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## Binomial Theorem

## Indices

## Surds

## Logarithms

## Techniques and Applications of Differentiation

## Techniques of Integration

## Applications of Integration

## Trigonometric Functions

## Sketching of Trigonometric Curves

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The O Level Additional Mathematics tuition syllabus is intended to prepare students adequately for Singapore A Level H2 Mathematics, where a strong foundation of mathematical skills is essential. The O Level Additional Mathematics tuition syllabus is categorised into three main strands, namely, Algebra, Geometry and Trigonometry & Calculus. Students are also required to be proficient in their process skills, namely reasoning, communication and connections, thinking skills and heuristics, applications and modelling. The O Level Additional Mathematics syllabus assumes knowledge of O Level Elementary Mathematics.

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O Level A. Math

The binomial theorem gives us a formula for expanding the product of two binomials. The formula allows us to expand any binomial raised to a power, which is very useful in algebra and calculus.

Indices are often used to show the power of a number in mathematical expressions. It is a number multiplied by itself some number of times.

Surds are irrational numbers that cannot be expressed as a finite series of numbers or fractions. They are the square roots of numbers that are not perfect squares.

The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to yield a given number. It is also the inverse of the exponential function.

One of the most important ideas in calculus, and one of its most difficult to grasp, is differentiation. Differentiation is a key concept used to determine instantaneous rates of change.

Integration is a useful method of solving problems by using limits and infinite series. It is the reverse of differentiation. It can also be used to calculate areas of complicated shapes.

The definite integral is a concept that can be used to represent the area under a curve, which we could use in a lot of calculations. It is often written as an integral sign with limits above and below it.

Trigonometric functions are real functions that relate an angle of a right-angled triangle to the ratios of two side lengths. The most familiar trigonometric functions are the sine, cosine, and tangent.

Trigonometric graphs are the visual representation of the functions that can be used to solve mathematical problems involving triangles. They can be used to find the amplitude, period, frequency and phase shift of a function.

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