadratic Expressions
Topic – Evaluating Values using Formula Substitution of Linear Expressions
Topic – Evaluating Values using Formula Substitution of Approximation Values
Topic – Evaluating Values using Formula Substitution of Quadratic Expressions

Formula Rearrangement

Video – Changing the Subject of a Formula (5:49)
Video – Changing the Subject on Both Sides (4:28)
Video – Changing the Subject involving Square Roots (2:53)
Video – Changing the Subject Involving Squares (2:04)
Video – Changing the Subject on Denominators (4:45)
Video – Changing the Subject on Both Numerators & Denominators (6:02)
Video – Rearrangement (6:55)
Topic – Rearranging Linear Formulas Subject to x
Topic – Rearranging Linear Formulas Subject to y
Topic – Rearranging Formulas involving Squares Subject to x
Topic – Rearranging Formulas involving Squares Subject to y
Topic – Rearranging Formulas involving Square Roots
Topic – Rearranging Formulas involving Multiple Variables

Factorising using Common Factors

Video – Factorising Expressions (10:07)
Video – Factorising & Negative Terms (3:41)
Video – Factorise by Common Factors (5:26)
Video – Factorise by Common Factors involving Brackets (5:15)
Video – Solving Quadratics by Common Factors (4:59)
Video – Understanding Factorise by Common Factors for Various Cases (3:07)
Video – Factorise by Common Factors for Various Cases (9:35)
Topic – Factorise using Common Factors
Topic – Factorise using Common Factors and Indices
Topic – Factorise Common Factors in Brackets
Topic – Factorise Common Factors in Brackets and Indices

Powers and Bases

Topic – Powers & Bases
Topic – Factor Form
Topic – Multiple Index Form
Topic – Writing Index Form from Normal Numerals
Topic – Writing Index by Factorising Normal Numerals in Two bases
Topic – Writing Index by Factorising Normal Numerals in Three Bases

Multiplication using Exponents

Video – Index Law of Addition (6:17)
Video – Index Equations using Index Law of Addition (3:17)
Video – Evaluation using Index Law of Addition (5:12)
Video – Simplification using Index Law of Addition (3:32)
Video – Addition Law of Exponents (4:12)
Video – Multiplication using Indices (3:32)
Topic – Equations by Adding Indices
Topic – Simplifying by Adding Indices
Topic – Evaluation by Adding Indices

Division using Exponents

Video – Simplification of Exponent in Fractions (2:24)
Video – Index Law of Subtraction (5:51)
Video – Simplification using Index Law of Subtraction (1:54)
Video – Mixed Simplification using Index Law of Subtraction (4:58)
Video – Evaluation using Index Law of Subtraction (4:14)
Video – Subtraction Law of Exponents (3:26)
Video – Division using Indices (5:20)
Topic – Simplifying by Subtracting Indices
Topic – Simplifying by Adding and Subtracting Indices
Topic – Evaluation by Subtracting Indices

Video – Index Law of Zero Power (5:52)
Video – Further Index Law of Zero Power (3:58)
Video – Zero Exponents (2:26)
Video – Index Equations Involving Zero Indices (1:45)
Topic – Zero Indices

Raising a Power to Another Power

Video – Index Law of Powers (4:35)
Video – Simplification using Index Law of Powers (6:53)
Video – Evaluation using Index Law of Powers (6:37)
Video – Index Law of Raising a Power to Another Power (4:19)
Video – Raising a Power to Another Base (5:27)
Video – Raising a Power to Another Indices (5:56)
Topic – Equations involving Power of Power
Topic – Simplifying by Power of Power

LINEAR EQUATIONS

What is a Linear Equation?

Topic – Identifying Linear Equations
Topic – Converting Worded Equations to Algebraic Equations
Topic – Equations Matching Statements

Basic Linear Equations

Video – One Step Equations (3:26)
Check – One Step Equations
Video – Two Step Equations (2:58)
Video – Equations with Variables on Both Sides (2:47)
Video – Basic Linear Equations 1 (2:52)
Video – Basic Linear Equations 2 (3:46)
Video – Basic Linear Equations 3 (2:46)
Video – Linear Equations (4:25)
Topic – Linear Equations involving Subtractions
Topic – Linear Equations involving Additions
Topic – Linear Equations involving Multiplications
Topic – Linear Equations involving Divisions
Topic – Linear Equations involving Multiplications & Divisions
Topic – Non-Monic Linear Equations
Topic – Linear Equations involving Brackets

Linear Equations Involving Expansions

Video – Equations with Brackets (3:21)
Video – Equations with Pronumerals on Both Sides 1 (3:19)
Video – Equations with Pronumerals on Both Sides 2 (4:29)
Video – Equations with Grouping Symbols 1 (5:51)
Video – Equations with Grouping Symbols 2 (4:37)
Topic – Linear Equations involving Single Brackets
Topic – Linear Equations involving Single Non-Monic Brackets
Topic – Linear Equations involving Single Brackets & Extra Variables
Topic – Linear Equations involving Multiple Brackets
Topic – Linear Equations involving Multiple Non-Monic Brackets
Topic – Linear Equations involving Squares

Linear Equations Involving Fractions

Video – Solving Equations involving Fractions (4:47)
Video – Equations with One Fraction 1 (5:18)
Video – Equations with One Fraction 2 (5:01)
Video – Equations with Multiple Fractions 1 (6:31)
Video – Equations with Multiple Fractions 2 (6:59)
Video – Equations With Single Pronumerals In The Denominator (2:28)
Video – Equations With Multiple Pronumerals In The Denominator (7:40)
Video – Equations With Compound Pronumerals In The Denominator (3:01)
Video – Equations With Compound Pronumerals In Both Denominators and Numerators (2:39)
Video – Linear Equations with Fractions 1 (5:45)
Video – Linear Equations with Fractions 2 (4:01)
Video – Linear Equations with Fractions: Variables in Denominators (3:37)
Video – Linear Equations with Fractions: Variables in Numerators & Denominators (2:20)
Video – Linear Inequalities involving Fractions (4:35)
Topic – Linear Equations involving Single Fractions
Topic – Linear Equations involving Single Non-Monic Fractions
Topic – Linear Equations involving Two Fractions
Topic – Linear Equations involving Variables in Both Numerators & Denominators

Problem Solving with Linear Equations

Video – Applications of Equations (6:36)
Video – Equations and Formulae (5:10)
Video – Equations and Geometry (3:35)
Video – Problem Solving with Linear Equations: Numbers (8:44)
Video – Problem Solving with Linear Equations: Ages (3:17)
Video – Problem Solving with Linear Equations: Coins (2:47)
Topic – Problem Solving involving Averages
Topic – Problem Solving involving Arithmetic
Topic – Problem Solving involving Sum
Topic – Problem Solving involving Costs
Topic – Problem Solving involving Geometry
Topic – Problem Solving involving Age
Topic – Problem Solving involving Speed

SIMULTANEOUS EQUATIONS

Linear Simultaneous Equations - Elimination Method

Video – Elimination Method for Simultaneous Equations (3:32)
Video – Elimination Method for Simultaneous Equations by Subtraction (4:29)
Video – Elimination Method for Simultaneous Equations by Addition (3:25)
Video – Elimination Method by Manipulating One Pronumeral (6:40)
Video – Elimination Method by Manipulating Two Pronumerals 1 (3:31)
Video – Elimination Method by Manipulating Two Pronumerals 2 (1:49)
Video – Elimination Method by Manipulating Two Pronumerals 3 (2:15)
Video – Simultaneous Equations by Elimination Method (7:42)
Video – Simultaneous Equations: Elimination Method (5:53)
Topic – Elimination Method by Subtracting Equations
Topic – Elimination Method by Adding Equations
Topic – Elimination Method by Considering One Coefficient
Topic – Elimination Method by Considering Two Coefficients

Linear Simultaneous Equations - Substitution Method

Video – Equation Method for Simultaneous Equations (2:16)
Video – Basic Substitution Method for Simultaneous Equations (6:43)
Video – Substitution Method for Simultaneous Equations (7:48)
Video – Simultaneous Equations by Substitution Method (5:26)
Video – Simultaneous Equations: Substitution Method (3:00)
Topic – Basic Substitution Method
Topic – Substitution Method by Non-Monic Equations
Topic – Substitution Method by Equating Equations
Topic – Substitution Method by Rearranging Equations
Topic – Substitution Method by Rearranging Non-Monic Equations

Numerical Application of Linear Simultaneous Equations

Video – Number Applications of Simultaneous Equations 1 (2:58)
Video – Number Applications of Simultaneous Equations 2 (2:54)
Video – Number Applications of Simultaneous Equations 3 (2:11)
Video – Number Applications of Simultaneous Equations 4 (1:42)
Video – Digit Applications of Simultaneous Equations (8:33)
Video – Coin Value Applications of Simultaneous Equations 1 (3:12)
Video – Coin Value Applications of Simultaneous Equations 2 (2:52)
Video – Age Applications of Simultaneous Equations 1 (2:04)
Video – Age Applications of Simultaneous Equations 2 (3:51)
Video – Geometry Applications of Simultaneous Equations 1 (3:14)
Video – Geometry Applications of Simultaneous Equations 2 (3:13)
Video – Cost Applications of Simultaneous Equations 1 (2:59)
Video – Cost Applications of Simultaneous Equations 2 (2:01)
Video – Measurement Applications of Simultaneous Equations (2:23)
Video – Review Problem Solving of Simultaneous Equations (6:09)

NUMBER SEQUENCES

Number Sequences

Video – Number Sequences (2:23)
Video – Describing Number Sequences (4:06)
Topic – Descriptions of Number Sequences
Topic – Writing Terms from Patterns
Topic – Pattern of Number Sequences by Adding or Subtracting
Topic – Pattern of Number Sequences by Multiplying or Dividing
Topic – Pattern of Number Sequences involving Indices

Describing Sequences

Topic – Evaluation of Following Terms from Patterns
Topic – Evaluation of Terms using Rules

General Term of a Number Sequence

Video – General Term of a Number Sequence (5:54)
Topic – Term Values from General Terms
Topic – Term Values from General Terms involving Indices
Topic – Term Values from General Terms involving Indices and Bases

QUADRATIC GRAPHS

Quadratic Graphs from Tables of Values

Video – Sketching Parabolas from Tables: Concave Upwards (3:34)
Video – Sketching Parabolas from Tables: Concave Downwards (2:52)

Quadratic Graphs Vertices Origin

Video – Graphs of Parabola Vertex at the Origin (5:12)
Topic – Quadratics Vertices at Origin
Topic – Quadratics Vertices at Origin and Passing Points

Quadratic Graphs Up Down

Video – Graphs of Parabola Shift Up Down (6:10)
Video – Sketching Parabolas from Tables: Concavity (2:36)

Parabola Touches X-axis

Video – Parabola Touches X-axis Upwards (4:36)
Video – Parabola Touches X-axis Downwards (3:01)

Parabola in Vertex Form

Video – Vertex and Intercepts of Parabola (4:10)
Video – Parabola in Vertex Form Upwards (5:30)
Video – Parabola in Vertex Form Downwards (4:51)

Parabola in Intercept Form

Video – Parabola in Intercept Form Upwards (2:09)
Video – Parabola in Intercept Form Downwards (2:15)

X-intercept Y-intercept

Video – Graphs of Parabola x-intercepts and y-intercepts (5:58)
Video – Graphs of Parabola using Quadratic Formula (4:30)
Video – Sketching Parabola (3:29)
Video – Graphs of Parabola Concave Downwards with No x-intercepts (6:27)
Video – Transformation of Parabola Up Down (6:59)
Video – Quadratic Graphs: Axes Intercepts (11:25)

Axis of Symmetry

Video – Axis of Symmetry (6:45)
Topic – Axis of Symmetry on the Right and Concave Up
Topic – Axis of Symmetry on the Left and Concave Up
Topic – Axis of Symmetry on the Right and Concave Down
Topic – Axis of Symmetry on the Left Hand and Concave Down
Topic – Axis of Symmetry Non-Monic Quadratics

Vertex of a Parabola

Video – Vertex on the Left Side (4:25)
Video – Vertex on the Right Side (1:33)
Video – Non-Monic Parabola Downwards (1:56)
Video – Non-Monic Parabola Upwards (3:14)

Quadratic Graphs by Completing the Square

Video – Finding Vertex using Completing Square (3:12)
Video – Sketching Parabola in Left Side by Completing Square (6:13)
Video – Sketching Parabola in Right Side by Completing Square (2:28)
Video – Sketching Parabola Concave Down by Completing Square (3:39)
Video – Sketching Non-Monic Parabola Concave Up by Completing Square (3:15)
Video – Sketching Non-Monic Parabola Concave Down by Completing Square (2:26)
Video – Graphs of Parabola Concave Upwards with No x-intercepts (5:16)
Video – Translating Graphs of Quadratic Functions (2:15)

Displacement-Time Graphs

Video – Time-Distance Graphs: Return Trip (9:06)
Video – Time-Distance Graphs: One Way Trip (4:06)
Video – Description of Behaviours by Time-Distance Graphs (2:32)
Video – Displacement-time Graphs (8:46)
Video – Displacement-Velocity Graphs: Lines (7:12)
Video – Displacement-Velocity Graphs: Curves (6:09)

Velocity-Time Graphs

Video – Kinematics: Parabolic Velocity Graphs (3:48)
Video – Velocity-Time Graphs: Straight Lines 1 (5:15)
Check – Velocity-Time Graphs: Straight Lines 1
Video – Velocity-Time Graphs: Straight Lines 2 (4:19)
Video – Velocity-Time Graphs: Straight Lines 3 (7:20)
Video – Velocity-Time Graphs: Piecewise Graphs 1 (4:24)
Video – Velocity-Time Graphs: Piecewise Graphs 2 (4:34)
Video – Velocity-Time Graphs: Piecewise Graphs 3 (6:19)
Video – Velocity-Time Graphs: Curves (7:18)

Acceleration-Time Graphs

Video – Acceleration-Time Graphs: Concave Downwards (8:27)
Video – Acceleration-Time Graphs: Concave Upwards (6:43)

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