Maths Topics

Guide for an end of year exam, you will need to anotate

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  • Created on: 26-04-11 17:36
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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 steps
forward, because:
If I walk 3 steps forward and then 5 steps backward, I'll end up 2 steps behind where I
started, i.e., as if I walked 2 steps backward. To describe this example as an addition, I need
to describe all my walking in terms of steps forward. So I can say that if I walk 3 steps
forward and then -5 steps forward, it's the same as if I had walked -2 steps forward,
because:
Subtracting Negative Numbers
If I walk 9 steps forward and then 6 steps backward, it's the same as if I had walked 3 steps
forward, because:
If I walk 9 steps forward and then 6 steps forward, it's the same as if I has walked 15 steps
forward. To turn that into a subtraction problem, I have to describe the 6 steps forward as -6
steps backward. That is, if I walk 9 steps forward and then -6 steps backward, it's the same
as if I had walked 15 steps forward, because:
Multiplying Negative Numbers
If I walk 3 steps forward 5 times, then in total I will have walked 15 steps forward. This
corresponds to the multiplication:

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If I walk 3 steps backward 5 times, then in total I will have walked 15 steps backward.…read more

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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 figures
the four figures are 1201
answer = 120,100
Example #3
13.27 ................to 3 significant figures
the 13.272 rounds up to 13.3
the three figures are 133
answer = 13.…read more

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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 by the 3. This gives 15.
Now convert each factor to 15 this by dividing the denominator of each into 15 and
multiplying the result by each numerator.…read more

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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 circle so that the line segment then becomes the radius
of the circle.
4.…read more

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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 segment
After doing this Your work should look like this
Start with a line
segment PQ.
1. Place the compass
on one end of the line
segment.…read more

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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 of the
line. Draw an arc on
each side of the line so
that the arcs cross the
first two.…read more

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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
Start with a line and point
R which is not on that
line.…read more

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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 to adjust
the compass width in
between. Label these
points P and Q
Step 4 At this point, you can
adjust the compass width.
Recommended: leave it as
is.…read more

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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.…read more

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