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Master Slope and Equation of Tangent Lines | Calculus Guide

GCE N(A)-Level A Maths: Master Key Concepts & Skills

Linear Inequalities

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Express linear inequalities graphically and algebraically

Graph the Inequality

Linear Inequalities – Word Problem 

Linear inequalities

Solving one-step linear inequalities

One-step Linear Inequalities

One-step linear inequalities

One-step Linear Inequalities Decimal

One-step Linear Inequalities Decimal with Fraction

One-step Linear Inequalities Fraction

Solve One Step Linear Inequalities Find Solution– Word Problem

One-step Linear Inequalities — Word Problem

Solving multi-step linear inequalities

Multi-step Linear Inequalities

Two-step Linear Inequalities

Multi-step linear inequalities

Two-step linear inequalities

Solve Multi-step Linear Inequalities – Word Problem 

Solve Multi Step Linear Inequalities Solve Equation – Word Problem

Solve Multi Step Linear Inequalities Equation – Word Problem

Algebraic Expressions

Equivalent algebraic expressions

Equivalent expressions of polynomials

Adding and subtracting algebraic expressions

Adding and subtracting polynomials

Multiplying monomial by monomial

Multiply a Monomial by a Monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Applications of algebraic expressions

Applications of polynomials

Linear Functions

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Gradient equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Gradient intercept form: y = mx + b

Slope intercept form: y = mx + b

General form: Ax + By + C = 0

Gradient-point form: \(y - y_1 = m (x - x_1)\)

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

Rate of change

Applications of linear relations

Simultaneous Equations

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

Determining number of solutions to linear equations

Solving simultaneous linear equations by graphing

Solving systems of linear equations by graphing

Solving simultaneous linear equations by elimination

Solving systems of linear equations by elimination

Solving simultaneous linear equations by substitution

Solving systems of linear equations by substitution

Factorisation

Factorising difference of cubes: \(a^3-b^3\)

Factoring difference of cubes

Factorising sum of cubes: \(a^3+b^3\)

Factoring sum of cubes

Factorising perfect square trinomials:&nbsp;(a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Factoring perfect square trinomials

Factorise by taking out the greatest common factor

Factor by taking out the greatest common factor

Factor by taking out GCF

Factorise by grouping

Factor by grouping

Factorising difference of squares: x^2 - y^2

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factorise trinomials

Factoring trinomials

Factoring Trinomials

Solving polynomials with unknown coefficients

Solving polynomials with unknown constant terms

Quadratic Functions

Introduction to quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Quadratic function in vertex form: y = a(x-p)^2 + q

Completing the square

Completing the Square

Quadratic Equations and Inequalities

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Solving a quadratic equation with TWO REAL SOLUTIONS

Solving a quadratic equation with TWO COMPLEX SOLUTIONS

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

Solving quadratic inequalities

Surds

Solving equations with surds

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

Conversion between entire radicals and mixed radicals

Adding and subtracting surds

Adding and subtracting radicals

Combining Like Radicals

Adding and Subtracting Radicals

Multiplying surds

Multiplying Radicals

Multiplying radicals

Operations with surds

Operations with radicals

Operations with Radicals

Square and square roots

Square Root of a Perfect Square

Cubic and cube roots

Cube root of a perfect cube

Rationalize the denominator 

Solving Simultaneous Equations

Solving 3 variable systems of equations by substitution

Solving 3 variable systems of equations by elimination

Word problems relating 3 variable systems of equations

Solving 3 variable systems of equations with no solution, infinite solutions

Solving 3 variable systems of equations (no solution, infinite solutions)

System of Equations With No Solution

System of Equations With Infinite Solutions

System of Equations With Infinite Solutions - Extended

System of linear equations

System of linear-quadratic equations

System of quadratic-quadratic equations

Laws of Indices

Indices: Product rule (a^x)(a^y) = a^(x+y)

Exponents: Product rule (a^x)(a^y) = a^(x+y)

Indices: Division rule (a^x / a^y) = a^(x-y)

Exponents: Division rule: a^x / a^y = a^(x-y)

Indices: Power rule (a^x)^y = a^(x * y)

Exponents: Power rule: (a^x)^y = a^(xy)

Exponents: Power rule

Negative indices

Exponents: Negative exponents

Zero index: a^0 = 1

Exponents: Zero exponent: a^0 = 1

Rational indices

Exponents: Rational exponents

Standard form

Scientific notation

Algebraic Fractions

Solving equations with algebraic fractions

Solving rational equations

Simplifying algebraic fractions and restrictions

Simplifying rational expressions and restrictions

Adding and subtracting algebraic fractions

GCE N(A)-Level A Maths

math

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