Spm Add Maths Formula List Form4

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ONESCHOOL.NET Add Maths Formulae List: Form 4 (Update 18/9/08)01 FunctionsAbsolute Value Function Inverse Function If

f ( x), if f ( x) 0 f ( x) f ( x), if f ( x) < 0

y = f ( x) , then f 1 ( y) = x

Remember: Object = the value of x Image = the value of y or f(x) f(x) map onto itself means f(x) = x

02 Quadratic EquationsGeneral Form Quadratic Formula

ax 2 + bx + c = 0where a, b, and c are constants and a 0. Forming Quadratic Equation From its Roots: If and are the roots of a quadratic equation

b b 2 4 ac x= 2aWhen the equation can not be factorized. Nature of Roots

+ =

b

a

=

c a

The Quadratic Equation

b 4 ac > 0 two real and different roots b 2 4 ac = 0 two real and equal roots b 2 4 ac < 0 no real roots b 2 4 ac 0 the roots are real

2

x 2 ( + ) x + =0or x 2 (SoR) x + ( PoR) = 0

http://www.one-school.net/notes.html

1

03 Quadratic FunctionsGeneral Form f ( x) = ax 2 + bx +

ONESCHOOL.NETCompleting the square: f ( x) = a( x + p) 2 +

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. (i) (ii) (iii) (iv)

q the value of x, x = p min./max. value = q min./max. point = ( p, q) equation of axis of symmetry, x = p

Alternative method: a > 0 minimum (smiling face) a < 0 maximum (sad face) c Quadratic Inequalities a > 0 and f ( x) > 0 a > 0 and f ( x) < 0 Nature of Roots b 4ac > 0 intersects two different points at x-axis b 2 4ac = 0 touch one point at x-axis b 2 4ac < 0 does not meet x-axis2

f ( x) = ax 2 + bx +

a

b

a

b

x < a or x > b

a< x 0 dx2Rates of Change Chain rule dA dA dr = dt dr dt-1Small Changes and Approximation Small Change:yIf x changes at the rate of 5 cmsdx =5 dtdy dy y x x dx dxDecreases/leaks/reduces NEGATIVES values!!!Approximation: ynew = yoriginal + y =y + x original dy dx x = small changes in x10 Solution of TriangleONESCHOOL.NETSine Rule: a b c = = sin A sin B sin C Use, when given 2 sides and 1 non included angle 2 angles and 1 sidea A b B A 180 (A+B)Cosine Rule:a = b + c 2bc cosA b2 = a 2 + c2 2ac cosB 2 2 2 c = a + b 2ab cosC2 2 2Area of triangle:aCbb +c a cos A = 2bc222A=aUse, when given 2 sides and 1 included angle 3 sidesa A b b a c1 a b sin C 2C is the included angle of sides a and b.ONESCHOOL.NETCase of AMBIGUITYA If C, the length AC and length AB remain unchanged, the point B can also be at point B where ABC = acute and A B C = obtuse. If ABC = , thus ABC = 180 .180 - Remember : sin = sin (180 ) Case 2: When a = b sin A CB just touch the side opposite to CC B B Case 1: When a < b sin A CB is too short to reach the side opposite to C.Outcome: No solution Case 3: When a > b sin A but a < b. CB cuts the side opposite to C at 2 pointsOutcome: 1 solution Case 4: When a > b sin A and a > b. CB cuts the side opposite to C at 1 pointsOutcome: 2 solution Useful information:b a cOutcome: 1 solution In a right angled triangle, you may use the following to solve the problems. (i) Phythagoras Theorem: c = a 2 + b2 (ii) Trigonometry ratio: sin = c b , cos =c a , tan a = (base)(height)b(iii) Area =11 Index NumberPrice Index Composite indexONESCHOOL.NETI=P1I=Wi I i Wi100 P0 I = Price index / Index number I A,B I B,C = I A,C 100I = Composite Index W = Weightage I = Price index