A Level Math paper 1 Link tutorial

Prior Knowledge

Solving Equations (Linear type)

• Before you start - What is a term?
• Equations with a positive x-term
• Equations with a negative x-term
• Equations with two x terms and 2 constants
• Equations with brackets
• Fractional equations (1)
• Fractional equations (2)
• Fractional equations (3)
• Fractional equations (4)
• Fractional equations (5)

Pythagoras' Theorem

• The theorem

Trigonometry: Right-Angled Triangles

• Naming the sides
• Trig ratios sinθ, cosθ and tanθ
• Finding a length (1)
• Finding a length (2)
• Finding an angle

1. Quadratics

Completing the Square

• How to do it
• Applications
  • Sketching graphs
• Exam questions

Quadratic Equations

• Equations
  • Solve by factorising
  • Solve by completing the square
  • Solve by formula
  • Exam questions
  • Extension - Solving in some function of x
  • Roots and the Discriminant
    • Roots and Discriminant
  • Exam questions

Quadratic Graphs

• Sketching quadratic graphs

Polynomials

• Polynomials

Simultaneous Equations

• Elimination method for linear types
  • Elimination method for linear equations
• Substitution Method for linear and non linear types
  • Substitution method
• Exam Questions

Inequalities

• (Linear inequalities revision)
  • introduction
  • rules for reversing the inequality sign
  • solving a linear type
  • solving a double inequality
  • Exam Questions
• Quadratic inequalities
  • solving quadratic inequalities
  • Exam Questions

2. Functions

Notation

• f(x) notation

Domain and Range

• Domain and Range 1
• Domain and Range 2

Combining Functions

• Combination of functions
  • Examples : 1 | 2

Inverse Functions

• The inverse of a function
  • Examples : 1 | 2 | 3
• Graphical relationship between f(x) and its inverse
  • Examples : 1 | 2
• Exam Questions

3. Coordinate Geometry

Gradient

• Line segment
• Parallel lines
• Perpendicular lines

Lines

• Equation of a line
• Distance between two points
• Mid-point of a line segment
• Equation of a parallel line
• Equation of a perpendicular bisector

Intersection of graphs

• Two straight lines
• Parabola and a straight line
  • Nature of intersection
  • Tangent to a curve (one root)
• Hyperbola and straight line

Exam questions

4. Circular Measure

• Arcs, Sectors and Segments
  • Radians
  • Arc length and sector area
  • Area of a segment
    • Examples
• Exam questions

5. Trigonometry

Trigonometric Ratios

• Trig. ratios for 30, 60 and 90 degrees
• Trig. ratios for 45, 45 and 90 degrees
• Trig. ratios for positive multiples of 30, 45 and 60 degrees
• Trig. ratios for negative multiples of 30, 45 and 60 degrees

Graphs

• Trigonometric graphs

• Transformations
  • Translations
  • Reflections
  • Stretches
  • Combining transformations

Equations

• The quadrant rule (or CAST diagram)
  • How to work with various different ranges
  • How to solve equations with multiple angles
• Equations that factorise
  • Solving trigonometric equations that factorise 1
  • Solving trigonometric equations that factorise 2
  • Solving trigonometric equations that factorise 3

Identities

• Two basic trigonometric identities: tanθ ≡sinθ/cosθ and sin²θ+cos²θ ≡1
  • Proving trignometric identities 1
  • Proving trignometric identities 2
  • Proving trignometric identities 3
• The identities: cos(θ) ≡ cos(-θ), sin(θ) ≡ -sin(-θ)

Solving equations using identities

• Solving trigonometric equations using identities 1
  • Solving trigonometric equations using identities 2
  • Solving trigonometric equations using identities 3
  • Solving trigonometric equations using identities 4
• Exam questions

6. Vectors

• What is a vector and a scalar quantity?
• Notation
• Position vectors
• Equal and negative vectors
• Addition and subtraction of vectors
  • example 1
  • example 2
• Magnitude of a 2 dimensional vector
• Unit vectors
• Magnitude of a 3 dimensional vector

Scalar Product (Dot Product)

• Scalar product
  • example
• Perpendicular vectors
  • example

Exam Questions

• Exam questions

7. Series

Binomial Expansion

• nCr method / Pascal's triangle method
  • nCr - What is it?
  • Binomial expansion nCr method
  • finding particular terms
  • Binomial expansion Pascal's triangle method
• Binomial formula
  • Binomial expansion formula as an alternative to the nCr method

• Binomial expansion
  • Exam questions

Arithmetic Progressions (sequences and series)

• Arithmetic sequences and series
• Sum of the first n terms
• Finding a and d given two terms
• Working with consecutive terms
• Exam questions

Geometric Series

• Introduction
  • Example 1
  • Example 2 (consecutive terms example)
  • Example 3 (investment example)
• Proof of Sum of first n terms, Sn
• Sum to infinity
  • Example
• Exam questions

8. Differentiation

Introduction

• The gradient function dy/dx
  • Differentiation from 1st principles (not required but may prove useful)
• terms of the form axⁿ
  • Extending to root types
  • Extending to fractional types
• Second Derivatives
  • The second derivative
• Exam Questions
  • Exam questions

Tangents and Normals

• Tangents and normals
• Exam Questions
  • Exam questions

The Chain Rule

• The chain rule
  • polynomial to a rational power types

Connected Rates of Change

• Introduction (example 1)
• Using three rates of change (example 2)
• Cone type problems(example 3)
• Exam Questions

Stationary Points

• Stationary points. What are they?
• Finding stationary points (example)
• Nature of a stationary point
• Finding stationary points and their nature example
• Exam questions
• Applications (Optimisation)
• Exam questions

Increasing and Decreasing functions

• Increasing and decreasing functions
• Exam questions

9. Integration

Introduction

• terms of the form axⁿ
  • fractional and root type terms
• Exam questions

Equations of curves

• Finding the equation of a curve given dy/dx
  • Using f'(x) notation
• Exam questions

(ax+b)ⁿ types

• How to do these
  • examples

Definite Integration

• Definite integration
• Infinite integrals
• Application - Area to the x-axis
  • Area under a curve
  • Finding the area below the x-axis
  • Finding the area above and below the x-axis
  • Finding the area bounded by two curves
• Area to the y-axis
  • Finding the area bounded by a curve and the y-axis
• Exam questions

• Volume of Revolution about the x-axis
  • Volume of revolution
    • Example
    • Exam Questions
  • Volume of Revolution generated between two curves
• Volume of Revolution about the y-axis
• Volume of revolution
• Volume generated between curves
• Exam Questions

Exam Papers

June 2013	Paper and video worked Solutions
Nov 2013	Paper and video worked Solutions