1. Algebra

• Advanced Operations and Expressions
• Simplification of complex algebraic expressions using the distributive property and factoring
• Multiplying and dividing algebraic expressions (polynomia
• Quadratic Equations
• Solving quadratic equations using factorization and the quadratic formula
• Word problems involving quadratic equations
• Understanding the discriminant and nature of roots
• Simultaneous Equations
• Solving systems of linear equations in two variables using substitution and elimination methods
• Applications of simultaneous equations in real-life scenarios
• Exponents and Radicals
• Laws of exponents (product rule, quotient rule, power rule
• Simplifying expressions with exponents and radicals (square roots and cube roots)
• Sequences and Series
• Arithmetic and geometric sequences and series
• Finding the sum of an arithmetic and geometric series
• Real-life Applications

2. Number Theory

• Advanced Prime Numbers and Divisibility
• Divisibility rules for larger numbers (7, 11, etc.)
• Prime factorization and applications in solving complex problems
• Modular Arithmetic and Congruences
• More advanced mod operations and properties of congruence
• Solving linear congruences
• Theorems in Number Theory
• Euclid’s Algorithm for finding GCD
• Introduction to perfect numbers and their properties
• Real-life Applications

3. Geometry

• Properties of Triangles and Circles
• Triangle congruence (SSS, SAS, ASA) and similarity theorems
• Properties of special triangles (45°-45°-90°, 30°-60°-90°
• Understanding properties of circles (chords, tangents, arcs, and sectors)
• Pythagoras Theorem and Applications
• Advanced problems using the Pythagorean Theorem
• Real-world applications of the theorem
• Coordinate Geometry
• Distance formula, midpoint formula, and slope of a line
• Equation of a line (slope-intercept form and point-slope form)
• Applications of coordinate geometry in problem-solving
• Solid Geometry
• Surface area and volume of 3D shapes (cylinders, cones, spheres, prisms)
• Application of volume and surface area in real-life problems
• Real-life Applications

4. Statistics

• Advanced Data Representation
• Histograms, frequency polygons, and box plots
• Cumulative frequency and interpretation
• Measures of Central Tendency and Dispersion
• Calculating and interpreting mean, median, mode, range, variance, and standard deviation
• Real-life applications of these measures in analyzing data
• Probability
• Probability of independent and dependent events
• Conditional probability and its real-world applications
• Introduction to combinatorics (permutations and combinations)
• Introduction to Correlation and Regression
• Understanding correlation (positive, negative, and no correlation)
• Basic introduction to linear regression and interpreting the line of best fit
• Real-life Applications