Grade 12 Mathematics Syllabus
Quadratics
- Solving quadratic equations
- Graphing quadratic functions
- Finding the vertex, axis of symmetry, and roots of a quadratic function
- Solving problems involving quadratic equations and functions
Functions
- Exploring various types of functions (linear, quadratic, exponential, logarithmic, etc.)
- Graphing functions and identifying their key features
- Finding inverse functions and their properties
- Solving problems using functions
Algebra
- Simplifying algebraic expressions
- Solving equations and inequalities
- Working with matrices and determinants
- Performing operations on complex numbers
- Applying algebraic concepts to solve real-world problems
Coordinate Geometry
- Understanding the Cartesian coordinate system
- Graphing lines, circles, and other conic sections
- Finding equations of lines and conic sections
- Solving problems involving coordinate geometry
Circular Measure
- Understanding radians and degrees
- Converting between degrees and radians
- Finding arc lengths and areas of sectors
- Applying circular measure to solve problems
Trigonometry
- Exploring trigonometric functions (sine, cosine, tangent, etc.)
- Solving right triangles using trigonometric ratios
- Applying trigonometric identities and equations
- Solving problems involving trigonometry
Series
- Understanding arithmetic and geometric sequences
- Finding the sum of finite and infinite series
- Applying series in real-world situations
Differentiation
- Understanding the concept of a derivative
- Finding derivatives of various functions
- Applying differentiation to solve problems related to rates of change and optimization
Integration
- Understanding the concept of an integral
- Finding definite and indefinite integrals
- Applying integration to solve problems related to area, volume, and accumulation
Logarithmic and Exponential Functions
- Exploring the properties of logarithmic and exponential functions
- Solving equations and inequalities involving logarithmic and exponential functions
- Applying logarithmic and exponential functions in real-world situations
Numerical Solution of Equations
- Understanding numerical methods for solving equations (bisection, Newton-Raphson, etc.)
- Applying numerical methods to find approximate solutions to equations
Forces and Equilibrium
- Understanding the concept of forces and equilibrium
- Analyzing forces in different situations
- Applying principles of forces and equilibrium to solve problems
Kinematics of Motion in a Straight Line
- Understanding motion in a straight line
- Analyzing position, velocity, and acceleration
- Solving problems involving kinematics of motion in a straight line
Momentum
- Understanding the concept of momentum
- Analyzing momentum in different situations
- Applying principles of momentum to solve problems
Newton’s Laws of Motion
- Understanding Newton's laws of motion
- Applying Newton's laws to analyze motion and forces
- Solving problems involving Newton's laws of motion
Energy, Work, and Power
- Understanding the concepts of energy, work, and power
- Analyzing different forms of energy
- Solving problems involving energy, work, and power
Representation of Data
- Collecting and organizing data
- Representing data using graphs, charts, and tables
- Analyzing and interpreting data
Permutations and Combinations
- Understanding permutations and combinations
- Solving problems involving permutations and combinations
Probability
- Understanding basic probability concepts
- Calculating probabilities of events
- Applying probability in real-world situations
Discrete Random Variables
- Understanding discrete random variables
- Calculating probabilities and expected values of discrete random variables
- Applying discrete random variables in real-world situations
The Normal Distribution
- Understanding the properties of the normal distribution
- Calculating probabilities using the standard normal distribution
- Applying the normal distribution in real-world situations
The Poisson Distribution
- Understanding the properties of the Poisson distribution
- Calculating probabilities using the Poisson distribution
- Applying the Poisson distribution in real-world situations
Linear Combinations of Random Variables
- Understanding linear combinations of random variables
- Calculating means and variances of linear combinations
- Applying linear combinations in real-world situations
Continuous Random Variables
- Understanding continuous random variables
- Calculating probabilities and expected values of continuous random variables
- Applying continuous random variables in real-world situations
Sampling and Estimation
- Understanding sampling methods and sampling distributions
- Estimating population parameters using sample data
- Applying sampling and estimation techniques in real-world situations
Hypothesis Tests
- Understanding hypothesis testing
- Conducting hypothesis tests for means, proportions, and variances
- Interpreting and drawing conclusions from hypothesis tests
This course is helpful for the following exams: Grade 12