SON OF MORE REVISION 20040203
This sheet should be done entirely without calculators. The idea is to help remember some numbers and some rules and to apply some skills. The few unit conversions you are required to know have been manipulated here to show how you can use them to advantage. The remainder apply the same algebra / number skills I have made you work on so far. You may need to write the middle questions 6 to 12 in your book
1 The number of gallons in a litre is 1 / ___________ = ____________
2 A kilometre is 1/ ___________ of a mile, or 0. __________ miles to 3 d.p.
3 There are ________ litres in a cubic metre.
4 (-19) ² = ___________ 18 ² = ______ -(17) ² = ___________
5 31 ² - 19 ² = 50 x ____ = _____ 32 ² - 18 ² = 50 x ______ = _____
6 ( x + y ) ( x – y ) = but ( x + y ) ( x + y ) =
and ( x - y ) ( x – y ) =
Using this rule and non-calculator (and NWNM !!) then if x =100, y = 2
7 102 x 98 =
8 102² =
9 98² =
Similarly
10 207² =
11 193 ² =
12 207 x 193 =
AND, using the same idea in reverse (which is a hint in both directions)
10 (28 + 7) (28 - 7) =
11 107 x 93 =
12 89 x 71 =
13 If you have never seen this before, treat it as an intelligence test. the numbers are simple and each new step has enough hint that you might well guess intelligently. Things of the same kind, brackets especially, are supposed to line up vertically
TRY to fill in the gaps here: 2 x – 5 y = 9 so ( 2 -5 ) ( x ) = ( 9 )
and also 3 x + 4 y = 11 ( ) ( y ) ( )
PREMULTIPLY both ( 4 +5 ) ( 2 -5 )( x ) = ( 4 ) ( 9 )
sides by the same thing ( ) ( 3 )( y ) = ( ) ( )
Do matrix multiplication ( 0 ) ( x ) = ( ) = ( )
(I’ve given you enough) ( 0 ) ( y ) ( ) ( )
DIVIDE both sides by ( x ) = ( ) a pair of
the nasty number ( y ) ( ) fractions
