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Revision for maths
Negative Numbers

Multiplication and division
Positive ×/ positive = positive
Positive ×/ negative = negative
Negative ×/ positive = negative
Negative ×/ negative = positive


Adding Negative Numbers

If I walk 3 steps forward and then 5 steps forward, it's the same as if I walked 8…

Page 2

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If I walk 3 steps backward 5 times, then in total I will have walked 15 steps backward.
Restating this in terms of steps forward, I can say that if I walk -3 steps forward 5 times,
then in total I will have walked -15 steps forward, corresponding to the…

Page 3

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Rounding to a number of significant figures
The required number is found by ignoring any zeros infront or behind the line of numerals and
rounding where needed.
Example #1
0.001292 ................to 3 significant figures
the three figures are 1 2 9
answer = 0.00129
Example #2
120,101 ................to 4 significant…

Page 4

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Fractions/Ratio

Example: Divide 90 in the ratio 3 : 2
Total of ratio numbers = 3 + 2 = 5






Therefore 90 shared in the ratio 3 : 2 is 54 and 36



The common denominator is found by multiplying the two denominators together. In this
case, multiply the 5…

Page 5

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Fraction Division - The second fraction is turned upside down(inverted), the two fractions
are multiplied together.







Constructions/Loci

Construction of a Perpendicular Bisector

1. Draw a straight line segment.
2. Put your compass on one of the points at the end of the line segment.
3. Using your compass expand the…

Page 6

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A cow is tethered to a post with a rope of length 4m. It walks around the post with the rope
pulled tight.

The cow's path is a circle of radius 4m.





The cow's path is known as the locus.
The plural of locus is loci.

Midpoint of a line…

Page 7

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2. Set the compass
width to a
approximately two
thirds the line length.
The actual width does
not matter.

3. Without changing
the compass width,
draw an arc on each
side of the line.






4. Again without
changing the compass
width, place the
compass point on the
the other end…

Page 8

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5. Using a
straightedge, draw a
line between the points
where the arcs
intersect.






6. Done. This line is
perpendicular to the
first line and bisects it
(cuts it at the exact
midpoint of the line).






Perpendicular point to a line
After doing Your work should look
this like this…

Page 9

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Step 1 Place the compass on the
given external point R.






Step 2 Set the compass width to
a approximately 50% more
than the distance to the
line. The exact width does
not matter.




Step 3 Draw an arc across the
line on each side of R,
making sure not…

Page 10

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Step 5 Place a straightedge
between R and the point
where the arcs intersect.
Draw the perpendicular
line from R to the line, or
beyond if you wish.






Step 6 Done. This line is
perpendicular to the first
line and passes through the
point R. It also bisects the
segment…

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