Chapter 1: SETS AND VENN DIAGRAMS
Introduction
Set theory is a fundamental branch of mathematics that studies sets, which are collections of objects. It serves as a foundational system for nearly all mathematical concepts.
====================================Chapter 2 FUNCTIONS
Introduction
Functions are fundamental to calculus, analysis, and applied mathematics. This summary covers relations, function notation, domain and range, the modulus function, composite functions, sign diagrams, and inverse functions.
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Chapter 3: QUADRATICS
Introduction
A quadratic function is a polynomial function of degree 2. It has the general form:
$f(x) = ax^2 + bx + c \quad \text{where } a, b, c \in \mathbb{R} \text{ and } a \neq 0.$
Quadratic functions appear in physics (projectile motion), economics (profit maximization), and engineering (optimization).
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Chapter 4: SURDS, INDICES, AND EXPONENTIALS
Introduction
Surds, indices, and exponentials form the foundation of algebraic manipulation and calculus. This summary covers irrational roots, exponent rules, rational powers, exponential equations, and both general and natural exponential functions.
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Chapter 5: LOGARITHMS
Introduction
Logarithms are the inverse operations of exponentials. They are essential for solving exponential equations, modelling phenomena across science and finance, and simplifying multiplicative relationships into additive ones.
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Chapter 6: POLYNOMIALS
Introduction
Polynomials are fundamental algebraic expressions that appear throughout mathematics. Understanding their structure, roots, and factorisation is essential for calculus, algebra, and mathematical modelling. This summary covers real polynomials, zeros and factors, the Remainder Theorem, and the Factor Theorem.
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Chapter 7:Straight line graph
Introduction
Straight line graphs are fundamental to algebra and calculus. They model linear relationships between variables and serve as the foundation for understanding more complex functions. This summary covers equations of lines, intersections, transforming relationships to linear form, and extracting relationships from data.
====================================Chapter 8: THE UNIT CIRCLE AND RADIAN MEASURE
Introduction
The unit circle and radian measure form the foundation of trigonometry. They provide a unified framework for defining trigonometric functions, understanding periodic behaviour, and solving real-world problems involving angles and circular motion.
====================================Chapter 9: TRIGONOMETRIC FUNCTIONS
Introduction
Trigonometric functions describe periodic phenomena such as waves, oscillations, and circular motion. This summary covers periodic behaviour, the sine, cosine, and tangent functions, trigonometric equations, identities, and solving equations in quadratic form.
===========================================Chapter 10: COUNTING AND THE BINOMIAL EXPANSION
Introduction
How many different passwords can you create using 4 letters? How many ways can a committee of 3 people be chosen from a group of 10? How many possible outcomes are there when flipping a coin 5 times? These questions all belong to the branch of mathematics known as combinatorics — the art of counting without listing every possibility.
At first glance, counting might seem too simple to deserve serious study. However, when the number of possibilities grows into the millions or billions, systematic methods become essential. Moreover, the techniques we develop for counting lead directly to one of the most elegant and powerful results in algebra: the Binomial Theorem.
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Chapter 11: VECTORS
Introduction
In many areas of mathematics, physics, and engineering, we encounter quantities that require more than just a number to be fully described. For example, telling someone that a car is traveling at 60 km/h does not tell them where it is going; the direction is essential. Similarly, describing a force of 10 Newtons is incomplete without specifying whether it is pushing up, down, left, or right. This leads us to a fundamental distinction between two types of quantities:Chapter 12: MATRICES
Introduction
Matrices are rectangular arrays of numbers that provide a powerful framework for representing and solving systems of linear equations, performing linear transformations, and organizing data. This summary covers matrix structure, operations, multiplication, inverses, and solving simultaneous equations.Clip to view complete summary =============================================
Question and Solutions
Past Paper Questions (Topic by topic)
- Functions
- Quadratic functions 2012 to 2018
- Quadratic functions 2018 to 2020
- Coordinate Geometry (2012-2018)
- Coordinate Geometry (2018-2020)
- Indices and Surds
- Surds 2018
- Surds 2020
- Factors of polynomials (2018)
- Factors of polynomials(2020)
- Simultaneous equations
- Logarithm (2018)
- Logarithm (2018-2020)
- Exponent
- Straight line graphs
- Circular measure
- Circular measure (2018-2000)
- Trigonometry
- Permutations and combinations
- AP and GP
- Binomial Theorem (2018)
- The Binomial Theorem (2020)
- Vectors in two dimensions
- Vectors in two dimensions (2018-2000)
- Calculus
- Differentation
- Integration
- Application of Differentation (2014-2018)
- Application of Differentation(2018-2020)
- Application of Differentation (plus2020)
- Area Under Curve
- Area Under Curve (2020)
- Kinematic
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