Spm-Add-Maths-Formula-List-Form4

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General Form f ( x) = ax + bx+ c where a, b, and c are constants and a ≠ 0. *Note that the highest power of an unknown of a quadratic function is 2. a > 0 ⇒ minimum ⇒ ∪ (smiling face) a < 0 ⇒ maximum ⇒ ∩ (sad face) Quadratic Inequalities a > 0 and f( x ) > 0 a > 0 and f( x ) < 0 a b a b x < a or x> b a< x< b http://www.one-school.net/notes.html 2 03 Quadratic Functions 2 Completing the square: f ( x) = a( x+ p) + q ONE-SCHOOL.NET (i) the value of x, x =− p (ii) min./max. value = q (iii) min./max. point = ( − p, q) (iv) equation of axis of symmetry, x = − p Alternative method: f ( x) = ax + bx+ c (i) b the value of x, x =− 2a (ii) b min./max. value = f ( − ) 2a (iii) equation of axis of symmetry, Nature of Roots 2 2 x =− b 2a 2 b − 4 ac> 0 ⇔ intersects two different points − = at x-axis ⇔ touch one point at x-axis 2 b 4 ac 0 04 Simultaneous Equations To find the intersection point ⇒ solves simultaneous equation. Remember: substitute linear equation into non- linear equation. 2 b − 4 ac< 0 ⇔ does not meet x-axis
Fundamental if Indices Zero Index, Negative Index, Fractional Index Fundamental of Logarithm x loga y= x⇔ a = y loga a = 1 x loga a = x loga 1= 0 0 a = 1 1 a− = 1 a a − 1 b ( ) = b a 1 n n a a = m n n m a a = http://www.one-school.net/notes.html 05 Indices and Logarithm 3 Laws of Indices a a × a = a m n m+ n ÷ a = a m n m−n ( a ) a × = m n m n ( ab) = a b n n n a n a ( ) = b b Law of Logarithm n n log mn = log m + log n a a a m loga = logam− logan n log a m n = n log a m Changing the Base log log a a b = log log c b a c 1 b = log a b ONE-SCHOOL.NET
Page 1: ONE-SCHOOL.NET Add Maths Formulae L
Page 5: Area of triangle: Area of Triangle
Page 8 and 9: The variance is a measure of the me
Page 10 and 11: Differentiation of a Function III n
Page 12 and 13: Gradients of tangents, Equation of
Page 14 and 15: Sine Rule: a sin A = b sin B c sin
Page 16: http://www.one-school.net/notes.htm

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