KEY+THINGS+TO+KNOW+FOR+UNIT+2!!!

__**Distance**__ - 8 km is approximately the same as 5 miles

__**Powers**__

anything to the power zero = 1 anything to the power (-1) is 'one over' the number (aka the reciprocal) In general - a negative power means 'one over' - so 2 to the power (-3) is one over 2 to the power 3 = 1 over 8 anything to the power 'one half' is the square root of the number anything to the power 'one third' is the cube root of the number

__**Area of a trapezium**__ The formula is given at the front of the paper but....

Half the sum of the parallel sides, times the distance between 'em That is how you calculate the Area of a Trapezium

__**Algebraic Proof**__ Odd and Even numbers...

If n is any positive integer....

2n MUST be even (2n + 1) MUST be odd

Even x anything = even Odd x odd = odd

Even + even = even Even + odd = odd Odd + odd = even

__**Simplifying algebraic fractions**__

ALWAYS start by factorising top and bottom and look for a common factor. NEVER start by crossing something out from top and bottom!

__**Writing a recurring decimal (eg 0.6555555555...) as a fraction.....**__

You can start by writing x = 0.6555555 (use recurring symbol) 10x = 6.555555555 100x = 65.5555555555

Now subtract middle from bottom

90x = 59 so x = 59/90

__**Adding or Subtracting Algebraic fractions**__

You MUST make sure there is a common denominator - one method that will always work (but isn't necessarily the quickest or easiest!) is to multiply the given denominators together - and remember that whatever you do to the bottom you must do to the top.

__**Surds**__ (i) rationalising the denominator...if the denominator is just something like Ö 5 then you just need to multiply top and bottom by Ö 5. This will make the denominator 5. You may need to simplify the final answer. (ii) to square a bracket like (3 + Ö 2), make sure you write it out twice and expand as normal. ie - (3 + Ö 2)(3 + Ö 2) - this answer will be 11 + 6 Ö 2

__**Parallel and Perpendicular lines**__ In general, a straight line has equationy = mx + c, where m is the gradient and x is the y-intercept. Sometimes the equation may be arranged differently eg y = 4 - 3x has gradient -3 and y-intercept 4.

PARALLEL lines have the SAME gradient - eg y = 4x and y = 4x + 2, y = 6 - 2x and y = 3 - 2x etc

To find a PERPENDICULAR gradient, take the 'negative reciprocal' of the gradient you have. eg y = 3x + 2 has gradient 3 - the perpendicular gradient is -1/3.

Remember - gradient is JUST A NUMBER!!!

__**Questions involving circles, tangents and angles**__ You are expected to know/understand/use/quote three rules... (i) a triangle formed by 2 radii (radiuses) and a chord is ISOSCELES. This means that the two 'base angles' have to be equal. (ii) a tangent is ALWAYS perpendicular to the radius it meets on the circumference (iii) if you have two tangents meeting at a point then that point is equidistant from the two 'touching points' where the tangents meet the circle.

If you are doing a STARRED question or a PROVE question then you should quote these results as your reasons.

__**PLANS and ELEVATIONS**__ The PLAN view is ALWAYS from ABOVE... The question will make it clear which is front and which is side.....