Form 3

CIRCLE THEOREM

• Angle at the centre

          = 2 × angle at the
         circumference
          x = 2y

• Angles in the same segment are equal x = y

• Angles in the segment are equal x = y

• Angle in a semicircle ÐACB = 90° . Sum of opposite angles of a cyclic quadrilateral = 180° a + b = 180° . The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle b = a

• Angle between a tangent and a radius = 90° ÐOPQ = 90°. The angle between a tangent and a chord is equal to the angle in the alternate segment  x = y. If PT and PS are tangents to a circle,PT = PS ÐTPO =РSPO ÐTOP = ÐSOP.

Here are the summary for this chapter. 

EXPANSION OF ALGERBRAIC
EXPRESSIONS

(a) (2x1)(x-3)
     =2 – 6x + x – 3 
     = 2x2 – 5x − 3
(b) (x + 3)2 
    = x2 + 2 × 3 × x + 32
    = x2 + 6x + 9
(c) (x – y)(x + y) 
     = x2 + xy – xy – y2 
     = x2 – y2


SIMULTANEOUS LINEAR EQUATIONS

(a) Substitution Method:
     y = 2x – 5 --------(1)
     2x + y = 7 --------(2)
Substitute (1) into (2)
    2x + 2x – 5 = 7 
    4x = 12 
      x = 3
Substitute x = 3 into (1), 
      y = 6 – 5 
      y = 1

(b) Elimination Method:

Solve:

      3x + 2y = 5 ----------(1)
       x – 2y = 7 ----------(2)
(1) + (2), 
      4x = 12,
        x = 3
Substitute into (1) 
       9 + 2y = 5
             2y = 5 – 9 
             2y = −4
               y = −2
ALGEBRAIC FORMULAE

Given that k – (m + 2) = 3m, express m in terms of
k.

Solution:

k – (m + 2) = 3m 
k – m – 2 = 3m
k – 2 = 3m + m
k – 2 = 4m
m = k – 2/4