## Topics with syllabus and resources

1 Integers

syllabus ▼

- Multiplication and Division of Integers
- Properties of Integers
- Properties of multiplication of integers
- Word problems including integers

- Concepts :
- Introduction of Integer question (20)
- Properties of Addition and Subtraction of Integers
- Closure Under Addition question (4)

- Closure Under Subtraction question (4)

- Commutative Property question (4)

- Multiplication of Integers
- Multiplication of a Positive and a Negative Integer question (10)

- Properties of Multiplication of Integers
- Multiplicative Identity question (7)

- Making Multiplication Easier question (14)

- Division of Integers question (19)
- Properties of Division of Integers question (4)

2 Fractions and Decimals

syllabus ▼

- Let’s recal fractions
- Multiplication of Fractions (fraction x whole number & fractionx fraction)
- Division of fractions (whole number/fraction; reciprocal of a fraction; fraction/whole number; fraction/fraction)
- Multiplication & Division of Decimal Numbers (decimal x decimal; decimal x whole number; decimal x 10, 100, 1000)
- Word Problems on Fractions and Decimal Numbers

- Concepts :
- Introduction of Fractions question (22)
- Multiplication of Fractions
- Multiplication of a Fraction by a Whole Number question (33)

- Multiplication of a Fraction by a Fraction question (23)

- Division of Fractions
- Division of Whole Number by a Fraction question (19)

- Division of a Fraction by Another Fraction question (8)

- Concept of Decimal Numbers question (28)
- Multiplication of Decimal Numbers by 10, 100 and 1000 question (23)
- Division of Decimal Numbers
- Division by 10, 100 and 1000 question (11)

- Division of a Decimal Number by a Whole Number question (8)

- Division of a Decimal Number by Another Decimal Number question (10)

- Multiplication of Decimal Numbers question (8)

3 Data Handling

syllabus ▼

- Introduction: Why should we organize data?
- Data collection and organizing data
- Arithmetic Mean & Range
- Mean, Median & Mode
- Chance & Probability

- Concepts :
- Introduction of Data Handling
- Collecting Data
- Organisation of Data question (1)
- Concept of Representative Values
- Concept of Arithmetic Mean question (6)
- Arithmetic Mean - Range question (4)
- Concept of Mode question (5)
- Mode - Mode of Large Data
- Concept of Median question (1)
- Use of Bar Graphs with a Different Purpose - Choosing a Scale question (6)
- Chance and Probability - Chance question (9)

4 Simple Equations

syllabus ▼

- Recall : Expressions and Equations
- Setting up an equation
- Solving an equation
- Tracing Back: from solution to equation
- Application of simple equations to practical situations

- Concepts :
- Mind-reading Game
- Setting up of an Equation question (11)
- Concep of Equation question (29)
- Solving an Equation question (37)
- More Equations question (15)
- From Solution to Equation question (2)
- Applications of Simple Equations to Practical Situations question (14)

5 Lines and Angles

syllabus ▼

- Introduction to Lines and Angles
- Related Angles: Complementary and supplementary angles
- Related Angles: Adjacent, vertically opposite and linear pair of angles
- Pairs of Lines : Intersecting Line and Transversal
- Angles made by transversal
- Check for parallel lines

- Concepts :
- Introduction to Lines and Angles
- Related Angles
- Complementary Angles question (9)

- Supplementary Angles question (13)

- Adjacent Angles question (3)

- Concept of Linear Pair question (3)
- Concept of Vertically Opposite Angles question (5)
- Pairs of Lines - Intersecting Lines question (5)
- Pairs of Lines - Transversal question (1)
- Pairs of Lines - Angles Made by a Transversal
- Pairs of Lines - Transversal of Parallel Lines question (1)
- Checking for Parallel Lines question (4)

6 The Triangle and Its Properties

syllabus ▼

- Introduction : Recall the triangles
- Medians & Altitudes of a triangle
- Exterior Angle of a triangle & its property
- Angle sum property of a triangle
- Equilateral & Isosceles Triangles
- Sum of the length of two sides of a triangle
- Right-Angled Triangles and Pythagoras Property

- Concepts :
- Introduction of Triangle
- Medians of a Triangle
- Altitudes of a Triangle question (4)
- Exterior Angle of a Triangle and Its Property question (12)
- Angle Sum Property of a Triangle question (12)
- Two Special Triangles : Equilateral and Isosceles question (2)
- Sum of the Lengths of Two Sides of a Triangle question (8)
- Right-angled Triangles and Pythagoras Property question (9)

7 Congruence of Triangles

syllabus ▼

- The idea of congruence in geometry
- Congruence of plane figures, line segments, angles
- Criteria for congruence of triangles
- Congruence among right-angled triangles

- Concepts :
- Congruence of Plane Figures question (1)
- Congruence Among Line Segments question (3)
- Congruence of Angles
- Congruence of Triangles question (8)
- Criteria for Congruence of Triangles question (12)
- Congruence Among Right- Angled Triangles

8 Comparing Quantities

syllabus ▼

- Comparing Quantities
- Equivalent Ratios
- Percentage : Another way of comparing quantities
- Converting fractional and decimal numbers to percentage
- Converting percentage to fractions or decimal numbers
- Uses of Percentage : Interpreting and converting percentages
- Uses of Percentage : Ratio to Percent, Increase of Decrease as percent
- Profit or Loss as Percentage
- Introduction to simple interest for one and multiple years

- Concepts :
- Introduction of Comparing Quanttitite
- Concept of Equivalent Ratios question (6)
- Percentage – Another Way of Comparing Quantities
- Meaning of Percentage
- Converting Fractional Numbers to Percentage question (4)
- Converting Decimals to Percentage question (8)
- Concept of Estimation question (3)
- Use of Percentages -interpreting Percentages question (4)
- Use of Percentages - Converting Percentages to “How Many” question (9)
- Ratios to Percents question (6)
- Increase Or Decrease as per Cent question (2)
- Prices Related to an Item Or Buying and Selling question (3)
- Profit Or Loss as a Percentage question (4)
- Charge Given on Borrowed Money Or Simple Interest question (2)
- Interest for Multiple Years question (2)

9 Rational Numbers

syllabus ▼

- Introduction to rational numbers and their need
- Positive and negative natural numbers and their representation on number line
- Rational numbers in standard form
- Representation of rational number as a decimal
- Comparison of rational numbers
- Rational numbers between two rational numbers
- Operations in rational numbers
- Word problems on rational numbers (all operations)

- Concepts :
- Need for Rational Numbers
- Concept of Rational Numbers
- Positive and Negative Rational Numbers
- Rational Numbers on a Number Line
- Rational Numbers in Standard Form
- Comparison of Rational Numbers
- Rational Numbers Between Two Rational Numbers question (42)
- Operations on Rational Numbers - Addition question (7)
- Operations on Rational Numbers - Subtraction question (5)
- Operations on Rational Numbers - Multiplication question (6)
- Operations on Rational Numbers - Division question (7)

10 Practical Geometry

syllabus ▼

- Construction of a line parallel to a given line, through a point not on the line
- Construction of Triangles : An idea
- Constructing a triangle when the lengh of its sides are known (SSS Criterion)
- Constructing a triangle when the length its two sides and the measure of the angle between them are known (SAS Criterion)
- Constructing a triangle when the measure of two of its angles and the length of the side included between them is given (ASA Criterion)
- Constructing a Right-Angled Triangle when the length of one leg and its Hypotenous are given (RHS Criterion)

- Concepts :
- Construction of a Line Parallel to a Given Line, Through a Point Not on the Line question (3)
- Construction of Triangles
- Constructing a Triangle When the Lengh of Its Sides Are Known (SSS Criterion) question (4)
- Constructing a Triangle When the Measures of Two of Its Angles and the Length of the Side Included Between Them is Given. (ASA Criterion) question (3)
- Constructing a Right-angled Triangle When the Length of One Leg and Its Hypotenuse Are Given (RHS Criterion) question (3)
- Constructing a Triangle When the Lengths of Two Sides and the Measure of the Angle Between Them Are Known. (Sas Criterion) question (3)

11 Perimeter and Area

syllabus ▼

- Triangles
- Area of a parallelogram & triangle
- Circles : Circumference & Area
- Perimeter of Polygons
- Conversion of units and its applications

- Concepts :
- Squares and Rectangles question (8)
- Triangles as Parts of Rectangles
- Generalising for Other Congruent Parts of Rectangles
- Area of a Parallelogram question (8)
- Area of a Triangle question (7)
- Circle
- Circumference of a Circle question (11)

- Area of Circle question (10)

- Conversion of Units question (2)
- Concept of Application of Conversion question (10)
- Perimeter of Polygons

12 Algebraic Expressions

syllabus ▼

- Introduction: Formation of an equation
- Terms of an expression : Factors and coefficients of a term
- Like and unlike terms : Monomials, Binomials, Trinomials and Polynomials
- Addition and subtraction of algebraic expressions
- Finding the value of an expression
- Using algebraic expression – formulas and rules [Perimeter formula; area formula]
- Simple linear equations
- Patterns in numbers and geometry

- Concepts :
- Concept of Expressions Formed question (8)
- Terms of an Expression question (5)
- Like and Unlike Terms question (8)
- Monomials, Binomials, Trinomials and Polynomials question (12)
- Addition and Subtraction of Algebraic Expressions question (29)
- Finding the Value of an Expression question (32)
- Using Algebraic Expressions – Formulas and Rules question (4)

13 Exponents and Powers

syllabus ▼

- Why exponents and powers?
- Exponents: The shorthand for repeated multiplications
- Laws of exponents
- Decimal number system and expressing large numbers in the standard form

- Concepts :
- Concept of Exponents question (37)
- Laws of Exponents
- Multiplying Powers with the Same Base question (17)

- Dividing Powers with the Same Base question (8)

- Taking Power of a Power question (2)

- Multiplying Powers with the Same Exponents question (1)

- Miscellaneous Examples Using the Laws of Exponents question (6)
- Decimal Number System question (1)
- Expressing Large Numbers in the Standard Form question (20)

14 Symmetry

syllabus ▼

- Recalling reflection symmetry
- Line Symmetry
- Rotational Symmetry
- A comparison between line symmetry and rotational symmetry

- Concepts :
- Introduction of Symmetry
- Lines of Symmetry for Regular Polygons question (52)
- Concept of Rotational Symmetry question (14)
- Line Symmetry and Rotational Symmetry question (7)

15 Visualizing Solid Shapes

syllabus ▼

- Introduction to plane figures and solid shapes (faces, edges and vertices)
- Building 3-D Shapes
- Oblique Sketches
- Isometric Sketches
- Different sections of a solid (slicing/cutting & shadow)

- Concepts :
- Introduction of Plane Figures and Solid Shapes question (7)
- Concept of Faces, Edges and Vertices question (1)
- Nets for Building 3-d Shapes question (2)
- Drawing Solids on a Flat Surface - Oblique Sketches question (3)
- Drawing Solids on a Flat Surface - Isometric Sketches question (6)
- Drawing Solids on a Flat Surface - Visualising Solid Objects question (5)
- Viewing Different Sections of a Solid - Another Way is by Shadow Play question (3)