Grade 10 Advanced Maths – Revision Taster Course


Grade 10 Maths Complete Revision Guide: Ideal for K-12, SG and UAE curriculums (free taster course)

What you will learn

Linear Systems and Matrices

Quadratic Functions and Relations

Polynomials and Polynomial Functions

Inverses and Radical Functions and Relations

Circles

Transformations and Symmetry

Probability and Measurement

Exponential and Logarithmic Functions and Relations

Rational Functions and Relations

Trigonometric Functions

Trigonometric Identities and Equations

Sequences and Series

Description

(Please read carefully)

Welcome to this Grade 10 Mathematics revision course and thanks for choosing to learn with us.

This course follows the Grade 10 mathematics syllabus the K-12, Singapore and United Arab Emirates (UAE) curriculum. It is designed for adults who can work with their children if they are falling behind or have missed lessons in school.

If you are the parent of a current student, you will more than likely be aware of the amount of material that needs to be learned – and in such a short space of time too. This course has been designed with the primary purpose of breaking down all of the material into simpler pieces, which are both clear and easy to understand, thus making the overall learning process much more enjoyable as opposed to being somewhat overwhelming.

If your son or daughter finds mathematics to be challenging, you will see that the course starts by introducing the prerequisite topics that will help them in this course. These include solving simple systems of equations and drawing straight lines. These are certainly very handy if your son or daughter has just returned from their school break and need to have their memories given a quick refresh. This course has been tried and tested on students in both online and face to face settings – and the improvements made have been quite significant.

Every lesson will have a number of questions for students to do at the end. The questions vary in difficulty and have been specially designed to ensure that they have a good understanding of the relevant topics. There will also be a final test at the end of each section to see how much they’ve learned. Don’t worry if they get some of the answers incorrect – the topic(s) they need to revisit will be shown at the end of the question along with the correct answers. The course is also suitable for the more able mathematician who just needs some extra practice for their exam.


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Important Points:

Please kindly note that this is a course designed to help individuals quickly and effectively improve upon their mathematics. This course refers to mathematics which is normally taught to students in Grade 10. In some instances, depending on the syllabus, it may be taught at a later grade, or possibly not even at all. Please kindly check that this area of mathematics is on your son or daughter’s syllabus before joining this course.

We hope this course will prove to be useful and we welcome any positive feedback or suggestions on how it can be improved.

The majority of proceedings from this course will go to charity.

English
language

Content

Introduction

Course Introduction
Introductory Lesson: Simple Equations

Linear Systems and Matrices

Lesson 1: Simple Systems of Equations (Prerequisite Lesson)
Lesson 2: Drawing a Straight Line on a Graph (Prerequisite Lesson)
Lesson 3: Graphing Linear Inequalities (Prerequisite Lesson)
Lesson 4: Solving Systems of Equations
Lesson 5: Solving Systems of Inequalities
Lesson 6: Linear Programming
Lesson 7: Systems of Equations in Three Variables
Lesson 8: Looking at Matrices
Lesson 9: Operations with Matrices
Lesson 10: Multiplying Matrices
Lesson 11: Solving Systems using Cramer’s Rule
Lesson 12: Solving Systems using Inverse Matrices
Lesson 13: Practice Questions

Quadratic Functions and Relations

Lesson 1: Algebraic Expressions (Prerequisite Lesson)
Lesson 2: Graphing Quadratic Functions
Lesson 3: Solving Quadratics by Graphing
Lesson 4: Solving Quadratics by Factoring
Lesson 5: Complex Numbers
Lesson 6: Completing the Square
Lesson 7: Using the Quadratic Formula
Lesson 8: Transformations of Quadratic Graphs
Lesson 9: Quadratic Inequalities
Lesson 10: Practice Questions

Polynomials and Polynomial Functions

Lesson 1: Operations with Polynomials
Lesson 2: Division of Polynomials
Lesson 3: Polynomial Functions
Lesson 4: Graphs of Polynomial Functions
Lesson 5: Solving Polynomial Equations
Lesson 6: The Remainder and Factor Theorems
Lesson 7: Roots and Zeros
Lesson 8: The Rational Zero Theorem
Lesson 9: Practice Questions

Inverses and Radical Functions and Relations

Lesson 1: Operations on Functions
Lesson 2: Inverse Functions and Relations
Lesson 3: Square Root Functions
Lesson 4: nth Roots
Lesson 5: Operations with Radical Expressions
Lesson 6: Rational Exponents
Lesson 7: Radical Equations and Inequalities
Lesson 8: Practice Questions

Circles

Lesson 1: Solving Simple Equations (Prerequisite Lesson)
Lesson 2: Solving Quadratic Equations (Prerequisite Lesson)
Lesson 3: Looking at Triangles (Prerequisite Lesson)
Lesson 4: Circles and Circumference
Lesson 5: Measuring Angles and Arcs
Lesson 6: Arcs and Chords
Lesson 7: Inscribed Angles
Lesson 8: Tangents of Circles
Lesson 9: Secants, Tangents and Angle Measures
Lesson 10: Special Segments in a Circle
Lesson 11: Equations of Circles
Lesson 12: Areas of Circles and Sectors
Lesson 13: Practice Questions

Transformations and Symmetry

Lesson 1: Reflections
Lesson 2: Translations
Lesson 3: Rotations
Lesson 4: Compositions of Transformations
Lesson 5: Symmetry
Lesson 6: Dilations
Lesson 7: Practice Questions

Probability and Measurement

Lesson 1: Representing Sample Spaces
Lesson 2: Permutations and Combinations
Lesson 3: Geometric Probability
Lesson 4: Simulations
Lesson 5: Independent and Dependent Events
Lesson 6: Mutually Exclusive Events
Lesson 7: Practice Questions

Exponential and Logarthmic Functions and Relations

Lesson 1: Graphing Exponential Functions
Lesson 2: Solving Exponential Equations
Lesson 3: Logarithms and Logarithmic Functions
Lesson 4: Solving Logarithmic Equations
Lesson 5: Properties of Logarithms
Lesson 6: Common Logarithms
Lesson 7: Base e and Natural Logarithms
Lesson 8: Exponential and Logarithmic Functions
Lesson 9: Practice Questions

Rational Functions

Lesson 1: Operations with Rational Expressions
Lesson 2: Adding and Subtracting Expressions
Lesson 3: Graphing Reciprocal Functions
Lesson 4: Graphing Rational Functions
Lesson 5: Variation Functions
Lesson 6: Rational Equations and Inequalities
Lesson 7: Practice Questions

Trigonometric Functions

Lesson 1: Right Angle Trigonometry
Lesson 2: Degrees and Radians
Lesson 3: Trigonometric Functions of Angles
Lesson 4: The Law of Sines (Sine Rule)
Lesson 5: The Law of Cosines (Cosine Rule)
Lesson 6: Circular and Periodic Functions
Lesson 7: Graphing Trigonometric Functions
Lesson 8: Graphing Reciprocal Functions
Lesson 9: Inverse Trigonometric Functions
Lesson 10: Practice Questions

Trigonometric Identities and Equations

Lesson 1: Trigonometric Identities
Lesson 2: Verifying Trigonometric Identities
Lesson 3: Sum and Difference Identities
Lesson 4: Double-Angle and Half-Angle Identities
Lesson 5: Solving Trigonometric Equations
Lesson 6: Practice Questions

Sequences and Series

Lesson 1: Introduction to Sequences (Prerequisite Lesson)
Lesson 2: Arithmetic Sequences and Series
Lesson 3: Geometric Sequences and Series
Lesson 4: Infinite Geometric Series
Lesson 5: Sequences as Functions
Lesson 6: Recursion and Iteration
Lesson 7: Practice Questions

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