Page 294 - ICSE Math 8

RATIO AND PROPORTION

Ratio Dividing a Quantity, A, in the given Ratio
In ratio x : y  x 
st
1 part:   × A
 x + y 
nd  y 
2 part:   × A
 x + y 
In ratio x : y : z  x 
1 part:  st  × A
 x + y + z 
 y 
2 part:  nd  × A
 x + y + z 
 z 
3 part:  rd  × A
 x + y + z 

ALGEBRAIC IDENTITIES

Algebraic Identity Formula

2
2
Identity 1 (a + b) = a + 2ab + b 2
2
2
Identity 2 (a – b) = a – 2ab + b 2
2
Identity 3 (a + b)(a – b) = a – b 2
2
Identity 4: Special Products (x + a)(x + b) = x + (a + b)x + ab
2
(x + a)(x – b) = x + (a – b)x – ab
2
(x – a)(x + b) = x + (b – a)x – ab
2
(x – a)(x – b) = x – (a + b)x + ab
3
3
(a + b) = a + 3ab(a + b) + b 3
3
3
(a – b) = a – 3ab(a – b) – b 2
2
2
2
2
(a + b + c) = a + b + c + 2(ab + ac + bc)
SYMMETRY, REFLECTION AND ROTATION
Reflection
About Reflected coordinates
x-axis A(x, y) → A’(x, – y)
y-axis A(x, y) → A’(–x, y)
Origin A(x, y) → A’(–x, –y)
Rotation
Through 90° Anticlockwise: A(x, y) → A′(–y, x)
About the origin Clockwise: A(x, y) → A′(y, –x)
Through 180° A(x, y) → A’(–x, –y)
About the origin

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