Standard Form and Angles in circles/Circle Theorem

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STANDARD INDEX FORM:

Examples of Standard Index Form are:

  • 4372= 4.372x`10(to the power of 3)
  • 691 000= 6.91x10(to the power of 5)
  • 3.71x10(to the power of four)= 37100

FOR SMALL POSITIVE NUMBERS, n is a NEGATIVE INTEGER. (Minus from minute numbers) and is EQUAL to the number of places the decimal point has moved.

Examples include:

  • 0.0356=3.56x10(to the power of minus 2)
  • 0.00013=1.3x10(to the power of minus 4)
  • 4.5712x10(to the power of minus 5)=0.0000045712

CALCULATIONS WITH SIF:

Examples:

1. 4.2x10(to the power of 4) + 8.6 x 10 (to the power of 3)

=42000+8600

=50600

=5.066 x 10 (to the power of 4)

2. 9.37 x 10 (to the power of minus 2) - 1.6 x 10 (to the power of minus 3)

=0.0937 - 0.0016

=0.0921

=9.21 x 10 (to the power of minus 2)

ANGLES IN CIRCLES:

a sector, an arc and chord (http://www.mathsrevision.net/gcse/circle.gif)

The red line in the second diagram is called a chord. It divides the circle into a major segment and a minor segment.

ANGLES SUBTENDED ( To be produced by drawing straight lines.) BY THE SAME ARC:

Angles subtended on the same arc (http://www.mathsrevision.net/gcse/Circle1.gif)

Angles formed from two points on the circumference are equal to other angles, in the same arc, formed from those two points.

The angle at the centre of the arc, is TWICE the angle SUBTENDED at any point of the CIRCUMEFERENCE by the SAME ARC.

THE CIRCUMFERENCE OF A CIRCLE= 2 X Pi x R

Angle in a Semi-Circle

angle in a semi-circle (http://www.mathsrevision.net/gcse/Circle9.gif)

Angles formed by drawing lines from the ends of the diameter of a circle to its circumference form a right angle. So c is a

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