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  • IGCSE
    • IGCSE Unit Resources >
      • Unit 1 - Percentages
      • Unit 2 - Sets
      • Unit 3 - Indices and Surds
      • Unit 4 - Circle Theorems
      • Unit 5 - Formulae
      • Unit 6 - Vectors
      • Unit 7 - Quadratic Equations
      • Unit 8 - Tree Diagrams
      • Unit 9 - Coordinate Geometry
      • Unit 10 - Sequences
      • Unit 11 - Statistical Diagrams
      • Unit 12 - Composite and Inverse Functions
      • Unit 13 - Similarity
      • Unit 14 - Variation
      • Unit 15 - Algebraic Fractions
      • Unit 16 - Advanced Trigonometry
      • Unit 17 - Quadratic Functions
      • Unit 18 - Volumes and Surface Area
      • Unit 19 - Graphs
      • Unit 20 - Logarithms
      • Unit 21 - Transforming Graphs
    • IGCSE Revision Materials
  • IB
    • Mathematical Studies >
      • MSSL Unit Resources >
        • Unit 1 - Number Review
        • Unit 2 - Sequences and Series
        • Unit 3 - Statistics 1
        • Unit 4 - Functions 1
        • Unit 5 - Trigonometry and Mensurations
        • Unit 6 - Functions 2
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        • Unit 8 - Differentiation
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        • Unit 13 - Logic
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      • HL Unit Resources >
        • Unit 1 - Algebra
        • Unit 2 - Functions & Equations
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        • Unit 4 - Exponentials and Logarithms
        • Unit 5 - Statistics and Probability
        • Unit 6 - Differential Calculus
        • Unit 7 - Discrete Probability Distributions
        • Unit 8 - Integral Calculus
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        • Unit 12 - Vectors
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      • AASL Unit Resources >
        • Unit 0 - Proof
        • Unit 1 - Algebra Functions Basics
        • Unit 2 - Functions, Equations and Inequalities
        • Unit 3 - Sequences and Series
        • Unit 4 - Exponentials and Logarithms
        • Unit 5 - Trigonometric Functions and Equations
        • Unit 6 - Differentiation 1
      • AASL Revision Materials
      • AASL Key Skills Generator

Unit 2 - Functions and Equations

Unit Objectives
​
Prior Knowledge:
  • Find composite and inverse functions
  • Solve quadratics using factorization or quadratic formula​
By the end of this unit students should be able to:
  • Understand the concepts of; a function, domain, range, image value, one-to-one, many-to-one [2.1]
  • Identify Odd and Even functions. [2.1]
  • Find and graph inverse functions including domain restrictions and identifying self-inverse functions. [2.1]
  • Graph functions identifying key features; turning points, axis intercepts, asymptotes, domain and range. [2.2]
  • Graph absolute value of a function, function of the absolute value and reciprocal of a function. [2.2]
  • Transform functions and their graphs. [2.3]
  • Sketch and identify rational functions with any linear numerator and denominator. [2.4]
  • Know and use the factor and remainder theorems. [2.5]
  • Solve polynomial equations using algebra and technology. [2.6]
  • Complete the square of a quadratic and identify vertex and axis of symmetry. [2.6]
  • Use the discriminant to determine the nature of roots. [2.6]
  • Solve problems using the sum and product of roots of a polynomial. [2.6]
  • Solve inequalities of one function greater (or equal to) another function using graphical and algebraic methods for polynomials up to degree 3. [2.7]
  • Solve unfamiliar equations using technology. [2.6]
Lesson Resources​
1. Function
Lesson Sheet
Lesson Sheet Complete
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2. Special Functions
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3. Quadratic Equations
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Worksheet
4. Quadratic Functions
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5. Completing the Square
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6. Composite Functions
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7. Inverse Functions
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8. Graphing Modulus
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9. ​Modulus (In)Equations
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10. Graphs of 1 over f(x)
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11. Transformations of Graphs
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12. Polynomials
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13. Polynomial Divsion
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14. Factor and Remainder Theorem
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15. Polynomial Inequalities
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16. Sums and Products of Roots of Polynomials
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17. Systems of Equations
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For a whole range of mathematical activities for use in and out of the classroom, including random question generators, Bingo generators and worksheet generators, as well as computer based investigations and activities check out my main site: www.interactive-maths.com.

​If you are interested in codes, ciphers and codebreaking, then check out my secondary site, Crypto Corner, dedicated to providing information about all types of ciphers, as well as tools for encrypting, decrypting and breaking messages.
  • Home
  • IGCSE
    • IGCSE Unit Resources >
      • Unit 1 - Percentages
      • Unit 2 - Sets
      • Unit 3 - Indices and Surds
      • Unit 4 - Circle Theorems
      • Unit 5 - Formulae
      • Unit 6 - Vectors
      • Unit 7 - Quadratic Equations
      • Unit 8 - Tree Diagrams
      • Unit 9 - Coordinate Geometry
      • Unit 10 - Sequences
      • Unit 11 - Statistical Diagrams
      • Unit 12 - Composite and Inverse Functions
      • Unit 13 - Similarity
      • Unit 14 - Variation
      • Unit 15 - Algebraic Fractions
      • Unit 16 - Advanced Trigonometry
      • Unit 17 - Quadratic Functions
      • Unit 18 - Volumes and Surface Area
      • Unit 19 - Graphs
      • Unit 20 - Logarithms
      • Unit 21 - Transforming Graphs
    • IGCSE Revision Materials
  • IB
    • Mathematical Studies >
      • MSSL Unit Resources >
        • Unit 1 - Number Review
        • Unit 2 - Sequences and Series
        • Unit 3 - Statistics 1
        • Unit 4 - Functions 1
        • Unit 5 - Trigonometry and Mensurations
        • Unit 6 - Functions 2
        • Unit 7 - Statistics 2
        • Unit 8 - Differentiation
        • Unit 9 - Sets and Probability
        • Unit 10 - Functions 3
        • Unit 11 - Financial Maths
        • Unit 12 - Statistics 3
        • Unit 13 - Logic
      • IB Studies Revision Homework
      • MSSL Revision Materials
      • Studies Exam Question Practice
    • Mathematics Higher Level >
      • HL Unit Resources >
        • Unit 1 - Algebra
        • Unit 2 - Functions & Equations
        • Unit 3 - Trigonometry
        • Unit 4 - Exponentials and Logarithms
        • Unit 5 - Statistics and Probability
        • Unit 6 - Differential Calculus
        • Unit 7 - Discrete Probability Distributions
        • Unit 8 - Integral Calculus
        • Unit 9 - Continuous Probability Distributions
        • Unit 10 - Complex Numbers
        • Unit 11A - Statistics Option
        • Unit 11B - Sets and Groups Option
        • Unit 12 - Vectors
      • HL Revision Materials >
        • HL Weekly Quizzes
    • Mathematics AA SL >
      • AASL Unit Resources >
        • Unit 0 - Proof
        • Unit 1 - Algebra Functions Basics
        • Unit 2 - Functions, Equations and Inequalities
        • Unit 3 - Sequences and Series
        • Unit 4 - Exponentials and Logarithms
        • Unit 5 - Trigonometric Functions and Equations
        • Unit 6 - Differentiation 1
      • AASL Revision Materials
      • AASL Key Skills Generator