? Level Structure Based on Placement Tests

Level	Description	Placement Score Range	Focus
Level 1 – Foundation	New or struggling students	0–40%	Core concepts, slower pace, lots of support
Level 2 – Standard	Average-performing students	41–75%	Normal textbook pace, full curriculum
Level 3 – Advanced	High-achieving students	76–100%	Faster pace, deeper problem

Edexcel AS and A Level Mathematics – Pure Mathematics Year 1/AS

Estimated Tutoring Hours For Group Max 5 students

1. Algebra and Functions (Estimated 12 hrs)

• 1.1 Algebraic Expressions
• 1.2 Laws of Indices
• 1.3 Expanding Brackets and Factorising
• 1.4 Algebraic Fractions
• 1.5 Surds
• 1.6 Rationalising the Denominator
• 1.7 Functions
• 1.8 Modelling with Algebra

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2. Quadratics ( Estimated 12 hours )

• 2.1 Solving Quadratic Equations
• 2.2 Completing the Square
• 2.3 Functions (Quadratic Focus)
• 2.4 Quadratic Graphs
• 2.5 The Discriminant
• 2.6 Modelling with Quadratics
• Mixed Exercise

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3. Equations and Inequalities ( Estimated 15 hours)

• 3.1 Linear Simultaneous Equations
• 3.2 Quadratic Simultaneous Equations
• 3.3 Solving Simultaneous Equations Graphically
• 3.4 Linear Inequalities
• 3.5 Quadratic Inequalities
• 3.6 Inequalities on Graphs
• 3.7 Representing Regions
• Mixed Exercise

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4. Graphs and Transformations( Estimated time 14 hrs)

• 4.1 Cubic Graphs
• 4.2 Quartic Graphs
• 4.3 Reciprocal Graphs
• 4.4 Points of Intersection
• 4.5 Translating Graphs
• 4.6 Stretching Graphs
• 4.7 Transforming Functions
• Mixed Exercise
• Review Exercise

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5. Coordinate Geometry ( Estimated time 12 hrs )

• 5.1 Straight-Line Graphs
• 5.2 Length and Midpoint
• 5.3 Perpendicular Lines
• 5.4 Using Coordinate Geometry
• 5.5 Circles
• 5.6 Tangents and Normals
• Mixed Exercise

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6. Algebraic Methods ( Estimated time 6 hrs)

• 6.1 Algebraic Division
• 6.2 The Factor Theorem
• 6.3 Proof by Deduction and Contradiction
• Mixed Exercise

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7. Trigonometry ( Estimated time 10 hrs)

• 7.1 Radian Measure
• 7.2 Trigonometric Ratios and Graphs
• 7.3 Trigonometric Identities
• 7.4 Solving Trigonometric Equations
• Mixed Exercise

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8. Vectors ( Estimated time 6 hrs )

• 8.1 Vectors in Two Dimensions
• 8.2 Magnitude and Direction
• 8.3 Vector Geometry
• Mixed Exercise

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9. Differentiation ( Estimated time 14 hrs)

• 9.1 The Gradient of a Curve
• 9.2 Differentiating Simple Functions
• 9.3 Tangents and Normals
• 9.4 Increasing and Decreasing Functions
• 9.5 Second Derivatives
• 9.6 Stationary Points
• 9.7 Modelling with Differentiation
• Mixed Exercise

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10. Integration ( Estimated 10 hrs)

• 10.1 Integration as Reversing Differentiation
• 10.2 Definite Integrals
• 10.3 Area Under a Curve
• 10.4 Area Between Curves
• Mixed Exercise 1
• Review Exercise

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