Cambridge Notes
O Level
Subject 4037
Topic 2.2.5

Subject 4037 2.2.5 Notes — O Level

Cambridge O Level Subject 4037 (4037) revision notes — topic 2.2.5. Syllabus-aligned key concepts for CAIE exam preparation.

1. Functions

1.1 Function Definitions & Terminology
1.2 Domain and Range
1.3 Function Notation
1.4 Modulus Function Graphs
1.5 Inverse Function Existence
1.6 Finding Inverse Functions
1.7 Composite Functions
1.8 Graphs of Inverse Functions

2. Quadratic functions

2.1 MaximumMinimum of Quadratics
2.2 Sketching Quadratic Graphs
2.3 Discriminant and Roots
2.4 Solving Quadratic Equations
2.5 Solving Quadratic Inequalities

3. Factors of polynomials

3.1 Remainder and Factor Theorems
3.2 Factoring Polynomials
3.3 Solving Cubic Equations

4. Equations, inequalities and graphs

4.1 Solving Modulus Equations
4.2 Solving Modulus Inequalities
4.3 Solving via Substitution
4.4 Sketching Cubic Graphs
4.5 Solving Cubic Inequalities

5. Simultaneous equations

5.1 Solving Simultaneous Equations

6. Logarithmic and exponential functions

6.1 Log and Exponential GraphsProperties
6.2 Laws of Logarithms
6.3 Solving Exponential Equations

7. Straight-line graphs

7.1 Straight Line Equations
7.2 Parallel and Perpendicular Lines
7.3 Line Geometry Problems
7.4 Linear Law Transformations

8. Coordinate geometry of the circle

8.1 Circle Equations
8.2 Line and Circle Intersection
8.3 Circle Tangents
8.4 Solve problems involving the intersection of two circles.

9. Circular measure

9.1 Arc Length and Sector Area

10. Trigonometry

10.1 Trigonometric Function Definitions
10.2 Trigonometric Graph Properties
10.3 Sketching Trigonometric Graphs
10.4 Trigonometric Identities
10.5 Solving Trigonometric Equations
10.6 Proving Trigonometric Identities

11. Permutations and combinations

11.1 Permutations vs Combinations
11.2 PermutationCombination Formulas
11.3 Arrangement and Selection Problems

12. Series

12.1 Binomial Theorem Expansion
12.2 Binomial General Term
12.3 AP and GP Definitions
12.4 AP and GP Formulas
12.5 Sum to Infinity GP

13. Vectors in two dimensions

13.1 Vector Notation
13.2 Position and Unit Vectors
13.3 Vector Operations and Magnitude
13.4 Velocity Vectors

14. Calculus

14.1 Derivative Concept
14.2 Derivative Notation
14.3 Standard Derivatives and Chain Rule
14.4 Product and Quotient Rules
14.5 Gradients Tangents Normals
14.6 Stationary Points
14.7 Rates of Change and Approximations
14.8 Optimization Problems
14.9 Derivative Tests for Extrema
14.10 Integration Concept
14.11 Integrating Powers of x
14.12 Integrating Standard Functions
14.13 Definite Integrals and Areas
14.14 Calculus in Kinematics
14.15 Kinematics Graphs

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