Grade 11 Mathematics Exam Preparation

Exam Details

• Duration: 2 hours
• Marks: 100

Key Concepts and Techniques

Expressions Defined

• Square Roots: The number inside must be ≥ 0 (0 or positive).
• Fractions: The denominator must not be zero.
• Example: For the expression ( \frac{3x - 1}{x - 1} )
  • Numerator = 0 and Denominator ≠ 0
  • Critical values: numerator and denominator equal to 0 (i.e, set both to zero)

Solving Equations

• Factoring brackets directly for solutions.
• Inequalities: Solve by critical values (e.g., number lines).

Quadratic Formula

• Use when expressions cannot be factorized.
  • Equation format: ( ax^2 + bx + c = 0 )
  • Quadratic formula: ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} )

Exponential and Logarithmic Functions

• Converting bases and exponents based on given equations.

Simultaneous Equations

• Simplify one equation to isolate one variable and substitute in the second equation.

Advanced Algebra Techniques

Simplifying Expressions (Square roots)

• Split the number under the square root into factors where one of the factors is a perfect square.

Completing the Square

• Transform trinomial form of quadratics to turning point form.

Number Patterns and Sequences

• Identify linear and quadratic number patterns by differences (first and second differences).
• Use quadratic sequence formulas: [ 2a = 2, 3a + b = 4, a + b + c = 1 ]
• Calculate specific terms in a sequence using derived formula.

Graph Transformation

• Reflection and translations of graphs on the coordinate plane.

Asymptotes and Hyperbolas

• Recognize and write down the equations of vertical and horizontal asymptotes for hyperbolas.

Solve Exam Questions

Writing Coordinates and Plotting Graphs

• Express solutions to specific questions graphically and analytically.

Analyzing and Solving Graph Questions

• Determine the properties and transformations of given functions based on given questions.

Summarize and Simplify Complex Equations

• Break down each problem into manageable steps and ensure understanding of fundamental concepts.

Problem Areas

• Revisit and practice sections where you make mistakes or feel less confident regularly.