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

Course Content

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0 Starting Information

0.1 About 7 Tasks

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0.1 The AS & AL 9709 Mathematics syllabus

0.1 Choosing different combinations

0.1 The generalised experience of students

0.1 Calculator restrictions and recommendations

0.1 What if…

0.1 The design of this course

0.1 Contacting the author

1 Quadratics

1.1 Completing the square 25 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 Worksheet 1 solutions

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 Worksheet 2 solutions

1.1 Watch videos 2: Equating coefficients

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

1.1 Worksheet 3 solutions

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

1.1 Worksheet 4 solutions

1.1 Worksheet 5: Solve for 𝑥 algebraically

1.1 Worksheet 5 solutions

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

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1.2 Solving quadratic equations 13 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: Solving Quadratics

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 Solve exam example solutions

1.2 Complete the Post Quiz

1.2 Post Quiz: Solving Quadratic Equations

1.3 Quadratics in some function of 𝑥 12 Tasks | 2 Quizzes

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1.3 Pre Quiz: Quadratics in some function of 𝑥

1.3 Complete the terms and definitions

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

Spaced repetition for completing the square

1.3 Solve exam examples

1.3 Solve exam examples solutions

Complete the Post Quiz

Post Quiz: Quadratics in some function of 𝑥

1.4 Solving simultaneous equations 11 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 Solve exam examples solutions

1.4 Complete the Post Quiz

Post Quiz: Simultaneous equations

1.5 The discriminant 13 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

Spaced repetition for Quadratics in some function of 𝑥

1.5 Solve exam examples

1.5 Solve exam example solutions

1.5 Complete the Post Quiz

1.5 Post Quiz: The discriminant

1.5 Upload your learning outcomes checklist

2 Functions

2.1 Definition of a function 7 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

Spaced repetition for solving simultaneous equations

Spaced repetition for completing the square (again)

2.1 Complete the Post Quiz

Post Quiz: Function definitions

2.2 Domain, Range, & Composite Functions 10 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

Spaced repetition reminder for the discriminant

2.2 Solve exam examples

2.2 Solving exam examples solutions

2.2 Complete the Post Quiz

Post Quiz: Functions, domain, range, & composites

2.3 Many-one, One-one, & Inverse Functions 9 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 Solve exam examples solutions

2.3 Complete the Post Quiz

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

2.4 Function Transformations 13 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

Spaced repetition for solving simultaneous equations (again)

Spaced repetition for Functions, domain, range, & composites

2.4 Solve exam examples

2.4 Solve exam examples solutions

2.4 Complete the Post Quiz

2.4 Post Quiz: Function transformations

2.4 Upload your learning outcomes checklist

3 Coordinate Geometry

3.1 Straight lines: Gradients, Intercepts, Equation Forming, Perpendiculars, Distances, and Mid- & Intersection points 14 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

Spaced repetition for The discriminant (again)

Spaced repetition for Completing the Square, Many-one, one-one, & Inverse Functions

Answers for Completing the Square, one-one, & Inverse Functions

3.1 Solve exam examples

3.1 Solve exam examples solutions

3.1 Complete the Post Quiz

3.1 Post Quiz: Straight lines

3.2 The Circle Equation 14 Tasks | 2 Quizzes

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3.2 Complete the Pre Quiz: The Circle Equation

3.2 Pre Quiz: The Circle Equation

3.2 Complete the terms and definitions: Circles

3.2 Read learning outcomes: The Circle Equation

3.2 View exam examples: The Circle Equation

3.2 View Notes: The Circle Equation

3.2 Watch videos: The Circle Equation

3.2 Worksheet: The Circle Equation

3.2 Read and Progress through the content in your textbook: The Circle Equation

Spaced repetition for Solving Quadratic Equations

Spaced repetition for Definition of a Function

Spaced repetition for Function Transformations

3.2 Solve Exam Examples: The Circle Equation

3.2 Solve exam examples solutions

3.2 Complete the Post Quiz: The Circle Equation

3.2 Post Quiz: The Circle Equation

3.3 Algebra of Lines, Circles & Circle geometric properties 15 Tasks | 2 Quizzes

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3.3 Complete the Pre Quiz: Algebra of Lines, Circles & Circle geometric properties

3.3 Pre Quiz: Algebra of Lines, Circles & Circle geometric properties

3.3 Read learning outcomes: Algebra of Lines, Circles & Circle geometric properties

3.3 View exam examples: Algebra of Lines, Circles & Circle geometric properties

3.3 View Notes: Algebra of Lines, Circles & Circle geometric properties

3.3 Watch videos: Algebra of Lines, Circles & Circle geometric properties

3.3 Read and Progress through the content in your textbook: Algebra of Lines, Circles & Circle geometric properties

3.3 Worksheet: Algebra of Lines, Circles & Circle geometric properties.

Spaced Repetition (again) for Quadratics in some Function of 𝑥

Spaced Repetition for Domain, Range, & Composite Functions

Spaced Repetition for Straight Line Coordinate Geometry

Solution for spaced repetition of Straight Line Coordinate Geometry

3.3 Solve Exam Examples: Algebra of Lines, Circles & Circle geometric properties

3.3 Solve exam examples solutions

3.3 Complete the Post Quiz: Algebra of Lines, Circles & Circle geometric properties

Post Quiz: Algebra of Lines, Circles & Circle geometric properties

3.3 Upload your learning outcomes checklist

4 Circular Measure

4.1 Radian Definition, and Relationship between Radians & Degrees 11 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 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

Spaced repetition for Solving Simultaneous Equations

Spaced repetition for Many-one, One-one, & Inverse Functions

Spaced repetition for The Circle Equation

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 Arc lengths, Sector Areas, and Lengths, Angles, & Areas of Triangles 15 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

Spaced repetition (again, again) for The Discriminant

Spaced repetition for Function Transformations (again)

Spaced repetition for Lines, Circles & Circle Geometric Properties

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

4.2 Solve exam examples solutions

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

4.2 Upload your learning outcomes checklist

5 Trigonometry

5.1 Graphs: Sin, Cos & Tan functions 15 Tasks | 2 Quizzes

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

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

5.1 Pre Quiz: Graphs: Sin, Cos and 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

Amplitudes and periods: memo

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

Spaced repetition for the definition of a function (again)

Spaced repetition for Straight Line Coordinate Geometry (again)

Solution for spaced repetition on Straight Line Coordinate Geometry

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

5.1 Solve exam examples solutions

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 & Tan of 30°, 45°, 60° 12 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 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

Spaced repetition (again, again) for Domain, Range, & Composite Functions

Spaced repetition for The Circle Equation (again)

Solutions for spaced repetition for The Circle Equation

Spaced repetition for Using Radians in Arc Lengths, Sector Areas, and Lengths, Angles, & Areas of Triangles

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, and Solutions in specified intervals 17 Tasks | 2 Quizzes

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5.3 Complete the Pre Quiz: Inverse Trig, and Solutions in specified intervals

5.3 Pre Quiz: Inverse Trig, and Solutions in specified intervals

5.3 Complete the terms and definitions: Inverse Trig, and Solutions in specified intervals

5.3 Read learning outcomes: Inverse Trig, and Solutions in specified intervals

5.3 View exam examples: Inverse Trig, and Solutions in specified intervals

5.3 View Notes: Inverse Trig, and Solutions in specified intervals

5.3 Watch videos: Inverse Trig, and Solutions in specified intervals

5.3 Worksheet: Inverse Trig, and Solutions in specified intervals

5.3 Worksheet solutions: Inverse Trig, and Solutions in specified intervals

5.3 Read and Progress through the content in your textbook: Inverse Trig, and Solutions in specified intervals

Spaced repetition (again, again) for Solving quadratic equations (again)

Answers for Sr(a,a)fSqe(a)

Spaced repetition (again, again) for Many-one, one-one, & Inverse Functions

Spaced repetition for Algebraic problem solving with Lines, & Circles (again)

Spaced repetition for Graphs of the Sin, Cos & Tan functions

5.3 Solve Exam Examples: Inverse Trig, and Solutions in specified intervals

5.3 Solve exam examples solutions

5.3 Complete the Post Quiz: Inverse Trig, and Solutions in specified intervals

5.3 Post Quiz: Inverse Trig, and Solutions in specified intervals

5.4 Identities 15 Tasks | 2 Quizzes

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5.4 Complete the Pre Quiz: Identities

5.4 Pre Quiz: Identities

5.4 Complete the terms and definitions: Identities

5.4 Read learning outcomes: Identities

5.4 View exam examples: Identities

5.4 View Notes: Identities

5.4 Watch videos: Identities

5.4 Worksheet: Identities

5.4 Read and Progress through the content in your textbook: Identities

Spaced repetition: solving quadratic equations (again)

Spaced repetition (again, again): function transformations

Spaced repetition: Exact values of Sin, Cos & Tan of 30°, 45°, 60°

5.4 Solve Exam Examples: Identities

5.4 Solve Exam Example solutions

5.4 Complete the Post Quiz: Identities

5.4 Post Quiz: Identities

5.4 Upload your learning outcomes checklist

6 Series

6.1 Expansion of (a + b)ⁿ, where n is a positive integer 10 Tasks | 2 Quizzes

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6.1 Complete the Pre Quiz: Expansion of (a + b)n, where n is a positive integer

6.1 Pre Quiz: Expansion of (a + b)n, where n is a positive integer

6.1 Complete the terms and definitions: Expansion of (a + b)n

6.1 Read learning outcomes: Expansion of (a + b)n, where n is a positive integer

6.1 View exam examples: Expansion of (a + b)n, where n is a positive integer

6.1 View Notes: Expansion of (a + b)n, where n is a positive integer

6.1 Watch videos: Expansion of (a + b)n, where n is a positive integer

6.1 Worksheet: Expansion of (a + b)n, where n is a positive integer

6.1 Read and Progress through the content in your textbook: Expansion of (a + b)n, where n is a positive integer

6.1 Solve Exam Examples topicdes: Expansion of (a + b)n, where n is a positive integer

6.1 Complete the Post Quiz: Expansion of (a + b)n, where n is a positive integer

6.1 Post Quiz: Expansion of (a + b)n, where n is a positive integer

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