Approximation in series expansion

This question was posed by a student.

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Explanation

Exact versus approximation. The two curves depart from each other at x=pi/5

approximation

When we use the approximation to compute the volume, it differs significantly from the exact volume.

volume

Advanced graph transformation

Advanced graph transformation can be done in stages, using the replacement method. Each time, we replace x or y.

advanced transformation 1

advanced transformation 2

Sum and Difference of Two cubes

In 2013 alevel, factorisation of the difference of two cubes can be used in one of the questions

Here are the formulas students should remember:

sum and difference of two cubes

Students can use the mnemonic “SOAP” to help them remember the formula.

S: Same sign

O: Opposite sign

A: Always

P: Positive

Using GC in Differential Equations

The following example illustrates how we can use GC in Differential equations, and avoid the need to do integration to solve differential equation.

2016 RI MCT

Solution for part ii

Using GC in DE

Challenging graphing technique question 1

This question was posted by a student at Singapore JC maths.

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Solution for Part ii

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