MATHS PAPER 1 NOTES
Algebra
To simplify complex fractions, reduce the numerator and the denominator to simple fractions and divide (or simplify) the resulting fraction.
(any real quantity)² cannot be negative.
x² - y² =(x+y)
(x-y)
x³+y³ =(x+y)
(x²-xy+y²)
x³-y³ =(x-y)
(x²+xy+y²)
an inequality remains true when the same number is
added to it or subtracted from both sides.
An inequality remains true when both sides are
multiplied by the same +ve number.
When multiplying or dividing by a –ve number
reverse the inequality sign.
√ab = √a. √b
√[ = √a
√b
For an equation
ax² + bx + c
b² -4ac>0 => 2 distinct real roots
b² -4ac=0 => a repeated root
b² -4ac<0 =>
no real roots
Solving an equation ax² + bx + c
using α
and β
α +β = -b
a
α β = c
a
α²+β ²
= (α +β)² -2αβ
α³+β ³ = (α+β)³
-3αβ(α+β)
aˣ.aʸ = aˣ +ʸ
(aˣ) ʸ
= aˣʸ
a° = 1 a≠0
aˣ
= aˣˉʸ
aʸ
aˉʸ = 1
aʸ
㏒ոy
= x
y = nˣ
㏒ոxy
= ㏒ոx
+ ㏒ոy
㏒ոyˣ =x ㏒ոy
㏒ոx
= ㏒ոx
- ㏒ոy
y
For an equation
ax² + bx + c
a² + b² > 2ab
a² + b² + c² ≥ ab
+ bc + ca
a + b ≥ 2
b a
