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How to do Difficult Surd Algebraic manipulation questions example: Rationalise the denominator of the expression: 1+5^(1/2) / 3+5^(1/2). Give your answer in its simplest form:

The first thing to do, is to assess how far the student has managed to work, and then find the missing pieces within the students skill or knoweldge. I might decide to go through the question with the studen...
AV
Answered by Alexander V. • Maths tutor
3403 Views

How can you tell if a function is even or odd?

If you have a plot of the function, you can look at its symmetries. If the plot to the left of the y axis is the mirror image with respect to the y axis of the plot to the right, it's an even function. If th...
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Answered by Francois d. • Maths tutor
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The air pressure in the cabin of a passenger plane is modelled by the equation: P(x) = 3cos(x/2) - sin(x/2) where x is the altitude. Express P(x) in the form Rcos(x/2 +z) where z is acute and in degrees and then find the maximum pressure

This is a classic example of a trigonometry problem using the angle addition formulae. Recall that cos(A+B) = cos(A)cos(B) - sin(A)sin(B). Express R(x/2 -z) in similar form: Rcos(x/2 +z) = Rcos(x/2)cos(z) - ...
CP
Answered by Caspar P. • Maths tutor
3141 Views

Solve (72x^3 - 18x)/(12x^2 - 6x) = 0 for x.

So first you need to recognise that you are able to take 2x out of both the numerator and denominator of the fraction:(72x3 - 18x)/(12x2 - 6x) = 0 ---> (2x (36x 2 - 9))/ (2x (6x - 3)) = 0 , the 2x's cance...
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Answered by William R. • Maths tutor
3163 Views

What is a major use of completing the square?

Completing the square is a technique that converts a quadratic polynomial of the form:y=ax^2+bx+c into:y=a(x-d)^2+eThis converted form can be used to identify the location of the turning point. The turning p...
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Answered by Lewis M. • Maths tutor
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