ADDITIONAL MATHEMATICS

PROGRESSION

LINEAR LAW INTEGRATION

PROGRESSION

ARITHMETHIC PROGRESSION

(A.P.)

GEOMETRIC PROGRESSION

(G.P.)

PROGRESSIONS CAN DIVIDED INTO 2

ARITHMETHIC PROGRESSION

1 An arithmetic progression is a number sequence where the difference between each term after the first term and the preceding term is a constant. This constant is know as the common difference,(d).

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2 The nth term, Tn of an arithmetic progression is given by: Click hear to know about the formule

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3 the sum of the first n term, sn, of an arithmetic progression is given by:

Where

a = the first term ( T1 ),d = common difference

l = the last term

Sn = n [2a + (n – 1)d] or 2

Sn = n (a + l), 2

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Tn =a + (n – 1)d, where a = the first term ( T1 ),d = common difference.

The nth term formule

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Tn + 1-Tn, where Tn+1= (n – 1)th term and Tn = nth term.

The common difference,(d)

formule

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GEOMETRIC PROGRESSION1 A geometric progression is a number sequence where each

term after the first term is obtained by multiplying the preceding term by a constant know as the common ratio, r.

r = Tn + 1 , Tn

Where Tn +1 = (n + 1)th term and Tn = nth

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2 The nth term, Tn of an geometric progression is given by:

Tn = ar ,Where a = the first term ( T1 ),r = common ratio

n-1

3 the sum of the first n term, sn, of an arithmetic progression is given by:

Sn = a(r – 1) , r > 1 or r – 1 Sn = a(1 – r ) 1 – r

n

n

LINEAR LAW

LINEAR LAW CAN DIVIDED INTO 2

SUB TOPICT

APPLICATION OF LINERA LAW TO

NON-LINEAR FUNTIONS

LINE OF BEST FIT

LINE OF BEST FIT

1 The line of fit is a straight line that has the following properties:• Passes through as many point as possible• The number of point that do not lie on the straight line draw should

be more or less the same o n both sides of the straight line.

For example: y

x

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2 y = mx +c is a equation. When y is plot against x a straight line is obtained, where m is the gradient and the c is the y-intercept.

y

x

c

o

y = mx + c

APPLICATION OF LINERA LAW TO NON-LINEAR FUNTIONS

1 A non-linear funtion is a funtion that has one or more variable, x or y, which are not in the first degree. For example

y = mx + c2 A non-linear funtion that consists of variable,

x and y, (a curve line graph) can be reduce to the linear form

y = ax

y = pq

EXAMPLE

y = ax+bx

b

x 3 2

y = ax

log y = blog x + log aWhere ,

Y = log y, X = log x,

m = b,C = log a

b

y = pq

log y = (log q) x + log p

Where ,Y = log y,

X = x,m = log q,C = log p

x

y = ax + b x Where ,

Y = y xX = xm = ac = b

y = ax+bx3 2

2

2

INTEGRATION

1 Integration is the inverse process of differentiation.2 If dy = f(x) dx. dxFor example,

y = x + c 4

dy = x dx

4 3

INTEGRATION OF ALGEBRAIC FUNTION (INDIFINITE INTEGRAL)

(a) ∫ a dx=ax+c,where a and c are constant.

(b) ∫ x dx= x + c ,where c is a constant, n is an integer and n=-1 n+1(c) ∫ ax dx = ax +c , where a and c are constants, n is an integer and n + 1 n = -1

n n+1

n n+1