Mastering Maths Step by Step for Grade 8

Hard Copy ISBN 978– 0– 620– 67033– 3

eBook ISBN 978– 0– 620– 68647– 1

Contents

Symbols used in Mathematics (Basic):

Summary of Our Number System

Common Fractions

Decimals, Decimal Numbers and Percentages

Our Number System

Natural numbers or counting numbers (ℕ)

Whole numbers (ℕ0)

Integers (ℤ)

Rational Numbers (ℚ)

Irrational Numbers (ℚ1)

Real Numbers – (ℝ)

Our number system in diagram form:

Our number system in table form:

Properties of Addition

Addition is commutative:

Addition is the inverse of subtraction:

Addition is associative:

Properties of Subtraction

Subtraction is not commutative:

Subtraction is the inverse of addition:

Properties of Multiplication

Multiplication is Commutative:

Multiplication can be grouped:

Multiplication can be broken up:

Numbers multiplied by zero:

Properties of Division

Assigning Letters for Numbers – Introduction to Algebra

Solving for x and y etc

Properties of Expressions

Terms:

Coefficient:

Like and Unlike Terms

Like Terms

Unlike Terms

Combining Like Terms

Addition, Subtraction and Mixed:

Multiplication:

Mixed Terms – Addition, Subtraction and Multiplication:

Terms – Substitution:

Removing Brackets:

Indices and Exponents

Rules of Indices

Multiplication

Division

Negative powers

Base raised to two powers

Multiple bases to the same power

Fractional powers

Laws of indices

Factors, Factor Pairs, Prime Numbers and Prime Factors

Prime numbers between 1 and 100

How to work out prime factors of a number

Composite Numbers

Even and Odd Numbers

Multiples

Highest Common Factor (HCF)

Lowest Common Multiple (LCM)

Rectangular Numbers

Square Numbers

The perfect square or square numbers

Square Roots

Using prime factors to find the square root of large numbers without a calculator: Worked square root examples with answers:

Cube Numbers

Cube Root

Worked cubed root examples with answers:

Integers:

The Rules of Integers:

Properties of Zero

Worked Examples - Adding Integers

Rules for multiplying integers

Rules For Dividing Integers

Rules For Subtracting Integers

Substitution:

Decimal Numbers and Decimal fractions

Common Fractions to Decimal fractions to Decimal Numbers: Equivalent fractions

Mixed Number Fractions and Improper Fractions

Changing Mixed Number Fractions to Improper Fractions

Changing Improper Fractions to Mixed Number Fractions

Fractions and Whole Numbers

Fractions (Same denominator)

Adding:

Subtracting:

Adding:

Fractions (Changing one denominator)

Fractions (Changing both denominators)

Adding and Subtracting with Mixed Number Fractions

Subtracting with Mixed Number Fractions

Adding and Subtracting with Mixed Number Fractions in a Single Problem Comparing Fractions (<=>)

Method 2: Changing Denominators

Method 3: Cross Multiplication

Multiplying Of Fractions

Multiplying Of Fractions More Advanced

Division Of Fractions

Fractions – Mixed Operations

Ratio

Worked questions and examples of ratio:

Percentage

Converting fractions to percentages:

Simple Conversions with Fractions to Percentages

Rounding Off Percentages:

Theorem of Pythagoras

Numeric Patterns

By inspection:

Fibonacci sequence:

Creating the rule with a common difference and solve for n:

Finding the rule for variable difference and working out the nth term: Coordinates

What is an ordered pair?

Graphs – Straight line

Geometry: Geometry is the study of lines and shapes.

Parallel lines:

Lines of equal length:

Geometry: Polygons

Quadrilaterals

Angles of squares and rectangles (Quadrilaterals)

Regular polygons

Angles of polygons – Interior and Exterior Angles

Polygon – Concave and Convex

Geometry – Acute, Right, Obtuse, Revolution and Reflex Angles Naming an angle

Adjacent angles

Complementary angles

Supplementary angles

Vertically opposite angles

Parallel Lines

Transversal

Corresponding angles

Alternate angles

Co-interior angles

Calculating angles – Worked examples

Geometry: Triangles

Triangles

Triangles (polygon)

Triangles can be classified according to the lengths of the sides Triangles can be classified according to the size of angles

Calculating angles of a triangle

How to calculate the value of a, b, c, x etc.

Geometry : Area of a Triangle

Geometry: Circles

Basics on circles

Calculate the circumference – formulas

Calculate circumference, diameter and radius

Calculate the radius:

Worked circumference and area calculations

Geometry: Perimeter

Perimeter of a rectangle

Perimeter of a square

Perimeter of irregular shapes

Geometry – Area

Area of squares and rectangles

Formula for the area of a rectangle

Formula for area of a square

Area of a Circle and Triangle (Covered in previous chapters)

Area of a Parallelogram, Rhombus, Trapezoid and Kite

Area - Worked Examples

Surface area of Prisms and Cylinders

Geometry – Volume

Formula for Volume of a Prism, Cube and Cylinder

Worked examples of Prisms and Cylinders

Geometry – Nets

Properties of 3D shapes:

Face, Edges and Vertices of 3D shapes

Face, Edges and Vertices of Platonic Solids

How to represent data as a Pie Diagram

Example 1

Example 2

Construction of angles

Construction of the 90° angle

Construction of a 45° angle

Construction of a 60° angle

Construction of a 30° angle