SYLLABUS

Chapter 1: Integers

1.1: Introduction

1.2: Recall

1.3: Properties of Addition and Subtraction of Integers

• 1.3.1: Closure under Addition
• 1.3.2: Closure under Subtraction
• 1.3.3: Commutative Property
• 1.3.4: Associative Property
• 1.3.5: Additive Identity

1.4: Multiplication of Integers

• 1.4.1: Multiplication of a Positive and a Negative Integer
• 1.4.2: Multiplication of two Negative Integers
• 1.4.3: Product of three or more Negative Integers

1.5: Properties of Multiplication of Integers

• 1.5.1: Closure under Multiplication
• 1.5.2: Commutativity of Multiplication
• 1.5.3: Multiplication by Zero
• 1.5.4: Multiplicative Identity
• 1.5.5: Associativity for Multiplication
• 1.5.6: Distributive Property
• 1.5.7: Making Multiplication Easier

1.6: Division of Integers

1.7: Properties of Division of Integers

Chapter 2: Fractions and Decimals

2.1: Introduction

2.2: How Well Have You Learnt About Fractions?

2.3: Multiplication of Fractions

• 2.3.1: Multiplication of a Fraction by a Whole Number
• 2.3.2: Multiplication of a Fraction by a Fraction

2.4: Division of Fractions

• 2.4.1: Division of Whole Number by a Fraction
• 2.4.2: Division of a Fraction by a Whole Number
• 2.4.3: Division of a Fraction by Another Fraction

2.5: How Well Have You Learnt About Decimal Numbers

2.6: Multiplication of Decimal Numbers

• 2.6.1: Multiplication of Decimal Numbers by 10, 100 and 1000

2.7: Division of Decimal Numbers

• 2.7.1: Division by 10, 100 and 1000
• 2.7.2: Division of a Decimal Number by a Whole Number
• 2.7.3: Division of a Decimal Number by another Decimal Number.

Chapter 3: Data Handling

3.1: Introduction

3.2: Collecting Data

3.3: Organisation Of Data

3.4: Representative Values

3.5: Arithmetic Mean

• 3.5.1: Range

3.6: Mode

• 3.6.1: Mode of Large Data

3.7: Median

3.8: Use of Bar Graphs with A Different Purpose

• 3.8.1: Choosing A Scale

3.9: Chance and Probability

• 3.9.1: Chance.

Chapter 4: Simple Equations

4.1: A Mind-Reading Game!

4.2: Setting Up of an Equation

4.3: Review of What We Know

4.4: What Equation Is?

• 4.4.1: Solving an Equation

4.5: More Equations

4.6: From Solution to Equation

4.7: Applications of Simple Equations to Practical Situations

Chapter 5: Lines and Angles

5.1: Introduction

5.2: Related Angles

• 5.2.1: Complementary Angles
• 5.2.2: Supplementary Angles
• 5.2.3: Adjacent Angles
• 5.2.4: Linear Pair
• 5.2.5: Vertically Opposite Angles

5.3: Pairs of Lines

• 5.3.1: Intersecting Lines
• 5.3.2: Transversal
• 5.3.3: Angles Made by A Transversal
• 5.3.4: Transversal of Parallel Lines

5.4: Checking for Parallel Lines

Chapter 6: Triangles and its Properties

6.1: Introduction

6.2: Medians of a Triangle

6.3: Altitudes of a Triangle

6.4: Exterior Angle of a Triangle and Its Property

6.5: Angle Sum Property of a Triangle

6.6: Two Special Triangles: Equilateral and Isosceles

6.7: Sum of The Lengths of Two Sides of a Triangle

6.8: Right-Angled Triangles and Pythagoras Property

Chapter 7: Congruence of Triangles 

7.1: Introduction

7.2: Congruence of Plane Figures

7.3: Congruence Among Line Segments

7.4: Congruence of Angles

7.5: Congruence of Triangles

7.6: Criteria for Congruence of Triangles

7.7: Congruence Among Right-Angled Triangles

Chapter 8: Comparing Quantities

8.1: Introduction

8.2: Equivalent Ratios

8.3: Percentage – Another Way of Comparing Quantities

• 8.3.1: Meaning of Percentage
• 8.3.2: Converting Fractional Numbers to Percentage
• 8.3.3: Converting Decimals to Percentage
• 8.3.4: Converting Percentages to Fractions or Decimals
• 8.3.5: Fun with Estimation

8.4: Use of Percentages

• 8.4.1: Interpreting Percentages
• 8.4.2: Converting Percentages To “How Many”
• 8.4.3: Ratios to Percents
• 8.4.4: Increase or Decrease as Percent

8.5: Prices Related to An Item or Buying and Selling

• 8.5.1: Profit or Loss as A Percentage

8.6: Charge Given on Borrowed Money or Simple Interest

• 8.6.1: Interest for Multiple Years.

Chapter 9: Rational Numbers 

9.1: Introduction

9.2: Need for Rational Numbers

9.3: What Are Rational Numbers?

9.4: Positive and Negative Rational Numbers

9.5: Rational Numbers on a Number Line

9.6: Rational Numbers in Standard Form

9.7: Comparison of Rational Numbers

9.8: Rational Numbers Between Two Rational Numbers

9.9: Operations on Rational Numbers

• 9.9.1: Addition
• 9.9.2: Subtraction
• 9.9.3: Multiplication
• 9.9.4: Division.

Chapter 10: Practical Geometry

10.1: Introduction

10.2: Construction of A Line Parallel To A Given Line, Through A Point Not On The Line

10.3: Construction of Triangles

10.4: Constructing A Triangle When the Lengths of Its Three Sides Are Known (SSS Criterion)

10.5: Constructing A Triangle When the Lengths of Two Sides and The Measure of The Angle Between Them Are Known. (SAS Criterion)

10.6: Constructing A Triangle When the Measures of Two of Its Angles and The Length of The Side Included Between Them Is Given. (ASA Criterion)

10.7: Constructing A Right-Angled Triangle When the Length of One Leg and Its Hypotenuse Are Given (RHS Criterion). 

Chapter 11: Perimeter and Area 

11.1: Introduction

11.2: Squares and Rectangles

11.2.1: Triangles as Parts Of Rectangles

11.2.2: Generalising For Other Congruent Parts of Rectangles

11.3: Area of A Parallelogram

11.4: Area of A Triangle

11.5: Circles

• 11.5.1: Circumference of A Circle
• 11.5.2: Area of Circle

11.6: Conversion of Units

11.7: Applications.

Chapter 12: Algebraic Expressions 

12.1: Introduction

12.2: How Are Expressions Formed?

12.3: Terms of An Expression

12.4: Like and Unlike Terms

12.5: Monomials, Binomials, Trinomials and Polynomials

12.6: Addition and Subtraction of Algebraic Expressions

12.7: Finding the Value of An Expression

12.8: Using Algebraic Expressions – Formulas and Rules.

Chapter 13: Exponents and Powers

13.1: Introduction

13.2: Exponents

13.3: Laws of Exponents

• 13.3.1: Multiplying Powers with The Same Base
• 13.3.2: Dividing Powers with The Same Base
• 13.3.3: Taking Power of a Power
• 13.3.4: Multiplying Powers with The Same Exponents
• 13.3.5: Dividing Powers with The Same Exponents

13.4: Miscellaneous Examples Using the Laws of Exponents

13.5: Decimal Number System

13.6: Expressing Large Numbers in The Standard Form.

Chapter 14: Symmetry

14.1: Introduction

14.2: Lines of Symmetry for Regular Polygons

14.3: Rotational Symmetry

14.4: Line Symmetry and Rotational Symmetry.

Chapter 15: Visualising Solid Shapes 

15.1: Introduction: Plane Figures and Solid Shapes

15.2: Faces, Edges and Vertices

15.3: Nets for Building 3-D Shapes

15.4: Drawing Solids on A Flat Surface

• 15.4.1: Oblique Sketches
• 15.4.2: Isometric Sketches
• 15.4.3: Visualising Solid Objects

15.5: Viewing Different Sections of a Solid

• 15.5.1: One Way to View an Object Is by Cutting Or Slicing
• 15.5.2: Another Way Is by Shadow Play
• 15.5.3: A Third Way Is by Looking at It From Certain Angles To Get Different Views.