Some exam boards put certain topics in the Core 3 module, while others will have the same topics in the Core 4 module, and vice versa. We have therefore put the topics for Core 3 and 4 together.
Algebra, Series and Functions
Trigonometric identities to learn:
Differentiation was introduced back in Core 1... Basically all that's changed is that we can differentiate harder algebra.
To differentiate, you need to use this form:
It may look kind of scary, but it's much cleaner that using the chain rule, another way. What the algebra means is: the power (n) times the differential (f'(x)) times the original to the power of 1 less ([f(x)]^n-1).
First we take the power: 6.
All those together:
Easy, hm? if your struggling pm kevlar for more help!
The exam will give you all the usual graph questions:
Find the gradient of the curve at the point... this means, find the dy/dx and sub in the coordinates
Find the perpendicular line at the point... This means find the reciprical the dy/dx number and times by -1. Finally use the formula: y - y1 = m(x - x1) where x1 and y1 are the coorinates of the point.
Product and Quotient Rules
You need to learn these. They're not given in the formula booklet:
An easy way to remember this is by the rhyme "Low d-high minus high d-low, over the square of what's below", i.e. (v x du) minus (u x dv), all over (v^2)
NOTE: Quotient rule will be written in the AQA formulae book, but in the form g(x) and f(x) i've written both in there simplest forms for revision just remember prodUct U is cap as it starts with u then ends in u and remember the + sign, and quotient rule starts with v ends with v with a minus sign all over v^2
First, we notice two things times together. We can't practically expand the brackets, however, so we need the product rule. We call the first thing "u" and the second "v" and differentiate them separately, and then stick them into the product rule.
which simplifies to
The following indefinite integrals follow naturally from the differentiation work
When using iterration to find x1, x2 etc...
Type the given value for x0 into your calculator and press '='
Then enter the iterrative formula into your calculator and for xn, simply put 'Ans'. Then to find the value for x1, just press '='. Then, to find x2, simply press '=' again without any further work. Likewise for x3, x4 etc...
Two vectors are skew (cross on only 2 dimensions but not 3) when the three equations formed by the two lines, in terms of ks,js,is and kt,jt,it do not have common solutions of s and t for all three equations.