Master GCSE and iGCSE Maths: Algebra, Functions & Graphs

This is a High School Mathematics Course for Students Preparing for iGCSE, GCSE & Secondary School Maths Exams

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Udemy
platform
English
language
Math
category
instructor
3
students
12 hours
content
May 2022
last update
$24.99
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What you will learn

In this course students will learn exactly what they need to know for their high school maths exams using the GCSE maths and iGCSE maths curricula.

This course covers many GCSE maths and IGCSE maths curricula including Cambridge CIE 0580 (Core & Extended) and Pearson Edexcel Maths A (Foundation & Higher)

The details of the content covered are as follows:

Use letters to express generalised numbers and express basic arithmetic processes algebraically. Substitute numbers for words and letters in formulae.

Use letters to express generalised numbers and express basic arithmetic processes algebraically. Substitute numbers for words and letters in formulae.

Rearrange simple formulae.

Construct simple expressions and set up simple equations.

Manipulate directed numbers. Use brackets and extract common factors.

Expand products of algebraic expressions.

Use and interpret positive, negative and zero indices. Use the rules of indices.

Derive and solve simple linear equations in one unknown. Derive and solve simultaneous linear equations in two unknowns.

Use letters to express generalised numbers and express basic arithmetic processes algebraically.

Construct and rearrange complicated formulae and equations.

Manipulate directed numbers. Use brackets and extract common factors.

Expand products of algebraic expressions.

Manipulate algebraic fractions. Factorise and simplify rational expressions.

Use and interpret positive, negative and zero indices. Use and interpret fractional indices. Use the rules of indices.

Derive and solve linear equations in one unknown. Derive and solve simultaneous linear equations in two unknowns.

Derive and solve simultaneous equations, involving one linear and one quadratic.

Derive and solve quadratic equations by factorisation, completing the square and by use of the formula. Derive and solve linear inequalities.

Continue a given number sequence. Recognise patterns in sequences including the term to term rule and relationships between different sequences.

Interpret and use graphs in practical situations including travel graphs and conversion graphs. Draw graphs from given data.

Draw and interpret these graphs. Solve linear and quadratic equations approximately, including finding and interpreting roots by graphical methods.

Recognise, sketch and interpret graphs of functions.

Represent inequalities graphically and use this representation to solve simple linear programming problems.

Continue a given number sequence. Recognise patterns in sequences including the term to term rule and relationships between different sequences.

Express direct and inverse proportion in algebraic terms and use this form of expression to find unknown quantities.

Interpret and use graphs in practical situations including travel graphs and conversion graphs. Draw graphs from given data.

Apply the idea of rate of change to simple kinematics involving distance–time and speed–time graphs, acceleration and deceleration.

Calculate distance travelled as area under a speed–time graph.

Solve associated equations approximately, including finding and interpreting roots by graphical methods.

Draw and interpret graphs representing exponential growth and decay problems. Recognise, sketch and interpret graphs of functions.

Estimate gradients of curves by drawing tangents.

Discriminate between maxima and minima by any method.

Understand that symbols may be used to represent numbers in equations or variables in expressions and formulae.

Understand that algebraic expressions follow the generalised rules of arithmetic.

Use index notation for positive and negative integer powers (including zero).

Use index laws in simple cases.

Evaluate expressions by substituting numerical values for letters.

Collect like terms.

Multiply a single term over a bracket.

Take out common factors.

Expand the product of two simple linear expressions.

Understand that a letter may represent an unknown number or a variable.

Use correct notational conventions for algebraic expressions and formulae.

Substitute positive and negative integers, decimals and fractions for words and letters in expressions and formulae.

Use formulae from mathematics and other real-life contexts expressed initially in words or diagrammatic form and convert to letters and symbols.

Derive a formula or expression.

Change the subject of a formula where the subject appears once.

Solve linear equations, with integer or fractional coefficients, in one unknown in which the unknown appears on either side or both sides of the equation.

Set up simple linear equations from given data.

Calculate the exact solution of two simultaneous equations in two unknowns.

Solve quadratic equations by factorisation (limited to x2 + bx + c = 0).

Understand and use the symbols >,<.

Understand and use the convention for open and closed intervals on a number line.

Solve simple linear inequalities in one variable and represent the solution set on a number line.

Represent simple linear inequalities on rectangular Cartesian graphs.

Identify regions on rectangular Cartesian graphs defined by simple linear inequalities.

Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence.

Find subsequent terms of an integer sequence and the rule for generating it.

Use linear expressions to describe the nth term of arithmetic sequences.

Interpret information presented in a range of linear and non-linear graphs.

Understand and use conventions for rectangular Cartesian coordinates.

Plot points (x, y) in any of the four quadrants or locate points with given coordinates.

Determine the coordinates of points identified by geometrical information.

Determine the coordinates of the midpoint of a line segment, given the coordinates of the two end points.

Draw and interpret straight line conversion graphs.

Find the gradient of a straight line.

Recognise that equations of the form y = mx + c are straight line graphs with gradient m and intercept on the y-axis at the point (0, c).

Recognise, generate points and plot graphs of linear and quadratic functions.

Use index notation involving fractional, negative and zero powers.

Expand the product of two or more linear expressions.

Understand the concept of a quadratic expression and be able to factorise such expressions.

Manipulate algebraic fractions where the numerator and/or the denominator can be numeric, linear or quadratic.

Complete the square for a given quadratic expression.

Use algebra to support and construct proofs.

Understand the process of manipulating formulae or equations to change the subject.

Set up problems involving direct or inverse proportion and relate algebraic solutions to graphical representation of the equations.

Calculate the exact solution of two simultaneous equations in two unknowns.

Interpret the equations as lines and the common solution as the point of intersection.

Solve quadratic equations by factorisation.

Solve quadratic equations by using the quadratic formula or completing the square.

Form and solve quadratic equations from data given in a context.

Solve simultaneous equations in two unknowns, one equation being linear and the other being quadratic.

Solve quadratic inequalities in one unknown and represent the solution set on a number line.

Identify harder examples of regions defined by linear inequalities.

Understand and use common difference (d) and first term (a) in an arithmetic sequence.

Know and use nth term =+ − an d.

Find the sum of the first n terms of an arithmetic series (Sn).

Understand the concept that a function is a mapping between elements of two sets.

Understand the terms ‘domain’ and ‘range’ and which values may need to be excluded from a domain.

Understand and find the composite function fg and the inverse function f -1.

Recognise, plot and draw graphs.

Apply to the graph of y = f(x) the transformations y = f(x) + a, y = f(ax), y = f(x + a), y = af(x) for linear, quadratic, sine and cosine functions.

Interpret and analyse transformations of functions and write the functions algebraically.

Find the gradients of non-linear graphs.

Find the intersection points of two graphs, one linear 1 ( ) y and one non-linear 2 ( ) y , and and recognise that the solutions.

Calculate the gradient of a straight line given the coordinates of two points.

Find the equation of a straight line parallel to a given line; find the equation of a straight line perpendicular to a given line.

Understand the concept of a variable rate of change.

Differentiate integer powers of x.

Determine gradients, rates of change, stationary points, turning points (maxima and minima) by differentiation and relate these to graphs.

Distinguish between maxima and minima by considering the general shape of the graph only.

Apply calculus to linear kinematics and to other simple practical problems.

Description

Hello Students and Parents! 

THIS COURSE IS FOR YOU IF YOU (OR YOUR CHILD) WANT TO:

  • Master iGCSE Mathematics, GCSE Mathematics or Secondary School Mathematics.

  • Master Mathematics aimed at students aged 14-16 in Year 10-11 (Grade 9-10) at school.

  • Master the fundamentals of Mathematics.

Do you need help learning iGCSE Mathematics or GCSE Mathematics in a hurry? 

This course will give students the skills they need to feel confident and prepared for their maths exams. All concepts are explained clearly and concisely to ensure that students have the best opportunity to do well in your exams at short notice. Importantly, this course will also prepare students to study beyond (i)GCSE level to courses like A-level mathematics and IB Diploma Program mathematics.


Full iGCSE syllabus details are available within the course in a downloadable file for the CIE Cambridge and Pearson Edexcel exam boards.


This course (Part 1 of 4) covers all of the material studied in iGCSE mathematics and GCSE mathematics courses in the topics of ADD MAJOR TOPICS.

As soon as you sign up for this iGCSE Maths and GCSE Maths masterclass you will receive access to:

  1. NEW and updated iGCSE Maths & GCSE Maths video lessons for each section of the course.

  2. FREE digital iGCSE Maths resources, summary sheets and practice questions (with model answers provided).

  3. FREE topic-specific iGCSE Maths past exam paper questions and mark schemes.

This iGCSE Maths (O Level maths) masterclass is offered by IGCSEprep on Udemy. This masterclass covers all the content needed to write the IGCSE Maths exams offered by Pearson Edexcel (Foundation or Higher) or Cambridge CIE (Core or Extended) or other exam boards like Oxford AQA.

Screenshots

Master GCSE and iGCSE Maths: Algebra, Functions & Graphs - Screenshot_01Master GCSE and iGCSE Maths: Algebra, Functions & Graphs - Screenshot_02Master GCSE and iGCSE Maths: Algebra, Functions & Graphs - Screenshot_03Master GCSE and iGCSE Maths: Algebra, Functions & Graphs - Screenshot_04

Content

Introduction

How to use the Course Materials
Cambridge Official Resources
Edexcel Official Resources

Algebraic Manipulation

Algebraic Manipulation Pre-Check
Collecting Like Terms
Multiplying & Dividing Terms
Expanding Single Brackets
Factorising Single Brackets
Expanding Double Brackets
Factorising Double Brackets
Expanding Triple Brackets
Algebraic Manipulation Post-Check

Solving Equations

Solving Equations Pre-Check
Solving Two-Step Equations
Variables on Both Sides
Forming Equations
Dealing with Fractions
Fractions on Both Sides
Solving Equations Post-Check

Coordinate Geometry

Coordinate Geometry Pre-Check
Vertical & Horizontal Lines
Plotting Linear Graphs
Sketching Linear Graphs
Finding the Gradient
Distance Between Two Points
Equation of a Line
Midpoint of a Line
Parallel Lines
Perpendicular Lines
Coordinate Geometry Post-Check

Inequalities

Inequalities Pre-Check
Inequalities on a Number Line
Combining Inequalities
Solving Inequalities
Solving Two-Sided Inequalities
Graphing Inequalities
Inequalities Post-Check

Laws of Indices

Laws of Indices Pre-Check
Multiplying & Dividing Indices
Negative Indices
Fractional Indices
More Difficult Indices
Changing Bases (not uploaded)
Laws of Indices Post-Check

Formulae

Formulae Pre-Check
Substitution
Rearranging Simple Formulae
Powers, Roots & Fractions
Rearranging Difficult Formulae
Formulae Post-Check

Introduction to Quadratics

Introduction to Quadratics Pre-Check
Solving by Factorisation
Sketching Quadratics
Quadratic Formula
Introduction to Quadratics Post-Check

Simultaneous Equations

Solving Graphically
Linear by Elimination (Part 1)
Linear by Elimination (Part 2)
Linear by Substitution
Quadratic by Substitution

Sequences (Pearson)

Generating a Sequence
Nth Term of a Sequence
Sum of a Sequence

Sequences (CIE)

Generating a Sequence
Linear Sequences
Quadratic Sequences
Cubic Sequences
Geometric Sequences

Graphs of Polynomials

Recognising Graphs
Plotting Quadratic Graphs
Plotting Cubic & Reciprocal Graphs
Estimating Solutions
Exponential Graphs (CIE only)

Functions

Function Notation
Composite Functions
Inverse Functions
Domain & Range (Pearson only)

Proportion

Proportion Pre-Check
Direct Proportion
Inverse Proportion (Part 1)
Inverse Proportion (Part 2)
Proportion Post-Check

Advanced Quadratics

Factorising Harder Quadratics
Completing the Square (Part 1)
Completing the Square (Part 2)
Quadratic Inequalities

Algebraic Fractions

Simplifying Algebraic Fractions
Multiplying & Dividing
Adding & Subtracting
Solving Algebraic Fractions

Calculus

Gradient of a Tangent
Differentiating Expressions
Using the Gradient Function
Applying Differentiation

Algebraic Proof (Pearson only)

Prove That Questions
Show That Questions
Odd & Even Proofs

Related Topics

4454752
udemy ID
12/21/2021
course created date
5/14/2022
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