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Comprehensive study guides created by experienced educators. Everything you need to master O Level Additional Mathematics.

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Study guides covering all O Level Additional Math topics aligned with Singapore syllabus (4047)

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O Level Additional Mathematics Study Guides

Master O Level Additional Math with our comprehensive study guides. Packed with concise bite-sized concepts and extensive practice questions aligned with the Singapore O Level syllabus (4047).

Sec/IP LevelAdditional Mathematics
Binomial Theorem
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.

Topics Covered:

  • Pascal's Triangle
  • Binomial Coefficients
  • Binomial Expansion
  • Applications of Binomial Theorem
Sec/IP LevelAdditional Mathematics
Indices
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.

Topics Covered:

  • Laws of Indices
  • Negative Indices
  • Fractional Indices
  • Zero Index
Sec/IP LevelAdditional Mathematics
Surds
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.

Topics Covered:

  • Simplifying Surds
  • Operations with Surds
  • Rationalizing Denominators
  • Solving Equations with Surds
Sec/IP LevelAdditional Mathematics
Logarithms
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.

Topics Covered:

  • Laws of Logarithms
  • Change of Base
  • Logarithmic Equations
  • Applications of Logarithms
Sec/IP LevelAdditional Mathematics
Techniques and Applications of Differentiation
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.

Topics Covered:

  • Product Rule
  • Quotient Rule
  • Chain Rule
  • Implicit Differentiation

+ 2 more topics

Sec/IP LevelAdditional Mathematics
Techniques of Integration
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.

Topics Covered:

  • Integration by Substitution
  • Integration by Parts
  • Partial Fractions
  • Trigonometric Integration

+ 1 more topics

Sec/IP LevelAdditional Mathematics
Applications of Integration
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.

Topics Covered:

  • Area under a Curve
  • Area between Curves
  • Volume of Revolution
  • Definite Integrals

+ 1 more topics

Sec/IP LevelAdditional Mathematics
Trigonometric Functions
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.

Topics Covered:

  • Trigonometric Identities
  • Compound Angle Formulas
  • Double Angle Formulas
  • R-Formula

+ 1 more topics

Sec/IP LevelAdditional Mathematics
Sketching of Trigonometric Curves
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.

Topics Covered:

  • Basic Trigonometric Graphs
  • Amplitude and Period
  • Phase Shift
  • Vertical Translation

+ 1 more topics

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