Complete A-Level Maths Revision Notes For Edexcel: C3 (Core)
1 purchase
Course
Mathematics
Institution
Cambridge University (CAM)
I am a former student of the University of Cambridge, specialising in mathematics, physics and chemistry. I am studying for a PhD in physics, and tutor maths and all sciences to A-Level. These notes are relevant for Edexcel, AQA and OCR board exams.
E.g.4. 3x + 5 - 2x - 1 = (3x + 5)(x - 1) -(2x - 1)(x + 1) = 3x + 5 - 2x + 1 = x+6
(x + 2)(x + 1) (x + 2)(x - 1) (x + 2)(x + 1)(x - 1) x+2 x+2
Here, a common factor is found & the fractions multiplied by what they need to be to have the common
factor. Remember that if there’s a common factor, simply multiply the numerators. If not, or there’s a
mixture, times the fractions by what you need to until there is.
Rational Expressions: More Difficult Division
E.g.1. 2x2 + x - 4 = (x - 1)(2x + 3) - 1 = 2x + 3 - 1 . You have to make the numerator a
x-1 x-1 x - 1 factor of (x - 1), add remainders if
they are needed, then divide out.
E.g.2. 6x3 - 4x2 - 3x - 5 = (2x2 - 1)(3x - 2) - 7 , as to get from 2 to -5, you -7. = 3x - 2 - 7 .
2x2 - 1 2x2 - 1 2x2 - 1
Ranges & Domains
Domain Range
1 3
2 5 The function for this range, with their range (answers when put in to the function of
3 7 x) is 2x + 1. A domain = the inputs, the range = the outputs. Ranges are of f(x),
4 9 not just x. Note - Even function: f(-x) = f(x) and an Odd function: f(-x) = -f(x).
One - One Mapping
f(x) = x2, x > 0. f(x) = ±√x, x < 3.
This is one-one mapping, as This isn’t one-one mapping,
there is only one y value for as there are 2 y values for
each corresponding x value. each corresponding y value.
Notice that there’s a black Notice there’s an unfilled
dot, which shows where the dot, showing where the
curve’s been cut. curve’s cut, as it’s >, not >.
f(x) = x - 3, -1 < x < 10. f(x) = √x + 2, x > 0.
Notice again the black Another unfilled < dot.
point, showing where the Unnecessary really, as
curve is cut off. It is filled no values of x are < 0.
because it is <, not <, as F(x) may be written in
with inequalities. these as f:x→√x + 2.
One-One & Many-One
E.g.1. y = x3. This is a one-one, E.g.2. y = x2, -3 < x < 2. E.g.3. A square is cut out of this square.
as no ranges are the same. So this is a many-one. Find a domain for function A. A = 144 – x2
So the min value for x is 0. Using
Pythagoras: the max value for x = √72.
Domain = 0 < x < 6√2.
E.g.3 A function is defined by h: x → cosx, 0 < x < π. Is this a one-many or one-one function?
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller j-meizme. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $19.70. You're not tied to anything after your purchase.
