This document contains all examinable proofs (CAPS) and the acceptable reasonings in Euclidean Geometry. There is a blank copy attached to print (if you want it in your own handwriting) as well as one with the solutions.
Name: _________________ Surname: _____________________ Class ______
1) Number patterns: PAPER 1
a) Sum to 𝑛 terms in an arithmetic series
b) Sum to 𝑛 terms in a geometric series
2) Trigonometry: PAPER 2
a) Sine rule
b) Cos rule (V1 + V2)
c) Area rule
d) Compound Angles
3) Euclidean Geometry: PAPER 2
a) Theorem 1: The line segment joining the centre of a circle to the midpoint
of a circle is perpendicular to the chord.
b) Theorem 2: The angle which the arc of a circle subtends at the centre is
double the angle it subtends at any given point on the
circumference.
c) Theorem 5: The opposite angles of a cyclic quadrilateral are
supplementary.
d) Theorem 8: The angle between the tangent to a circle and the chord
drawn from the point of contact is equal to the angle
subtended by the chord in the alternate segment.
e) Theorem 9: A line drawn parallel to one side of a triangle divides the
other two sides proportionally.
f) Theorem 10: Equiangular triangles are similar.
,Sum to 𝑛 terms of an arithmetic series. page 2 of 16 pages
Consider an arithmetic sequence of 𝑛 terms with 1st term 𝑎, 𝑛𝑡ℎ term 𝑙 and
common difference 𝑑. Prove that in any arithmetic series the sum of the first
𝑛 𝑛
𝑛 terms is 𝑆𝑛 = (𝑎 + 𝑙) or 𝑆𝑛 = [2𝑎 + (𝑛 − 1)𝑑].
2 2
,Sum to 𝑛 terms of a geometric series. page 3 of 16 pages
Consider a geometric sequence of 𝑛 terms, 1st term 𝑎 and common ratio 𝑟.
Prove that in any geometric series the sum of the first 𝑛 terms is expressed by
𝑎(1−𝑟 𝑛 ) 𝑎(𝑟 𝑛 −1)
𝑆𝑛 = OR 𝑆𝑛 = .
1−𝑟 𝑟−1
________________________________________________________________
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 kalebroodt. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $2.76. You're not tied to anything after your purchase.
