NOTES AND FORMULAE ADDITIONAL MATHEMATICS FORM 41. QUADRATIC EQUATION

(a) ax2 + bx + c = 0

x =

Sum of roots:

+ =

Product of roots:

=

(b) Equation from the roots:x2 - (sum of roots)x + product of roots = 0

2. QUADRATIC FUNCTION(a) Types of roots

b2 - 4ac > 0 2 real and distinct/different roots.b2- 4ac = 0 2 real and equal roots/two same roots.b2 - 4ac < 0 no real root.

b2 - 4ac 0 got real roots.

b2 - 4ac > 0 b2 - 4ac = 0 b2 - 4ac < 0

(b) Completing the squarey = a(x - p)2 + qa +ve minimum point (p, q)a –ve maximum point(p, q)The axis of symmetry is x – p = 0 or x = p

(c) Quadratic inequalities(x – a)(x – b) 0Range x a, x b(x – a)(x – b) 0Range a x b

3. INDICES AND LOGARITHM

(a) x = an loga x = nIndex Logarithm Form Form

(b) Logrithm Law1. logaxy = logax + logay

2. loga = logax – logay3. loga xn = n logax4. loga a = 15. loga 1 = 0

6. loga b =

7. loga b =

4. COORDINATE GEOMETRY(a) Distance between A(x1, y1) and

B(x2, y2)

AB =

(b) Mid point AB

M

(c) P which divides AB in the ratio m : n

P

(d) Gradient AB

m =

m =

(e) Equation of straight line

(i) Given m and A(x1, y1)y – y1 = m(x – x1)

(ii) Given A(x1, y1) and B(x2, y2)

(a) Area of polygon

L =

(g) Parallel linesm1 = m2

(h) Perpendicular linesm1 m2 = -12.

5. STATISTICSMeasurement of Central Tendency(a) Mean

Prepared by Mr. Sim Kwang Yaw 1

For ungrouped data

For ungrouped data with frequency.

For grouped data, xi = mid-point

(b) MedianThe data in the centre when arranged in order (ascending or descending).

Formula

M = L +

L = Lower boundary of median class.n = Total frequencyF = cumulative frequency before the median classfm = frequency of median classC = class interval size

By Ogive

(c) ModeDate with the highest frequency

By Histogram :

Measurement of Dispersion(a) Interquartile Range

Formula :

Q1 =

Q3 =

Ogive :

Interquartile range = Q3 – Q1

(b) Variance, Standard Deviation

Variance = (standard deviation)2

=

For ungrouped data

=

For grouped data

6. CIRCULAR MEASURE(b) Radian Degree

Prepared by Mr. Sim Kwang Yaw 2

r =

(c) Degree Radian

o = rad

(d) Length of arcs = j

(e) Area of sector

L = j2 = js

(f) Area of segment

L = j2( r – sin o)

7. DIFFERENTIATION(a) Differentiation by First Principle

(b) (a) = 0

(c) (xn) = nxn-1

(d) (axn) = anxn-1

(e) Differentiation of product

(uv) = u + v

(f) Differentiation of Quotient

(g) Differentiation of Composite Function

(ax+b)n = an(ax+b)n-1

(h) Stationary point = 0

Maximum point:

= 0 and < 0

Minimum point:

= 0 and > 0

(i) Rate of Change

(j) Small changes:

Prepared by Mr. Sim Kwang Yaw 3