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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