P1 Tutorials

Prior Knowledge

Algebra Basics

  1. Expanding a single bracket
  2. Expanding two or more brackets
  3. Squaring a bracket
  4. Terms in expressions and equations
  5. Identity or equation - what is the difference?
  6. Linear Equations with a positive x term
  7. Linear equations with a negative x-term
  8. Linear equations with two x-terms
  9. Linear equations with brackets
  10. Fractional linear equations
  11. f(x) notation
  12. Polynomials

Polynomials

  1. Polynomials

Indices

  1. Introduction to indices (exponents)
  2. Multiplication rules for indices
  3. Division rule for indices
  4. Negative indices
  5. Fractions raised to a negative index
  6. Rational (fractional) indices
  7. Simplifying terms with negative powers
  8. Expressing terms in the form axn
  9. Equations in which the power has to be found
  10. Summary of indices
  11. Exam Questions - Indices

Surds

  1. Surds - introduction & simplifying
  2. Addition and subtraction of surds
  3. Multiplying surds
  4. Dividing surds
  5. Rationalising surds
  6. Exam Questions - Surds

Algebra and Functions 1

Completing the Square

  1. Completing the square
  2. Applications of completing the square
  3. Exam Questions - Completing the square

Simultaneous Equations

  1. Elimination method for linear equations
  2. Substitution method for linear and non-linear equations
  3. Exam Questions - Simultaneous equations

Quadratics

Quadratic Equations

  1. Solve by factorising
  2. Solve by completing the square
  3. Solve by the quadratic formula
  4. Exam Questions - Solved by the quadratic formula
  5. Solving equations with equal terms on both sides (Common error)
  6. Solving quadratic equations in some function of x

Quadratic Equations – Roots and Discriminant

  1. Roots and discriminant of a quadratic equation
  2. Exam Questions - Roots and discriminant

Quadratic Graphs

  1. Sketching quadratic graphs

Inequalities

Inequalities

  1. Linear inequalities
  2. Rules for reversing the inequality sign
  3. Solving a linear type
  4. Solving a double inequality
  5. Exam Questions - Solving a double inequality
  6. Quadratic inequalities
  7. Exam Questions - Quadratic inequalities

Algebra and Functions 2

Working with Functions

  1. f(x) notation
  2. Domain and range
  3. Exam Questions - Domain and range
  4. Combination of functions
  5. The inverse of a function
  6. Graphical relationship between f(x) and its inverse
  7. Exam Questions - Inverse functions
  8. Exam Questions - Functions

Coordinate Geometry

Gradient

  1. Line segment
  2. Parallel lines
  3. Perpendicular lines

Lines

  1. Equation of a straight line: y=mx+c
  2. Equation of a line given the gradient and point
  3. Distance between two points
  4. Mid-point of a line segment
  5. Equation of a parallel line
  6. Equation of a perpendicular bisector

Intersection of Graphs

  1. Intersection of two straight lines
  2. Intersection of a straight line and a parabola
  3. Intersection of a straight line and a hyperbola
  4. Nature of the intersection

Trigonometry

Trigonometric Ratios

  1. Trigonometric ratios for 30°, 45° and 60°
  2. Trig ratios for multiples of 30°, 45° and 60°

Trigonometric Graphs and Transformations

  1. Trigonometric graphs
  2. Translations of trig graphs
  3. Reflections of trig graphs
  4. Stretches of trig graphs
  5. Combining transformations
  6. Exam Questions - Trigonometric graphs and transformations

Applications of Trigonometry

  1. Radians
  2. Arcs, sectors and segments
  3. Exam Questions - Arcs, sectors and segments

Trigonometric Equations

  1. Quadrant rule to solve trig equations
  2. Trig equations with different ranges
  3. Trig equations with multiple angles
  4. Trig equations that factorise
  5. Solving equations with equal terms on both sides (Common error)

Trigonometric Identities

  1. Using the identities: tanθ ≡sinθ/cosθ and sin²θ+cos²θ ≡1
  2. Using the identities: cos(θ) ≡ cos(-θ), sin(θ) ≡ -sin(-θ)
  3. Solving equations using identities
  4. Exam Questions - Trigonometric identities

Vectors

Vectors

  1. What is a vector and a scalar quantity?
  2. Vector notation
  3. Position vectors
  4. Equal and negative vectors
  5. Multiplying a vector by a scalar
  6. Addition and subtraction of vectors
  7. Magnitude of a 2 dimensional vector
  8. Magnitude of a 3 dimensional vector
  9. Unit vectors

Scalar Product (Dot Product)

  1. Scalar product
  2. Perpendicular vectors
  3. Exam Questions - Scalar product

Sequences and Series

Arithmetic Progressions

  1. Arithmetic progressions
  2. Sum of the first n terms
  3. Finding a and d given two terms
  4. Working with consecutive terms
  5. Exam Questions - Arithmetic sequences and series
  6. Examsolutions Beastie - Arithmetic progressions

Geometric Series

  1. Geometric series
  2. Proof of sum of first n terms, Sn
  3. Sum to infinity
  4. Exam Style Questions - Geometric Series and Progressions
  5. Exam Questions - Geometric series

Binomial Expansion

  1. Binomial expansion
  2. Exam Questions - Binomial expansion for positive integer powers
  3. Exam Questions - Binomial expansion, comparing coefficients
  4. Exam Questions - Binomial expansion, estimating a value
  5. Exam Questions - Binomial expansion, other

Differentiation

Differentiation – Introduction

  1. The gradient function dy/dx
  2. Differentiation - terms of the form axn
  3. The second derivative
  4. Exam Questions - Differentiation: introduction

Tangents and Normals

  1. Equations of tangents and normals
  2. Exam Questions - Tangents and normals

The Chain Rule

  1. Chain rule: Polynomial to a rational power
  2. Chain rule: Exponential types
  3. Chain rule: Natural log types
  4. Chain rule: Trigonometric types

Connected Rates of Change

  1. Connected rates of change
  2. Using three connected rates of change
  3. Connected rates of change cone type problems
  4. Exam Questions - Connected rates of change

Stationary Points

  1. Stationary points
  2. Nature of a stationary point
  3. Exam Questions - Stationary points
  4. Applications of stationary points
  5. Exam Questions - Applications of stationary points

Increasing and Decreasing functions

  1. Increasing and decreasing functions
  2. Exam Questions - Increasing and decreasing functions

Integration

Integration – Introduction

  1. Integration - Terms of the form axn
  2. Exam Questions - Integration: introduction

Equations of Curves

  1. Finding the equation of a curve given the gradient function
  2. Exam Questions - Equations of curves

Integration – Common Functions

  1. Integration:(ax+b)n types
  2. Exam Questions - Integration:(ax+b)n types

Definite Integration

  1. Definite integration
  2. Exam Questions - Definite Integration
  3. Convergent and Divergent Integrals

Applications of Integration – Area bound by a curve

  1. Area bound by a curve and x-axis
  2. Exam Questions - Area bound by a curve and x-axis
  3. Area bound by a curve and y-axis
  4. Exam Questions - Area bound by a curve and y-axis

Applications of Integration – Volumes of revolution

  1. Volume of revolution about the x-axis
  2. Exam Questions - Volume of revolution about the x-axis
  3. Volume of revolution about the x-axis generated between curves
  4. Volume of Revolution about the y-axis
  5. Exam Questions - Volume of Revolution about the y-axis
  6. Volume of Revolution about the y-axis generated between curves