9709 AS PURE MATHEMATICS 1

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This course covers the learning outcomes for the Pure 1 component of 2023–2027, 9709 AS/AL Mathematics syllabus.

SECTIONS:

Quadratics

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1 Quadratics

1.1 Completing the square 18 Tasks | 2 Quizzes

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1.1 Pre Quiz: Completing The Square

1.1 Terms and definitions: Completing the square

1.1 Worksheet 1: Simplifying completed square expressions

1.1 Learning outcomes for completing the square

1.1 View notes 1: Why completing the square is important, and how it is used

1.1 View exam questions examples: completing the square

1.1 Watch videos: completing the square

1.1 Worksheet 2: Basic completing the square

1.1 Watch videos 2: Equating coefficients

1.1 Worksheet 3: Completing the square using “Equating coefficients”

1.1 Worksheet 4 (short): Stating the vertex from the completed square form

1.1 Worksheet 5: Solve for 𝑥 algebraically

1.1 Watch videos 3: Completing the square of a𝑥²+b𝑥+c where a≠1

1.1 Read & progress through the content in your textbook

1.1 Worksheet 6: More complex completing the square

1.1 Worksheet 7: Solve exam examples

1.1 Complete End of Chapter questions that relate to Completing the Square

1.1 Post quiz: Completing The Square

1.2 Solving quadratic equations 12 Tasks | 2 Quizzes

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1.2 Pre Quiz: Solving quadratic equations

1.2 Complete the terms and definitions

1.2 Read learning outcomes

1.2 View notes: Methods of solving quadratic equations

1.2 View exam examples

1.2 Watch video 1: Basic factors, factorisation of a𝑥²+b𝑥+c where a≠1, & The Quadratic Formula

1.2 Worksheet 1: Basic factors, factorisation of a𝑥²+b𝑥+c where a≠1, & The Quadratic Formula

1.2 Watch video 2: Solving quadratic inequalities

1.2 Worksheet 2: Solve quadratic inequalities

1.2 Read & progress through the content in your textbook

1.2 Solve exam examples

1.2 Complete the Post Quiz

1.2 Post Quiz: Solving Quadratic Equations

1.3 Quadratics in some function of 𝑥 10 Tasks | 2 Quizzes

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1.3 Pre Quiz: Quadratics in some function of 𝑥

1.3 Complete the terms and deinitions

1.3 Read learning outcomes

1.3 View notes: Identifying a quadratic in some function of 𝑥

1.3 View exam examples

1.3 Watch video

1.3 Worksheet: solving quadratics in functions of 𝑥

1.3 Read & progress through the content in your textbook

1.3 Solve exam examples

Complete the Post Quiz

Post Quiz: Quadratics in some function of 𝑥

1.4 Solving simultaneous equations 10 Tasks | 2 Quizzes

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1.4 Pre Quiz: Solving simultaneous equations

1.4 Complete the terms and definitions

1.4 Read learning outcomes

1.4 View notes: Solving simultaneous equations where one is linear and one non-linear

1.4 View exam examples

1.4 Watch video: Solving simultaneous equations

1.4 Worksheet: Solving simultaneous equations

1.4 Read & progress through the content in your textbook

1.4 Solve exam examples

1.4 Complete the Post Quiz

Post Quiz: Simultaneous equations

1.5 The discriminant 10 Tasks | 2 Quizzes

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1.5 Complete the Pre Quiz

1.5 Pre Quiz: The discriminant

1.5 Complete the terms and definitions

1.5 Read learning outcomes

1.5 View notes: The Discriminant

1.5 View exam examples

1.5 Watch video: The discriminant

1.5 Worksheet: The discriminant

1.5 Read & progress through the content in your textbook

1.5 Solve exam examples

1.5 Complete the Post Quiz

1.5 Post Quiz: The discriminant

2 Functions

2.1 Definition of a function 5 Tasks | 1 Quiz

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2.1 Read learning outcomes

2.1 View notes: Functions

2.1 Complete the terms and definitions: Functions

2.1 Read & progress through the content in your textbook

2.1 Complete the Post Quiz

Post Quiz: Function definitions

2.2 Domain, Range, & Composite Functions 8 Tasks | 2 Quizzes

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2.2 Complete the Pre Quiz

2.2 Pre Quiz: Functions, domain, range, & composites

2.2 Read learning outcomes

2.2 View exam examples

2.2 Watch videos: Functions, domain, range, & composites

2.2 Worksheet: Functions, domain, range, & composites

2.2 Read & progress through the content in your textbook

2.2 Solve exam examples

2.2 Complete the Post Quiz

Post Quiz: Functions, domain, range, & composites

2.3 Many-one, One-one, & Inverse Functions 8 Tasks | 2 Quizzes

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2.3 Complete the Pre Quiz

2.3 Pre Quiz: one-one functions & inverse functions

2.3 Read learning outcomes

2.3 View exam examples

2.3 Watch videos: inverse functions

2.3 Worksheet: inverse functions

2.3 Read and progress through the content in your textbook

2.3 Solve exam examples

2.3 Complete the Post Quiz

2.3 Post Quiz: many-one, one-one, & inverse functions

2.4 Function Transformations 9 Tasks | 2 Quizzes

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2.4 Complete the Pre Quiz

2.4 Pre Quiz: Function transformations

2.4 Read learning outcomes

2.4 View exam examples

2.4 View notes: Function transformations

2.4 Watch videos: Function transformations

2.4 Worksheet: Function transformations

2.4 Read & progress through the content in your textbook

2.4 Solve exam examples

2.4 Complete the Post Quiz

2.4 Post Quiz: Function transformations

3 Coordinate Geometry

3.1 Straight lines: Gradients, Intercepts, Equation Forming, Perpendiculars, Distances, and Mid- & Intersection points 10 Tasks | 2 Quizzes

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3.1 Complete the Pre Quiz

3.1 Pre Quiz: Straight lines

3.1 Complete the terms and definitions: Straight Lines

3.1 Read learning outcomes: Straight Lines (Gradients, Intercepts, Equation Forming, Perpendiculars, Distances, and Mid- & Intersection points)

3.1 View exam examples: Straight Lines (Gradients, Intercepts, Equation Forming, Perpendiculars, Distances, and Mid- & Intersection points)

3.1 View notes: Straight Lines (Gradients, Intercepts, Equation Forming, Perpendiculars, Distances, and Mid- & Intersection points)

3.1 Watch videos: Straight Lines (Gradients, Intercepts, Equation Forming, Perpendiculars, Distances, and Mid- & Intersection points)

3.1 Worksheet: Straight Lines (Gradients, Intercepts, Equation Forming, Perpendiculars, Distances, and Mid- & Intersection points)

3.1 Read & progress through the content in your textbook: Straight lines

3.1 Solve exam examples

3.1 Complete the Post Quiz

3.1 Post Quiz: Straight lines

3.2 Understand the Circle Equation including expanded form 10 Tasks | 2 Quizzes

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3.2 Complete the Pre Quiz: Understand the Circle Equation including expanded form

3.2 Pre Quiz: Understand the Circle Equation including expanded form

3.2 Complete the terms and definitions: Circles

3.2 Read learning outcomes: Understand the Circle Equation including expanded form

3.2 View exam examples: Understand the Circle Equation including expanded form

3.2 View Notes: Understand the Circle Equation including expanded form

3.2 Watch videos: Understand the Circle Equation including expanded form

3.2 Worksheet: Understand the Circle Equation including expanded form

3.2 Read and Progress through the content in your textbook: Understand the Circle Equation including expanded form

3.2 Solve Exam Examples: Understand the Circle Equation including expanded form

3.2 Complete the Post Quiz: Understand the Circle Equation including expanded form

3.2 Post Quiz: Understand the Circle Equation

3.3 Algebraic problem solving: Lines, Circles & Circle geometric properties 10 Tasks | 2 Quizzes

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3.3 Complete the Pre Quiz: Algebraic problem solving: Lines, Circles & Circle geometric properties

3.3 Pre Quiz: Algebraic problem solving: Lines, Circles & Circle geometric properties

3.3 Complete the terms and definitions: Algebraic Problem Solving

3.3 Read learning outcomes: Algebraic problem solving: Lines, Circles & Circle geometric properties

3.3 View exam examples: Algebraic problem solving: Lines, Circles & Circle geometric properties

3.3 View Notes: Algebraic problem solving: Lines, Circles & Circle geometric properties

3.3 Watch videos: Algebraic problem solving: Lines, Circles & Circle geometric properties

3.3 Worksheet: Algebraic problem solving: Lines, Circles & Circle geometric properties

3.3 Read and Progress through the content in your textbook: Algebraic problem solving: Lines, Circles & Circle geometric properties

3.3 Solve Exam Examples: Algebraic problem solving: Lines, Circles & Circle geometric properties

3.3 Complete the Post Quiz: Algebraic problem solving: Lines, Circles & Circle geometric properties

Post Quiz: Algebraic problem solving: Lines, Circles & Circle geometric properties

3.4 Relationship: Graphs – Equation, Intersection points – equations 10 Tasks | 2 Quizzes

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3.4 Complete the Pre Quiz: Relationship: Graphs – Equation, Intersection points – equations

Pre Quiz: Relationship: Graphs – Equation, Intersection points – equations

3.4 Complete the terms and definitions: Relationship Graphs / Intersection points

3.4 Read learning outcomes: Relationship: Graphs – Equation, Intersection points – equations

3.4 View exam examples: Relationship: Graphs – Equation, Intersection points – equations

3.4 View Notes: Relationship: Graphs – Equation, Intersection points – equations

3.4 Watch videos: Relationship: Graphs – Equation, Intersection points – equations

3.4 Worksheet: Relationship: Graphs – Equation, Intersection points – equations

3.4 Read and Progress through the content in your textbook: Relationship: Graphs – Equation, Intersection points – equations

3.4 Solve Exam Examples: Relationship: Graphs – Equation, Intersection points – equations

3.4 Complete the Post Quiz: Relationship: Graphs – Equation, Intersection points – equations

3.4 Post Quiz: Relationship: Graphs – Equation, Intersection points – equations

4 Circular Measure

4.1 Radian Definition, Relationship between Radians and Degrees 10 Tasks | 2 Quizzes

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4.1 Complete the Pre Quiz: Radian Definition, Relationship between Radians and Degrees

4.1 Pre Quiz: Radian Definition, Relationship between Radians and Degrees

4.1 Complete the terms and definitions: Radian Definition, Relationship: Radians and degrees

4.1 Read learning outcomes: Radian Definition, Relationship between Radians and Degrees

4.1 View exam examples: Radian Definition, Relationship between Radians and Degrees

4.1 View Notes: Radian Definition, Relationship between Radians and Degrees

4.1 Watch videos: Radian Definition, Relationship between Radians and Degrees

4.1 Worksheet: Radian Definition, Relationship between Radians and Degrees

4.1 Read and Progress through the content in your textbook: Radian Definition, Relationship between Radians and Degrees

4.1 Solve Exam Examples: Radian Definition, Relationship between Radians and Degrees

4.1 Complete the Post Quiz: Radian Definition, Relationship between Radians and Degrees

4.1 Post Quiz: Radian Definition, Relationship between Radians and Degrees

4.2 Circle: Arc length, Sector area. Lengths, angles, areas – triangles 10 Tasks | 2 Quizzes

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4.2 Complete the Pre Quiz: Circle: Arc length, Sector area. Lengths, angles, areas – triangles

4.2 Pre Quiz: Circle: Arc length, Sector area. Lengths, angles, areas – triangles

4.2 Complete the terms and definitions: Circles

4.2 Read learning outcomes: Circle: Arc length, Sector area. Lengths, angles, areas – triangles

4.2 View exam examples: Circle: Arc length, Sector area. Lengths, angles, areas – triangles

4.2 View Notes: Circle: Arc length, Sector area. Lengths, angles, areas – triangles

4.2 Watch videos: Circle: Arc length, Sector area. Lengths, angles, areas – triangles

4.2 Worksheet: Circle: Arc length, Sector area. Lengths, angles, areas – triangles

4.2 Read and Progress through the content in your textbook: Circle: Arc length, Sector area. Lengths, angles, areas – triangles

4.2 Solve Exam Examples: Circle: Arc length, Sector area. Lengths, angles, areas – triangles

4.2 Complete the Post Quiz: Circle: Arc length, Sector area. Lengths, angles, areas – triangles

4.2 Post Quiz: Circle: Arc length, Sector area. Lengths, angles, areas – triangles

5 Trigonometry

5.1 Graphs: Sin, Cos and Tan functions 10 Tasks | 2 Quizzes

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5.1 Complete the Pre Quiz: Graphs: Sin, Cos and Tan functions

5.1 Pre Quiz: Graphs: Sin, Cos and Tan functions

5.1 Complete the terms and definitions: Sin, Cos, Tan functions

5.1 Read learning outcomes: Graphs: Sin, Cos and Tan functions

5.1 View exam examples: Graphs: Sin, Cos and Tan functions

5.1 View Notes: Graphs: Sin, Cos and Tan functions

5.1 Watch videos: Graphs: Sin, Cos and Tan functions

5.1 Worksheet: Graphs: Sin, Cos and Tan functions

5.1 Read and Progress through the content in your textbook: Graphs: Sin, Cos and Tan functions

5.1 Solve Exam Examples: Graphs: Sin, Cos and Tan functions

5.1 Complete the Post Quiz: Graphs: Sin, Cos and Tan functions

5.1 Post Quiz: Graphs: Sin, Cos and Tan functions

5.2 Exact values: Sin, Cos and Tan of 30°, 45°, 60°, and related angles 10 Tasks | 2 Quizzes

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5.2 Complete the Pre Quiz: Exact values: Sin, Cos and Tan of 30°, 45°, 60°, and related angles

5.2 Pre Quiz: Exact values: Sin, Cos and Tan of 30°, 45°, 60°, and related angles

5.2 Complete the terms and definitions: Exact Values Sin, Cos Tan of Angles

5.2 Read learning outcomes: Exact values: Sin, Cos and Tan of 30°, 45°, 60°, and related angles

5.2 View exam examples: Exact values: Sin, Cos and Tan of 30°, 45°, 60°, and related angles

5.2 View Notes: Exact values: Sin, Cos and Tan of 30°, 45°, 60°, and related angles

5.2 Watch videos: Exact values: Sin, Cos and Tan of 30°, 45°, 60°, and related angles

5.2 Worksheet: Exact values: Sin, Cos and Tan of 30°, 45°, 60°, and related angles

5.2 Read and Progress through the content in your textbook: Exact values: Sin, Cos and Tan of 30°, 45°, 60°, and related angles

5.2 Solve Exam Examples: Exact values: Sin, Cos and Tan of 30°, 45°, 60°, and related angles

5.2 Complete the Post Quiz: Exact values: Sin, Cos and Tan of 30°, 45°, 60°, and related angles

5.2 Post Quiz: Exact values: Sin, Cos and Tan of 30°, 45°, 60°, and related angles

5.3 Inverse Trig Relationships as Examples of Inverse Functions 10 Tasks | 2 Quizzes

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5.3 Complete the Pre Quiz: Inverse Trig Relationships as Examples of Inverse Functions

5.3 Pre Quiz: Inverse Trig Relationships as Examples of Inverse Functions

5.3 Complete the terms and definitions: Inverse Trig Relationships

5.3 Read learning outcomes: Inverse Trig Relationships as Examples of Inverse Functions

5.3 View exam examples: Inverse Trig Relationships as Examples of Inverse Functions

5.3 View Notes: Inverse Trig Relationships as Examples of Inverse Functions

5.3 Watch videos: Inverse Trig Relationships as Examples of Inverse Functions

5.3 Worksheet: Inverse Trig Relationships as Examples of Inverse Functions

5.3 Read and Progress through the content in your textbook: Inverse Trig Relationships as Examples of Inverse Functions

5.3 Solve Exam Examples: Inverse Trig Relationships as Examples of Inverse Functions

5.3 Complete the Post Quiz: Inverse Trig Relationships as Examples of Inverse Functions

5.3 Post Quiz: Inverse Trig Relationships as Examples of Inverse Functions

5.4 sinθ/cosθ equivalent to tanθ – identities, expressions, equations 10 Tasks | 2 Quizzes

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5.4 Complete the Pre Quiz: sinθ/cosθ equivalent to tanθ – identities, expressions, equations

5.4 Pre Quiz: sinθ/cosθ equivalent to tanθ – identities, expressions, equations

5.4 Complete the terms and definitions: sinθ/cosθ equivalent to tanθ

5.4 Read learning outcomes: sinθ/cosθ equivalent to tanθ – identities, expressions, equations

5.4 View exam examples: sinθ/cosθ equivalent to tanθ – identities, expressions, equations

5.4 View Notes: sinθ/cosθ equivalent to tanθ – identities, expressions, equations

5.4 Watch videos: sinθ/cosθ equivalent to tanθ – identities, expressions, equations

5.4 Worksheet: sinθ/cosθ equivalent to tanθ – identities, expressions, equations

5.4 Read and Progress through the content in your textbook: sinθ/cosθ equivalent to tanθ – identities, expressions, equations

5.4 Solve Exam Examples: sinθ/cosθ equivalent to tanθ – identities, expressions, equations

5.4 Complete the Post Quiz: sinθ/cosθ equivalent to tanθ – identities, expressions, equations

5.4 Post Quiz: sinθ/cosθ equivalent to tanθ – identities, expressions, equations

5.5 Solutions of simple Trig Equations in a specified interval 10 Tasks | 2 Quizzes

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5.5 Complete the Pre Quiz: Solutions of simple Trig Equations in a specified interval

5.5 Pre Quiz: Solutions of simple Trig Equations in a specified interval

5.5 Complete the terms and definitions: Solutions to simple Trig Equations

5.5 Read learning outcomes: Solutions of simple Trig Equations in a specified interval

5.5 View exam examples: Solutions of simple Trig Equations in a specified interval

5.5 View Notes: Solutions of simple Trig Equations in a specified interval

5.5 Watch videos: Solutions of simple Trig Equations in a specified interval

5.5 Worksheet: Solutions of simple Trig Equations in a specified interval

5.5 Read and Progress through the content in your textbook: Solutions of simple Trig Equations in a specified interval

5.5 Solve Exam Examples: Solutions of simple Trig Equations in a specified interval

5.5 Complete the Post Quiz: Solutions of simple Trig Equations in a specified interval

5.5 Post Quiz: Solutions of simple Trig Equations in a specified interval

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