Topic 1 - Direct and inverse proportion
● Directly proportional: 𝑦 ∝ 𝑥 (𝑦 = 𝑘𝑥) (where k is constant)
1 𝑘
● Indirectly proportional: 𝑦 ∝ 𝑥
(𝑦 = 𝑥
) (where k is constant)
Topic 2 - Negative and fractional indices
𝑚
𝑛 𝑚
● 𝑎 𝑛 = 𝑎
Topic 4 & 5 - Arithmetic sequences & Sum of an arithmetic
series
●
𝑛 𝑛
● 2
(𝑎1 + 𝑎𝑛) = 2
[2𝑎1 + (𝑛 − 1)𝑑]
𝑎1 + 𝑎𝑛 = 2𝑎1 + (𝑛 − 1)𝑑
⇒ 𝑎1 = 𝑎𝑛 − (𝑛 − 1)𝑑
⇒ 𝑎𝑛 = 𝑎1 + (𝑛 − 1)𝑑
𝑎𝑛 − 𝑎1 = (𝑛 − 1)𝑑
𝑎𝑛 − 𝑎1
𝑑
= 𝑛 − 1
𝑎𝑛 − 𝑎1
⇒ 𝑛 = 𝑑
+ 1
𝑎𝑛 − 𝑎1
⇒ 𝑑 = 𝑛−1
1
, Topic 6 - Circle theorems
●
●
Alternate segment theorem
2
● Directly proportional: 𝑦 ∝ 𝑥 (𝑦 = 𝑘𝑥) (where k is constant)
1 𝑘
● Indirectly proportional: 𝑦 ∝ 𝑥
(𝑦 = 𝑥
) (where k is constant)
Topic 2 - Negative and fractional indices
𝑚
𝑛 𝑚
● 𝑎 𝑛 = 𝑎
Topic 4 & 5 - Arithmetic sequences & Sum of an arithmetic
series
●
𝑛 𝑛
● 2
(𝑎1 + 𝑎𝑛) = 2
[2𝑎1 + (𝑛 − 1)𝑑]
𝑎1 + 𝑎𝑛 = 2𝑎1 + (𝑛 − 1)𝑑
⇒ 𝑎1 = 𝑎𝑛 − (𝑛 − 1)𝑑
⇒ 𝑎𝑛 = 𝑎1 + (𝑛 − 1)𝑑
𝑎𝑛 − 𝑎1 = (𝑛 − 1)𝑑
𝑎𝑛 − 𝑎1
𝑑
= 𝑛 − 1
𝑎𝑛 − 𝑎1
⇒ 𝑛 = 𝑑
+ 1
𝑎𝑛 − 𝑎1
⇒ 𝑑 = 𝑛−1
1
, Topic 6 - Circle theorems
●
●
Alternate segment theorem
2
