Vectors

Vectors

Algebra

  • Expressions - Learn to simplify algebraic expressions by combining like terms.
  • Equations - Understand how to solve linear, quadratic and simultaneous equations.

Algebraic Fractions

  • Understand how to add, subtract, multiply, and divide algebraic fractions.

Completing the Square

  • Learn the process of completing the square for a quadratic expression.

Equations

  • Understand the techniques for solving linear, quadratic, cubic and reciprocal equations.
  • Acknowledge the significance of the discriminant in a quadratic equation.

Trigonometry

  • Understanding sine, cosine, and tangent ratios.
  • Be familiar with the sine and cosine rules.
  • Learn how to use trigonometry to solve problems involving right-angled triangles.

Trigonometric Equations

  • Learn how to solve trigonometric equations.
  • Understand the graphical representation of trigonometric functions.

Solution of Triangles

  • Familiarize yourself with the Sine rule, Cosine rule, and the area of a triangle.
  • Learn how to solve problems involving non-right-angled triangles.

Differentiation

  • Understand the concept of a derivative and its geometric interpretation.
  • Be familiar with the rules of differentiation and apply them.

Differentiation of a Basic Function

  • Learn how to differentiate basic functions such as polynomials, exponentials, sin x, cos x, e^x, ln x.

Applications of Differentiation

  • Learn how to use differentiation to find the gradient of a tangents and normals, rates of change, maximum and minimum points.

Integration

  • Understand the concept of a integral and its geometric interpretation.

Integration of a Basic Function

  • Learn how to integrate basic functions such as polynomials, exponentials, sin x, cos x, e^x, ln x.

Applications of Integration

  • Learn how to use integration to find the area under a curve, to calculate the length of a curve, to solve differential equations.

Logarithms

  • Understand the change of base rule and apply it.
  • Understand the laws of logarithms.

Law of Logarithms

  • Learn how to apply the laws of logarithms to simplify expressions and solve equations.

Matrices

  • Understand the basics of matrices including addition, subtraction, multiplication and the determinant of a matrix.
  • Learn how to solve a system of linear equations using matrices.

Matrix Calculations

  • Understand how to carry out various matrix calculations including scalar multiplication, matrix multiplication.

Matrix Equations

  • Learn to form and solve matrix equations.

Simultaneous Equations

  • Learn how to solve simultaneous linear equations algebraically and graphically.
  • Understand the geometric interpretation of simultaneous equations.

Vectors

  • Understand the concepts of magnitude and direction in relation to vectors.
  • Be familiar with vector arithmetic, including addition, subtraction and multiplication by a scalar.
  • Able to solve problems requiring the use of vectors in two or three dimensions.