PMO Syllabus PDF

The curriculum is structured to build competencies in Number Theory, Algebra, Geometry, Data Handling, and Problem-Solving Strategies. 1. Number Theory Objectives: Understand and perform operations with integers, fractions, decimals, and percentages. Identify prime...

The curriculum is structured to build competencies in Number Theory, Algebra, Geometry, Data Handling, and Problem-Solving Strategies. 1. Number Theory Objectives: Understand and perform operations with integers, fractions, decimals, and percentages. Identify prime numbers, factors, and work with ratios, proportions, LCM, and GCD. Understand rational and irrational numbers, and solve problems involving exponents and square roots. Topics: Prime Numbers, Composite Numbers, and Factorization Least Common Multiple (LCM) and Greatest Common Divisor (GCD) Fractions, Decimals, and Percentages Ratios, Proportions, Rational, and Irrational Numbers Exponents and Square Roots Activities: Prime factorization exercises LCM and GCD problem sets Fraction, decimal, and percentage operations practice Ratio and proportion problem-solving Solving problems involving exponents and roots 2. Algebra Objectives: Simplify and evaluate algebraic expressions. Solve linear and quadratic equations, as well as inequalities. Recognize patterns and sequences, and understand functions. Topics: Algebraic Expressions and Simplification Solving Simple Linear and Quadratic Equations Linear Inequalities and Graphing  Patterns and Sequences (Arithmetic Sequences) Polynomials, Factorization, Functions, and Graphs Activities: Solve linear and quadratic equations, and graph their solutions Simplify complex algebraic expressions Explore patterns and sequences with visual aids and manipulatives Factor polynomials and solve related problems 3. Geometry Objectives: Recognize and apply properties of geometric shapes, including triangles, quadrilaterals, and circles. Calculate perimeter, area, surface area, and volume of various shapes. Understand and apply theorems related to triangles, circles, and coordinate geometry. Topics: Properties of Rectangles, Squares, Triangles, and Circles Perimeter, Area, Surface Area, and Volume Calculations Introduction to Angles (Acute, Obtuse, Right) Theorems Related to Triangles and Circles Coordinate Geometry (Plotting Points, Slopes) Activities: Draw, measure, and solve problems involving geometric shapes Calculate area, perimeter, and volume using real-life scenarios Apply geometric theorems to solve problems Practice plotting and analyzing points on a coordinate plane 4. Data Handling Objectives: Organize, interpret, and analyze data using various graphs and charts. Calculate measures of central tendency and understand basic to advanced probability concepts. Topics:  Collecting Data, Creating Bar Graphs, Pictographs, and Line Graphs Measures of Central Tendency (Mean, Median, Mode) Data Interpretation from Complex Graphs (e.g., Pie Charts) Measures of Dispersion (Standard Deviation) Probability Concepts (Basic to Advanced) Activities: Create and interpret bar graphs, line graphs, and pie charts Analyze data sets to find mean, median, mode, and standard deviation Solve basic and advanced probability problems 5. Problem-Solving Strategies Objectives: Apply logical reasoning and develop strategies for complex problem-solving. Prepare for Olympiad-style questions through advanced practice. Topics: Logic Puzzles and Riddles Introduction to and Advanced Mathematical Proofs Mathematical Reasoning Techniques Olympiad-style Problem Sets Activities: Solve logic puzzles and work on advanced problem sets Practice mathematical proofs with guided examples Participate in mock Olympiad exams Textbooks: Aligned with all Pakistan Text Board curricula. Online Platforms: Art of Problem Solving for interactive exercises and practice tests.