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