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CIE IGCSE Additional Maths (0606)
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Notes required for CIE IGCSE Additional Maths (0606) which covers the whole syllabus. A* standard notes.
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IGCSE ADDITIONAL MATHEMATICS1. Functions
● One-one: each x value maps to 1 distinct y value (eg. f(x) = 3𝑥 − 1)
○ Line cuts through the graph once
2
● Many-one: for 2 input values, there is 1 output value (eg. f(x) =𝑥 − 2𝑥 + 3)
○ Line cuts through the graph twice
● One-many: For one input value there are 2 output values (eg. 𝑓(𝑥) = ± 𝑥)
● Domain: x value
○ Eg. 𝑓(𝑥) = 2𝑥 − 1, − 1 ≤ 𝑥 ≤ 3
■ Domain is − 1 ≤ 𝑥 ≤ 3
es
● Range: y value
○ Range is − 3 ≤ 𝑥 ≤ 5
■ Sub x = -1 into 𝑓(𝑥)= -3
ot
■ Sub x = 3 into 𝑓(𝑥)= 5
● Composite functions
○ 𝑓(𝑔(𝑥))or 𝑓𝑔(𝑥)
N
■ Sub all instances of x in 𝑓(𝑥)into 𝑔(𝑥)
2
○ 𝑓 (𝑥)
SE
■ 𝑓𝑓(𝑥)
● Modulus functions
○ Mod of any number is always positive
○ |𝑥| = 𝑥, | − 𝑥| = 𝑥
○ Equations
■ |𝑎𝑥 + 𝑏| = 𝑘 C
IG
● Solve 𝑎𝑥 + 𝑏 = 𝑘 & 𝑎𝑥 + 𝑏 =− 𝑘
■ |𝑎𝑥 + 𝑏| = 𝑐𝑥 + 𝑑
● Solve 𝑎𝑥 + 𝑏 = 𝑐𝑥 + 𝑑 & 𝑎𝑥 + 𝑏 = − (𝑐𝑥 + 𝑑)
○ Graph
ay
■ Draw the graph of 𝑦 = |𝑥|
■ Any parts of the graph below the x axis are
reelected in the x-axis
nj
● Inverse functions
−1
○ Inverse of 𝑓(𝑥) is 𝑓 (𝑥)
Sa
■ Only exists if 𝑓(𝑥)is one-one mapping
−1
○ Domain of 𝑓 = range of 𝑓(𝑥)
−1
○ Range of 𝑓 (𝑥)= domain of 𝑓(𝑥)
○ Finding inverse
a
■ Write function as 𝑦 =
ni
■ Interchange the x & y variables
■ Rearrange to make y the subject
○ Graph
So
■ 𝑓(− 𝑥): reflection in the y-axis
■ − 𝑓(𝑥): reflection in the x-axis
■ 𝑓(𝑥) + 𝑎: translation of a units parallel to y-axis
■ 𝑓(𝑥 + 𝑎): translation of -a units parallel to x-axis
2. Quadratic functions
● 𝑎 > 0(u shaped) = minimum point
● 𝑎 < 0(n shaped) = maximum point
● Find vertex using completing the square
2
○ (𝑥 − 1) + 2 → vertex point (1,2)
● Find y intercept: sub 𝑥 = 0
● Find x intercept: factorise/quadratic formula
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