Extra Tips Flashcards
When you are equating a fraction to 0, rememer…
Only the numerator will equate to 0 as the denominator will be timesed by 0 when rearranging
If finding a range when having a trig graph, remember…
Unless there is a value before the trig function, the maximum value is 1 and the minimum is -1.
E.g. 10cos(theta - 0.927) has a maximum value of 10 as because it can only be 10*1 max as 1 is the maximum value of cos
F’(x) is the gradient at any point but is also used to find turning/stationary points (min/max points) or point of inflexion. How do we find these?
Equate f’(x) to 0 then once you’ve found the value of x, substitite this back into f(x)
When solving a trig equation, try to make one value into the other
You will usually need to make a quadratic so one value may become squared
In partial fractions try and see if you can spot a…
Difference of two squares
An easy way of finding the range of a quadratic graph is to…
Complete the square. You get the b value, halve it and put it in brackets and square those. Then outside the brackets, take away the square of it.
e.g. x(^2) - 4x + 11
(x - 2)^2 -2^2 + 11 =
(x - 2)^2 + 7
Therefore the range would be f(x)>7
Make sure you read the question carefully. Specifically check the…
- signs
* powers
Remember your original units in the question
.
What is the equation of a line?
y-y1 = m(x-x1)
y=mx + c
If there is a part a/b or the word ‘hence’ then you will need to…
Use all parts of the question to come to answer. Try and see what numbers are the same and what needs to be changed or converted to include previous parts of the question.
The relation between e and ln:
e^(x - 1) = 6 - x
Would go to
x - 1 = ln(6 - x)
In trig equations, remember that…
You can use a calculator so if you get to a stage where no x’s are in your equation, use that
