# Math Syllabus Summary for O Level and A Level students

## O level Maths Syllabus

Welcome to the fascinating world of Singapore O Level Mathematics! Our comprehensive guide is divided into several chapters, each focusing on a specific topic within O Level Mathematics. From algebra and geometry to calculus and statistics, you will find all the essential building blocks

To help you navigate through the chapters seamlessly, we have provided links to each part, allowing you to effortlessly access the content you need to strengthen your mathematical prowess.For sections that are available, click on the links below to embark on your learning journey!

**Numbers and algebra**

- Numbers and their operations – primes, prime factorisation,
**HCF and LCM**. - Ratio and Proportion – ratios involving rational number, map scale,
**direct/inverse proportion** - Percentage – comparing two quantities by percentage, percentage quantities
- Rate and speed – average rate and average speed
- Algebraic expressions and Formulae – using letters to represent numbers
- Functions and graph – coordinates, sketching graphs and graph of exponential functions
- Equations and Inequalities – Solving Linear, simultaneous, quadratic and fractional equations.
- Set Language and Notation – set language and following notation (intersect/union)
- Matrices- Display, interpretation and solving matrices
- Problems in real-world contexts – interpretation of questions

**Geometry and Measurement **

- Angles, triangles and polygons
- Congruence and Similarity
- Properties of circles
- Pythagoras Theorem and Trigonometry
- Mensuration
- Coordinate Geometry
- Vectors in Two Dimensions

**Statistics and Probability **

- Data analysis – tables, bar graphs, pictogram, line graph, dot diagram and other diagrams
- Probability – single events, combined events, when to add or multiply probability
- Mean, median and mode

## A Level Math Syllabus

In this section, we embark on an enriching exploration of the fundamental concepts and advanced problem-solving techniques that will empower you to excel in this challenging subject. Our comprehensive guide is organized into distinct chapters, each dedicated to a specific topic within A Level Mathematics. From pure mathematics to applied mathematics, you will find all the essential components to confidently navigate this subject.

For sections that are available, click on the links below to embark on your A Level mathematical journey.

**Quadratics**

- Solve quadratic equations by substitution, or methods such as completing the square

**Functions**

- Understand the terms function, domain, range, one-on-one function, inverse function and composition of functions

**Coordinate Geometry**

- equation of straight line, graphs and associated algebraic equations

**Circular Measure **

- Understand radian, degrees, arc length and sector area of circle

**Trigonometry **

- Sketch graph of sine, cosine and tangent functions. Find solution to trigo equations lying in a specific interval
- Understand relationships
- Use trigonometrical identities for simplification/ solving of equations

**Series **

- Recognise arithmetic and geometric progressions
- Use the formulae for the nth term and for the sum of the first n terms to solve problems. Use the condition for the convergence of geometric progressions.

**Differentiation and integration **

- Understand the gradient of a curve at a point as the limit of the gradients of a suitable sequence of chords, and use of the notation.
- Use of the derivative of Xn togather with constant multiples, sums and differences of functions, and of composite functions using the chain rule.
- Apply differentiation to gradients, tangents and normals.
- use the derivatives of ex, ln x, sinx, cos x, tan x, together with constant multiples, sums, differences and composites
- Location stationary point and its information.
- Understand integration as a reverse of integration
- Solve problems involving constant of integration

**Algebra**

- understand the meaning of |x|, sketch the graph of y = |ax + b| and use relations such as |a| = |b| ⇔ a2 = b2 and |x – a| < b ⇔ a – b < x < a + b when solving equations and inequalities
- use the factor theorem and the remainder theorem

**Logarithmic and Exponential functions **

- understand the relationship between logarithms and indices, and use the laws of logarithms (excluding change of base)
- Use log to solve equations

**Vectors**

- Use standard notations, addition, subtraction, magnitude, and significance of symbols.
- Determine is two lines are parallel intersect and calculate the scalar product of two vectors.

**Complex Numbers **

- understand the idea of a complex number.
- Carry out operations of addition, subtraction, multiplication and division
- Use the result that, for a polynomial equation with real coefficients, any non-real roots occur in conjugate pairs.
- Represent complex numbers geometrically by means of an Argand diagram

**Numerical solution of equations **

- Locate approximately a root of an equation,by means of graphical considerations and/or searching for a sign change
- Understand and use notation for a sequence of approximations which converge to a root of an equation.

**Probability and Statistics **

- Understand the use of a normal distribution
- solve problems concerning a variable X.
- Recall conditions under which the normal distribution can be used as a approx to the binomial distribution
- Use formulae to calculate probabilities
- Understand poisson distribution
- Understand probability density function
- Sampling methods
- Hypothesis test

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