Syllabus
Mathematics
1. NUMBER OPERATIONS
- Addition, subtraction, multiplication, and division of numbers up to 10,000.
- Understanding place value and number properties.
- Rounding numbers to the nearest 10, 100, or 1,000.
2. FRACTIONS
- Addition, subtraction, multiplication, and division of fractions.
- Understanding equivalent fractions.
- Simplifying fractions.
- Comparing and ordering fractions.
3. DIVISIBILITY AND PRIME NUMBERS
- Rules of divisibility by 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 13.
- Identifying prime and composite numbers.
- Finding factors and multiples of numbers.
- Prime factorization.
4. MEASUREMENT
- Understanding systems of measurement (length, area, volume, mass, and time).
- Converting between different units of measurement.
- Solving problems involving units of measurement in real-life contexts.
geometry
5. GEOMETRY
- Recognizing and classifying geometric figures (e.g., triangles, quadrilaterals, circles, etc.).
- Understanding properties of shapes (sides, angles, and symmetry).
- Parallel and perpendicular lines.
- Area and perimeter of rectangles.
- Introduction to the area of other basic geometric shapes.
6. MATHEMATICAL LOGIC
- Using logical reasoning to solve mathematical puzzles.
- Understanding statements that are true or false.
- Applying logical thinking in problem-solving contexts.
- Data Interpretation
- Reading and interpreting bar graphs.
- Understanding and creating Venn diagrams.
- Solving problems using data presented in different formats (tables, charts, graphs).
7. WORD PROBLEMS
- Solving word problems involving addition, subtraction, multiplication, and division.
- Applying mathematical concepts to real-life scenarios.
- 1 Multi-step word problems.
- Patterns and Sequences
- Recognizing and continuing patterns in sequences.
- Identifying arithmetic and geometric sequences.
- Understanding number patterns and finding missing elements.
8. TIME AND CALENDAR
- Reading time on analog and digital clocks.
- Understanding AM and PM.
- Calculating elapsed time.
- Understanding days, weeks, months, and years.
Mathematics
1. NUMBERS AND ARITHMETIC
1.1 Arithmetic Operations:
- Addition, subtraction, multiplication, and division with whole numbers.
- Operations with decimals, fractions, mixed fractions, and improper fractions.
- Order of operations (using parentheses).
Factors and Multiples:
- Understanding factors, multiples, and divisibility rules.
- Identifying prime and composite numbers.
- Greatest Common Divisor (GCD) and Least Common Multiple (LCM).
1.2 Percentage:
- Converting between fractions, decimals, and percentages.
- Solving simple percentage problems (e.g., finding percentages, increasing or decreasing a
quantity by a percentage).
2. ALGEBRA AND EQUATIONS
2.1 Linear Equations:
- Solving simple one-step linear equations.
- Understanding and using variables in equations.
- Applying linear equations to solve word problems.
2.2 Simple Interest Calculations:
- Understanding the concept of interest.
- Calculating simple interest using the formula, where P is the principal amount, R is the rate,
and T is the time period.
mathematic
3. GEOMETRY
3.1 Properties of Geometric Figures:
- Understanding properties of squares, rectangles, triangles, parallelograms, and trapeziums.
- Identifying sides, angles, and diagonals.
3.2 Angles:
- Identifying and measuring acute, right, and obtuse angles.
- Understanding complementary and supplementary angles.
3.3 Perimeter and Area:
- Calculating the perimeter of polygons.
- Finding the area of triangles, squares, rectangles, parallelograms, and trapeziums.
3.4 Volume:
- Calculating the volume of cubes and cuboids using the formula, where l, w, and h are the length,
width, and height, respectively.
3.5 Line of Symmetry:
- Identifying lines of symmetry in various shapes.
- Understanding symmetry in regular polygons.
4. MEASUREMENT AND SIMPLE STATISTICS
4. 1 Measurement:
- Understanding different units of measurement for length, area, volume, and mass.
- Converting between different units of measurement.
4.2 Simple Statistics:
- Calculating and interpreting mean, median, and mode.
- Reading data from charts, graphs, and tables.
- Understanding range as a measure of data variability.
5. RATIOS AND PROPORTIONS
5.1 Understanding Ratios:
- Solving problems involving ratios.
- Using ratios to compare quantities.
5.2 Proportions:
- Solving simple proportions.
- Applying proportions to solve real-life problems.
- Problem solving and logical thinking
6. PROBLEM SOLVING AND LOGICAL THINKING
6.1 Word Problems:
- Translating word problems into mathematical expressions or equations.
- Solving multi-step word problems using arithmetic and basic algebra.
- Pattern Recognition and Logical Reasoning:
- Identifying patterns and sequences in numbers.
- Using logical reasoning to solve math puzzles.
All topics of Category 1 (Grades 3-4)
Mathematics
1. NUMBERS AND ARITHMETIC
1.1 Arithmetic Operations:
Addition, subtraction, multiplication, and division with whole numbers.
Operations with decimals, fractions, mixed fractions, and improper fractions.
Order of operations (using parentheses).
Factors and Multiples:
Understanding factors, multiples, and divisibility rules.
Identifying prime and composite numbers.
Greatest Common Divisor (GCD) and Least Common Multiple (LCM).
1.2 Percentage:
Converting between fractions, decimals, and percentages.
Solving simple percentage problems (e.g., finding percentages, increasing or decreasing a
quantity by a percentage).
2. ALGEBRA AND EQUATIONS
2.1 Linear Equations:
Solving simple one-step linear equations.
Understanding and using variables in equations.
Applying linear equations to solve word problems.
2.2 Simple Interest Calculations:
Understanding the concept of interest.
Calculating simple interest using the formula, where P is the principal amount, R is the rate,
and T is the time period.
Geometry
3. GEOMETRY
3.1 Properties of Geometric Figures:
Understanding properties of squares, rectangles, triangles, parallelograms, and trapeziums.
Identifying sides, angles, and diagonals.
3.2 Angles:
Identifying and measuring acute, right, and obtuse angles.
Understanding complementary and supplementary angles.
3.3 Perimeter and Area:
Calculating the perimeter of polygons.
Finding the area of triangles, squares, rectangles, parallelograms, and trapeziums.
3.4 Volume:
Calculating the volume of cubes and cuboids using the formula, where l, w, and h are the length,
width, and height, respectively.
3.5 Line of Symmetry:
4. 5. Identifying lines of symmetry in various shapes.
Understanding symmetry in regular polygons.
4. MEASUREMENT AND SIMPLE STATISTICS
4. 1 Measurement:
Understanding different units of measurement for length, area, volume, and mass.
Converting between different units of measurement.
4.2 Simple Statistics:
Calculating and interpreting mean, median, and mode.
Reading data from charts, graphs, and tables.
Understanding range as a measure of data variability.
5. RATIOS AND PROPORTIONS
5.1 Understanding Ratios:
Solving problems involving ratios.
Using ratios to compare quantities.
5.2 Proportions:
Solving simple proportions.
Applying proportions to solve real-life problems.
Problem solving and logical thinking
6. PROBLEM SOLVING AND LOGICAL THINKING
6.1 Word Problems:
Translating word problems into mathematical expressions or equations.
Solving multi-step word problems using arithmetic and basic algebra.
Pattern Recognition and Logical Reasoning:
Identifying patterns and sequences in numbers.
Using logical reasoning to solve math puzzles.
All topics of Category 1 (Grades 3-4)
Mathematics
1. NUMBERS AND ALGEBRA
1.1 Advanced Topics in Fractions:
Operations with fractions and mixed numbers.
Simplifying complex fractions.
Conversion between improper fractions and mixed numbers.
1.2 Squares and Square Roots:
Understanding perfect squares.
Calculating square roots (exact and approximate).
Simplifying square roots.
1.3 Rational and Irrational Numbers:
Identifying rational and irrational numbers.
Operations involving rational numbers.
Understanding decimal representations (terminating, repeating, and non-repeating).
1.4 Simple Algebraic Expressions:
Simplifying expressions using the distributive property and combining like terms.
Evaluating expressions for given variable values.
1.5 Equalities and Inequalities:
Solving linear equalities and inequalities.
Graphing inequalities on a number line.
Understanding absolute value inequalities.
2. EQUATIONS AND FUNCTIONS
2.1 System of Equations:
Solving systems of linear equations using substitution and elimination methods.
Application of systems in word problems.
2.2 Linear Functions:
Understanding slope and intercept.
Graphing linear functions.
Solving real-life problems using linear equations and graphs.
3. RATIOS, PROPORTIONS, AND COMBINATORICS
3.1 Ratio and Proportion:
Solving problems involving ratios, rates, and proportions.
Applying proportions to real-world problems.
3.2 Simple Combinatorics and Probability:
Basic counting principles (addition and multiplication rules).
Introduction to permutations and combinations.
Basic probability concepts and calculations.
Geometry
4. GEOMETRY
4.1 Regular Polygons:
Properties and characteristics of regular polygons.
Calculating interior and exterior angles.
4.2 Area and Circumference of a Circle:
Using formulas to calculate the area and circumference of circles.
Solving problems involving arc length and sector area.
4.3 Area and Perimeter of Composite Figures:
Calculating the area and perimeter of shapes composed of multiple geometric figures.
4.4 Pythagorean Theorem:
Applying the Pythagorean Theorem to find the length of a side in a right triangle.
Solving real-world problems using the Pythagorean Theorem.
4.5 Congruence and Similarity:
Understanding the properties of congruent and similar shapes.
Solving problems involving scale factors and transformations.
5. MEASUREMENT
5.1 Volume and Surface Area:
Calculating the volume and surface area of prisms and cylinders.
Solving problems involving composite three-dimensional figures.
6. COORDINATE GEOMETRY
6.1 Basic Concepts:
Plotting points on the Cartesian plane.
Understanding the distance between two points and the midpoint formula.
6.2 Graphing Linear Equations:
Finding the equation of a line given two points or a point and a slope.
Understanding the relationship between graphical and algebraic representations of lines.
7. MATHEMATICAL REASONING AND PROBLEM SOLVING
7.1. Solving Word Problems:
Translating word problems into mathematical expressions or equations.
Using algebraic and geometric approaches to solve complex problems.
7.2 Logical Reasoning and Pattern Recognition:
Identifying patterns and sequences.
Solving puzzles using logical reasoning techniques.
All topics of Category 2 (Grades 5-6)
Mathematics
1. ADVANCED ALGEBRA
1.1. Advanced Topics in Algebra:
Polynomial equations and inequalities.
Rational expressions and functions.
Techniques for solving higher-degree equations.
1.2. Remainder and Factor Theorems:
Understanding and applying the Remainder Theorem.
Using the Factor Theorem to factorize polynomials.
Solving polynomial equations using these theorems.
1.3. Non-Linear Equations:
Solving quadratic, cubic, and higher-degree equations.
Understanding the nature of roots (real, complex, equal, etc.).
Application of the quadratic formula and Vieta’s formulas.
2. INEQUALITIES AND MATHEMATICAL ANALYSIS
2.1. Advanced Topics in Inequalities:
Absolute value inequalities.
Systems of inequalities.
2.2. Summation of Series:
Arithmetic and Geometric series.
Summation techniques for more complex series.
Using sigma notation and properties of summation.
3. LOGARITHMS AND EXPONENTIALS
3.1. Advanced Topics in Logarithms:
Properties and laws of logarithms.
Solving logarithmic and exponential equations.
Applications in growth and decay problems.
4. BINOMIAL THEOREM
4.1. Application of the Binomial Theorem:
Expanding expressions using the binomial theorem.
Finding specific terms in a binomial expansion.
Applications in combinatorics and algebra.
5. COMBINATORICS AND PROBABILITY
5.1. Advanced Topics in Combinatorics:
Permutations and combinations.
Pigeonhole principle and inclusion-exclusion principle.
Advanced counting techniques.
5.2. Advanced Probability:
Conditional probability and Bayes’ theorem.
Probability distributions (basic concepts).
Solving complex probability problems.
Geometry
6. GEOMETRY AND TRIGONOMETRY
6.1. Advanced Topics in Coordinate Geometry:
Equations of lines, circles, ellipses, parabolas, and hyperbolas.
Solving geometric problems using coordinate methods.
Loci and geometric transformations.
6.2. Advanced Topics in Trigonometry:
Solving trigonometric equations.
Using identities and formulas (sum, difference, double-angle, half angle).
Trigonometric applications in geometry.
7. ADDITIONAL TOPICS
7.1. Functions and Graphing:
Understanding different types of functions (linear, quadratic, polynomial, trigonometric,
exponential, and logarithmic).
Analysing graphs of functions and their transformations.
7.2. Basic Calculus (Introductory Level):
Understanding limits and continuity.
Differentiation and simple applications.
