IAL Maths
You may find videos, worksheets and online self-checks for IAL Maths here.
PURE MATHS 1
CHAPTER 1 - Algebraic Expressions
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VIDEO 1 - Index Laws - Multiplication and Division
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VIDEO 2 - Index Laws - Powers and Distirbutive Law
q.1 c,d,f,g,h,i,k,l,n,o,q,r
q.2 b,c,g,h,k,m,n,q,r,s,v
q.3 a-f
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VIDEO 3 - Index Laws - Zero and Negative Powers
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VIDEO 4 - Index Laws - Fractional Indices
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VIDEO 5 - Surds
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VIDEO 6 - Rationalising the Denominator
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VIDEO 7 - Expanding Brackets
q.1 b,c,e,f,h,j,l,o,r
q.2 a,b,e,i,l,o,q,r,s,t,v,x
q.3-5
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VIDEO 8 - Factorisation
q.1 b,e,f,h,l,p,q,t,u,x
q.2 b,c,e,h,i,j,k
q.1 b-d, q.2 b,c, q.3 b,c, q.4 c,d, q.5 c,d, q.6-24
CHAPTER 2 - Quadratics and Functions
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WORKSHEET 1 - Exercise 2a (from textbook)
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WORKSHEET 2 - Exercise 2b (from textbook)
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VIDEO 3 - Solving Quadratic Equations (Completing to Square)
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WORKSHEET 3 - Exercise 2c & 2d (from textbook)
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WORKSHEET 4 - Functions Review
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NOTE: You may refer to Functions (Ch.36 / IGCSE) if you need.
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VIDEO 4 - Quadratic Graphs
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EXERCISE 2F, p.30, q.1 ( a, c, e, f, i, j)
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VIDEO 5 - The Discriminant
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EXERCISE 2G, p.32 , q.2 - 7
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CHAPTER REVIEW, p.33-4, q.2c-d, 3, 4c-d, 6 - 13.
CHAPTER 3 - Straight Line Graphs
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VIDEO 1: The Gradient
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EXERCISE 5A, p.86-7 q.1h, i, k, m, n, 3, 7, 9, 10
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VIDEO 2: The Line Equation
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EXERCISE 5B, p.88-9 q.1a, d, g, j, 2b, e, h, k, 3c, f, i, l, 5, 6, 8-12
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VIDEO 3: Finding Line Equations - Two Points
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EXERCISE 5C, p.90-1 q.1a, c, e, g, 2b, d, f, h, j, 3-6
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EXERCISE 5D, p.92, odd-numbered questions.
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VIDEO 5: Parallel & Perpendicular Lines
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EXERCISE 5E, p.93, all questions
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EXERCISE 5F, p.95-6 q.1a, d, g, j, 3, 7, 9-12
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VIDEO 6: Length of a Line Segment
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VIDEO 7: Area of a Triangle
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Online Self-Check
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EXERCISE 5G, p.98-9, q.1c, f, 2, 4, 6-12
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CHAPTER REVIEW, p.99-102, all questions.
CHAPTER 4 - Equations and Inequalities
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VIDEO 1: Linear Simultaneous Equations
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EXERCISE 3A p.38 q.4, 5
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VIDEO 2: Quadratic Simultaneous Equations
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EXERCISE 3B p.39-40, q.4 - 6
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VIDEO 3: Simultaneous Equations and Graphs
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VIDEO 4: Linear Inequalities
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VIDEO 5: Quadratic Inequalities
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VIDEO 6: Inequalities on Graphs
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VIDEO 7: Regions
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EXERCISE 3G p.53, q.1, 3, 5, 6, 8
CHAPTER 5 - Graphs and Transformations
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VIDEO 1: Cubic Graphs
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EXERCISE 4A p.61-2, q.1a, d, g, j, 2a, e, g, h, 3a, d, e, f, h, 4a, b, d, e, j, 5 - 7
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VIDEO 2: Reciprocal Graphs
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EXERCISE 4B p.63, q.1a, c, e, 2 - all
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VIDEO 3: Trigonometric Graphs
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VIDEO 4: Graphs of Two Functions
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EXERCISE 4C p.65-6, q.1a, b, d, h, j, 2 - 10
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VIDEO 5: Translations
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EXERCISE 4D p.69-70, q.1, 2, 4, 6, 7-9
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VIDEO 6: Stretching
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EXERCISE 4E p.74, q.1a, b, c, h, j, 2 - 9
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EXERCISE 6G p.128-9, q.2 - 5, 7 - 9
CHAPTER 6 - Trigonometry
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VIDEO 1: Cosine Rule
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EXERCISE 6A p.108-10, q.1b, e, f, 2d, e, f, 6, 8, 10, 12, 14 - 16
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VIDEO 2: Sine Rule
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EXERCISE 6B p.112-4, q.2a, c, e, 3b, d, 4d, f, 5, 6, 7c - f, 10 - 12
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EXERCISE 6C p.115-6, q.1, 3, 4, 6
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VIDEO 3: Bearings
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EXERCISE 6A p.108-10, q.3 - 5, 17
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EXERCISE 6E p.120-2, q.3 - 5
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VIDEO 4: Area of a Triangle
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EXERCISE 6D p.117-8, q.1a, 2b, 3 - 6
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EXERCISE 6E p.120-2, q.1a, b, e, i, 2a, 6, 8, 11, 12, 14, 15
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VIDEO 5: Radian Measure
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VIDEO 6: Sectors - Arc length and Perimeter
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EXERCISE 7B p.137-9, q.1a-iii, 1b-ii, 1c-ii, 4, 5, 8, 10, 13, 14
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VIDEO 7: Sectors - Area ***simple mistake in second example :(
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EXERCISE 7C p.142-5. q.1b, 2, 3c, 4, 6, 8, 10, 14 - 16
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VIDEO 8: Segments - Area and Perimeter
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EXERCISE 7C p.142-5, q.1d, 5, 9, 17
CHAPTER 7 - Differentiation 1
COMING SOON
CHAPTER 8 - Integration 1
COMING SOON
PURE MATHS 2
CHAPTER 1 - Algebraic Methods
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VIDEO 1 - Algebraic Fractions
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EXERCISE 1A p.2-3 q.2 g, m, n, o, q.3
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VIDEO 2 - Dividing Polynomials
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EXERCISE 1B p.5-6 q.1b, 1f, 2a, 2e, 3d, 4g, 4h, 5b, 6b, 9, 11, 14, 16-19
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VIDEO 3 - The Factor Theorem
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EXERCISE 1C p.10-1, q.5, 6, 7c, 8d, 9, 10, 14, 18, 19
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VIDEO 4 - The Remainder Theorem
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EXERCISE 1D p.12-3, q.1 d, h, q.2, 4, 6, 7-10
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VIDEO 5 - An Introduction to Mathematical Proof
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VIDEO 6 - Proof by Deduction
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EXERCISE 1E p.16-7 q.1, 5, 7, 11-20
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VIDEO 7 - Proof by Exhaustion
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VIDEO 8 - Proof by Counter-Example
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EXERCISE 1F p.19-20
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CHAPTER REVIEW p.21-3 q.4, 5, 7-9, 12, 14, 16-18, 20-22, 24-27
CHAPTER 2 - Coordinate Geometry--Circles
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VIDEO 1 - Midpoints in Circles
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EXERCISE 2A p.27 q.2, 4-8, 11, challenge question
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VIDEO 2 - Perpendicular Bisectors in Circles
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EXERCISE 2B p.28-9, q.1e, 2-5, challenge question
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VIDEO 3 - Equation of a Circle - Centre & Radius
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EXERCISE 2C p.31-2 q.1c, 1d, 2a, 2e, 3b, 3e, 4-7
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EXERCISE 2C p.31-2 q.9, 10b, 10c, 10e, 11-13
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VIDEO 5 - Straight Lines & Circles
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EXERCISE 2D p.34 q.2, 5-12
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VIDEO 6 - Tangent & Chord Properties
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EXERCISE 2E p.38-40 q.2,4-11
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VIDEO 7 - Circles & Triangles
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EXERCISE 2F p.43-4, q.2,4-9
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CHAPTER REVIEW p.44-7, q.2,3,5,7-25
CHAPTER 3 - Exponentials and Logarithms
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VIDEO 1: Exponential Functions
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EXERCISE 3A p.51-2 q.2, 4-7
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VIDEO 2: Introduction to Logarithms
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EXERCISE 3B p.53-4 q.1, 2, 5, 6, 7b, 8b
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VIDEO 3: Laws of Logarithms
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EXERCISE 3C p.56 q.1-3
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VIDEO 4: Logarithmic Equations
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EXERCISE 3C p.56 q.4-6
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EXERCISE 3D p.58 q.1e-h, 2e-h, 3-5
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VIDEO 5: Changing the Base
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EXERCISE 3E p.59 q.3
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CHAPTER REVIEW p.60-1, all questions
CHAPTER 4 - Binomial Expansions
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VIDEO 1 - Expanding Brackets & Pascal's Triangle
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EXERCISE 4A p.64-5 q.2c,d,g,h, 3b,c,f,h, 4-9
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EXERCISE 4B p.66 q.1b,d, 2c,e,f, 3b,d,f, 4-6, 8-11
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VIDEO 3 - Binomial Expansions
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EXERCISE 4C p.68 q.1c,e,f, 2c,d,e, 3b,d,f, 4c,f,i, 5-7
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EXERCISE 4D p.70-1 q.1c,d,g,h,k,l, 2-10
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VIDEO 4 - Estimations Using Binomial Expansions
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EXERCISE 4E p.72-3 q.2-4, 6, 7, 9
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CHAPTER REVIEW p.73-5 q.2-4, 7-10, 13, 15, 16, 18, 20
CHAPTER 5 - Sequences and Series
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VIDEO 1 - Arithmetic Sequences
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EXERCISE 5A p.82-3 q.1b,c, 2c,e,f, 3d,e,f, 5-10
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VIDEO 2 - Arithmetic Series
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EXERCISE 5B p.85-7 q.1d,f,g,h, 2c,d 3-13
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VIDEO 3 - Geometric Sequences
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EXERCISE 5C p.90-1 q.3, 4c,d, 5-13
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VIDEO 4 - Geometric Series
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EXERCISE 5D p.93-4 q.1b,c,e,f, 2, 4-11
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VIDEO 5 - Geometric Series: Sum to Infinity
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EXERCISE 5E p.96-7 q.1a,b,c,g,h, 2, 5-11
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VIDEO 6 - Sigma Notation
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EXERCISE 5F p.98-9 q.1c,d, 2b,c, 3b,c, 4c,d, 5a,c, 6, 7, 8c, 9-12
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VIDEO 7 - Recurrence Relations
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EXERCISE 5G p.101-2 q.1e,f, 2d-h, 3d-f, 4-7
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EXERCISE 5H p.103, q.2-5 (read the information on p.102)
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EXERCISE 5I
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CHAPTER REVIEW
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WORKSHEET - past paper questions
CHAPTER 6 - Trigonometric Identities and Equations
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VIDEO 1: Introduction To Unit Circle
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VIDEO 2: Using the Unit Circle
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VIDEO 2.1: More Examples
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EXERCISE 6D p.126-7 q.3-13
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VIDEO 3: Harder Trigonometric Equations
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EXERCISE 6E p.129-30 all questions
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VIDEO 4: Trigonometric Identities
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EXERCISE 6C p.122-3 q.1-3, 4a,c,d,e, 5, 6, 10-12
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VIDEO 5: Identities in Equations
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EXERCISE 6F p.132-3 all questions
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CHAPTER REVIEW
CHAPTER 7 - Differentiation 2
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VIDEO 1: Maxima-Minima & Modelling Problems
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EXERCISE 7D p.147-8, q.4-10
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VIDEO 2: Increasing and Decreasing Functions
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EXERCISE 7A p.138, q.1a,c,d,h, 2c,f,g, 3, 4
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VIDEO 3: Stationary Points
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EXERCISE 7B p.142-3. q.3b,c,e-i, 5-7 (extension: q.4)
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VIDEO 4: Graphs of Gradient Functions
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EXERCISE 7C p.145 q.1,2
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CHAPTER REVIEW p.148-51 q.1, 3-5, 7-10, 12-14
CHAPTER 8 - Integration 2
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VIDEO 1: Definite Integrals
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EXERCISE 8A p.154-5 q.2-8
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VIDEO 2: Area Under Curves
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EXERCISE 8B p.156-7 q.2,3, 6-9
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EXERCISE 8C p.159 q.1b,d,e 2, 3
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EXERCISE 8D p.161-3 q.1, 3, 4, 6, 8-11
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EXERCISE 8E p.165 q.1-5
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VIDEO 3: The Trapezium Rule
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EXERCISE 8F p.1, 3, 4, 6-10
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CHAPTER REVIEW p.169-72 (all)
PURE MATHS 3
CHAPTER 1 - Algebraic Methods
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EXERCISE 1A p.3 q.1-4
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EXERCISE 1B p.4-5 q.2c,d,f, 3d-f, 4, 5c, 6, 7
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EXERCISE 1C p.7-8 q.2, 3, 5, 6, 8, 10
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CHAPTER REVIEW p.8-9 q.5, 6, 8-10
CHAPTER 2 - Functions and Graphs
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VIDEO 1: Recall - Functions
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VIDEO 2: Modulus Function
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EXERCISE 2A, p.14-5 q.3b,c, 4b,d,f,h, 5, 6b,c,e, 8 - 13
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VIDEO 3: Piecewise Defined Function
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EXERCISE 2B p.19-20 q.6-8
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VIDEO 4: Mappings and Functions
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EXERCISE 2B p.19-20 q.1,2,3c,d,4b,e,5,9,11,12
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VIDEO 5: Composite Functions
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EXERCISE 2C p.22-3 q.3-11
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VIDEO 6: Inverse Functions
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EXERCISE 2D p.26-7 q.1b,c, 2, 3, 4a,c,d,f, 5-7, 9-12
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VIDEO 7: Graphs of Modulus Functions
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EXERCISE 2E p.30-2 q.1-4, 7-10
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EXERCISE 2F p.34-5 all questions
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EXERCISE 2G p.38-9 q.2,4,7,8,10
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CHAPTER REVIEW p.40-44 q.2-5, 8-11, 13, 15-17, 19-24
CHAPTER 3 - Trigonometric Functions 2
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VIDEO 1 - Trigonometric Functions -the other ones
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EXERCISE 3A p.48 q.2e,f,g, 3b,c,f,h,j,k, 4-6
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EXERCISE 3B p.52-3 q.3-5, 7e,f,g,h, 9, 10
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VIDEO 2 - Trigonometric Identities
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EXERCISE 3C p.56-7 q.1-4,
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EXERCISE 3D p.60-1 q.1, 6, 10-12
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VIDEO 3 - Trigonometric Equations
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EXERCISE 3C p.56-7 q.5c,d,g,h, 6d,e,h, 7c,d, 8-11
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EXERCISE 3D p.60-1 q.2-5, 7, 8e-h, 9
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VIDEO 4 - Inverse Trigonometric Functions
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Online Self-Check
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EXERCISE 3E p.64-5 q.1a,c,d,g,h, 2, 3a,c, 4-9
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CHAPTER REVIEW p.66-8 q.1, 3, 4-9, 12-20, 22-24
CHAPTER 4 - Trigonometric Addition Formulae
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VIDEO 1: Addition Formulae
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EXERCISE 4A p.73-5, q.2-8, 9d,f,h,i,j, 10b,c, 11-16
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EXERCISE 4B p.76-7, q. 1b,d, 2d,f,h,i,j, 3-5, 7, 9
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VIDEO 2: Double Angle Formulae
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EXERCISE 4C p.79-81 q.4 e-h, 5c,d, 6, 7b,d-i, 8-11, 13-19
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EXERCISE 4F p.91-2 q.1c,d,g-i, 2c,e,f,h, 3, 4, 6-9
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EXERCISE 4E p.88-90 q.5, 7, 9, 10, 14, 15
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VIDEO 5: Solving Trigonometric Equations
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Online Self-Check
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EXERCISE 4D p.84-5 q.2 1b,c, 2, 4, 5c,d,f,h-k, 6-9, 11-14
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CHAPTER REVIEW p.93-5 q.2-5, 7, 9-11, 14-17, 20-24
CHAPTER 5 - Exponentials and Logarithms 2
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EXERCISE 5A p.104-5 q.3-7
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EXERCISE 5B p.107-8 q.1c,d, 2, 3b,d,e, 4, 5
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EXERCISE 5C p.109-10 q.1c-e, 2c-f, 3, 5c,d, 6, 8
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EXERCISE 5D p.113-6 q.2, 4, 5, 8, 9
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EXERCISE 5E p.117-8 q.2-6
CHAPTER 6 - Differentiation 3
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VIDEO 1 - Differentiation - Basics
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VIDEO 2 - The Chain Rule
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EXERCISE 6A p.125 q.1-3
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EXERCISE 6B p.127-8 q.1, 2
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EXERCISE 6C p.130-1 q.1, 2, 11
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EXERCISE 6F p.140-2 q.1a-c, 2a-d,g,h, 3
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VIDEO 3 - The Product Rule
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EXERCISE 6D p.133 q.1, 2, 7, 9
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EXERCISE 6F p.140-2 q.1d, 2e, 4a,d
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VIDEO 4 - The Quotient Rule
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EXERCISE 6E p.135-6 q.1, 2, 9, 11
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EXERCISE 6F p.140-2 q.2f, 4b,c,e,f
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VIDEO 5 - Derivative with respect to y
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EXERCISE
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VIDEO 6 - Applications of Derivatives
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EXERCISE 6A p.125 q.6-9
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EXERCISE 6B p.127-8 q.4, 5, 7-12
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EXERCISE 6C p.130-1 q.4, 5, 12, 13
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EXERCISE 6D p.133, q.3c, 4-6, 8, 10
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EXERCISE 6E p.135-6 q.6-8, 10, 12
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EXERCISE 6F p.140-2 q.5, 10, 12
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CHAPTER REVIEW p.142-3 q.1-9
CHAPTER 7 - Integration 3
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VIDEO 1 - Integration by Recognition
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VIDEO 2 - Integration by Substitution
CHAPTER 8 - Numerical Methods Soon
PURE MATHS 4
CHAPTER 1 - Proof by Contradiction
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VIDEO 1 - Proof by Contradiction
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EXERCISE 1A p.4,5 q.2, 3, 4a,c, 5a, 6-8, 10
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CHAPTER REVIEW p.5 q.1, 2, 6
CHAPTER 2 - Partial Fractions
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VIDEO 1: Partial Fractions - Introduction
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VIDEO 2: Partial Fractions - Proper Fractions
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EXERCISE 2A p.9 q.1b,d,e,g,h 2, 5, 7b, Challenge
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VIDEO 3: Partial Fractions - Proper Fractions with Repeated Factors
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EXERCISE 2B p.11 q.2, 4, 7, 8a,b
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EXERCISE 2C p.13-4, q.1a-d, 2, 4a-c, 5, 6a,b, 8a,b, Challenge
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VIDEO 5: Partial Fractions - Fractions with Irreducible Factors
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WORKSHEET: Partial Fractions - Irreducible Factors
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CHAPTER REVIEW p.14 q.3, 4b, 5, 6a, 7b, 9, 10b, 11, 12a, 13