Course outline

Aim

• To build confidence and understanding of mathematical ideas.
• To enable the student to interpret and solve mathematical problems.
• To improve examination technique and to make the student aware of common examination errors.
• To make the student fully aware of the content and emphasis of the specification.
• To strengthen revision methods.

Key Topics Covered

1. Algebra and functions

• Simple algebraic division; use of the Factor Theorem and the Remainder Theorem.

2. Coordinate geometry in the (x, y) plane

• Coordinate geometry of the circle using the equation of a circle in the form (x-a)² + (y-b)²=r² and including use of the following circle properties:
  (i) the angle in a semicircle is a right angle;
  (ii) the perpendicular from the centre to a chord bisects the chord;
  (iii) the perpendicularity of radius and tangent.

3. Sequence and series

• The sum of a finite geometric series; the sum to infinity of a convergent geometric series, including the use of |r| <1.
• Binomial expansion of (1+x)ⁿ for positive integer n. The notations n! and .

4. Trigonometry

• The sine and cosine rules, and the area of a triangle in the form ½ab sin C.
• Radian measure, including use for arc length and area of sector.
• Sine, cosine and tangent functions. Their graphs, symmetries and periodicity.
• Solution of simple trigonometric equations in a given interval.
• Knowledge and use of and sin²θ + cos² ≡ 1.

5. Exponentials and logarithms

• y=a^x and its graph.
• Laws of logarithms.
• The solution of equations of the form a^x=b.

6. Differentiation

• Applications of differentiation to maxima and minima and stationary points.
• Increasing and decreasing functions.

7. Integration

• Evaluation of definite integrals.
• Interpretation of the definite integral as the area under a curve.
• Approximation of area under a curve using the trapezium rule.