Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

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Performance objectives

• Sketch and interpret various functions and their transformations.
• Apply analytical geometry principles to solve problems involving lines.
• Simplify and solve trigonometric expressions and equations.
• Apply circle and triangle theorems in Euclidean geometry.

Lesson summary

This week focuses on consolidating our understanding of key Grade 11 Mathematics topics covered thus far in preparation for upcoming assessments. This revision is crucial because mathematics builds upon itself. A solid foundation in the topics we revisit this week will directly impact your ability to grasp more advanced concepts later in the year and in Grade

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2. Understanding these concepts is essential not just for passing exams but also for developing critical thinking and problem-solving skills applicable in various fields, from finance to engineering, relevant to South Africa's growing economy.

Lesson notes

2.1 Functions and Graphs Definition: A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Types of Functions (and their key characteristics): Linear Function: `f(x) = mx + c` where `m` is the gradient and `c` is the y-intercept. The graph is a straight line. Understanding the gradient is vital - in real life, it can represent the rate of change (e.g., fuel consumption rate per km).

Quadratic Function: `f(x) = ax² + bx + c` where `a`, `b`, and `c` are constants and `a ≠ 0`. The graph is a parabola.

Key features: Turning Point: The minimum or maximum point of the parabola. Can be found by completing the square or using the formula `x = -b / 2a`. x-intercepts: Where the graph intersects the x-axis (solve `f(x) = 0`). y-intercept: Where the graph intersects the y-axis (when `x = 0`).

Axis of Symmetry: The vertical line that passes through the turning point.

Exponential Function: `f(x) = a^x` where `a > 0` and `a ≠ 1`.

Key features: Always passes through (0, 1) (if not transformed). Has a horizontal asymptote at y = 0 (if not transformed). Represents exponential growth (if `a > 1`) or decay (if `0 0`) or down (if `k 0`) or left (if `h 1`) or compresses it (if `0 < |a| < 1`).

Reflection about the x-axis: `-f(x)`.