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What does 'standard form' mean?
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Number x 10power
Where
Number is less than 10 but greater than or equal to 1.
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How do you multiply numbers that expressed in 'standard form'?
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Multiply
the numbers.
Multiply
the 10's (add powers)
Convert to
Standard Form (if necessary)
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What is the 'upper bound' of a number?
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Upper Bound
< number + 0.5
eg, for 17,
the UB < 17.5
NB in
calculations, use 17.5
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What is the 'Lower Bound' of a number?
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Lower Bound
≤ number - 0.5
eg. for 17,
LB ≤ 16.5
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How do you add two rounded numbers so as to get the MAXIMUM
result?
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Upper Bound + Upper Bound
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How do you add two rounded numbers to get the MINIMUM
result?
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Lower Bound + Lower Bound
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How do you subtract two rounded numbers to get the MAXIMUM
result?
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Upper Bound - Lower Bound
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How do you subtract two rounded numbers to get the MINIMUM
result?
|
Lower Bound - Upper Bound
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How do you mulitply two rounded numbers to get the MAXIMUM
result?
|
Upper Bound x Upper Bound
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How do you multiply two rounded numbers to get the MINIMUM
result?
|
Lower Bound x Lower Bound
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How do you divide two rounded numbers to get the MAXIMUM result?
|
Upper Bound ÷ Lower Bound
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How do you divide two rounded numbers to get the MINIMUM result?
|
Lower Bound ÷ Upper Bound
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How do you calulate the limits of accuracy of your answer to a
question?
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Use Upper and Lower bounds to calculate the lowest possible
answer and the highest possible answer.
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What is a rational number?
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Any number which can be written as a fraction.
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What is an irrational number?
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Any number
which cannot be written as a fraction?
eg √2
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How do you
convert a recurring decimal to a fraction
(eg
0.121212...)
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let r =
0.121212...
100r =
12.121212...
subtract,
99r = 12
divide, r =
12/99
OR
(Number of
recurring digits)/(same number of 9s)
eg
0.1212... is 12/99)
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What is an x am?
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an+m
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What is an ÷ am ?
|
an-m
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What is (an)m ?
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anm
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What is a0 ?
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1
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What is a1 ?
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a
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What is a-1 ?
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1/a
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What is (a/b)-1 ?
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b/a
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What is a-n ?
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1/(an)
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What is (a/b)-n ?
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(b/a)n
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what is a½ ?
|
√a
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What is (a)1/n ?
|
nth root of a
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What is (a)n/m ?
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(mth root of a)n
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What is (a)-n/m ?
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1/(mth root of a)n.
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What is (a/b)-n/m ?
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(mth root of b/a)n
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If A is proportional to B, how is this written as an
equation?
|
A = kB
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If A is inversely proportional to B, how is this written as an
equation?
|
A = k/B
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If A is proportional to the square of B, how is this written as
an equation?
|
A = kB2
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If A is proportional to the square root of B, how is this
written as an equation?
|
A = k√B
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If A is inversely proportional to the square of B, how is this
written as an equation?
|
A = k/(B2)
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If A is inversely proportional to the square root of B, how is
this written as an equation?
|
A = k/(√B)
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What is the formula for solving a quadratic equation?
|
if ax2
+ bx + c = 0
then,
x = [-b ±
√(b2 - 4ac)]/2a
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What is the sine rule?
|
a/sinA = b/sinB = c /sinC
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What is the 'ambiguous case' in the sine rule?
|
- When
finding an angle using 'sine rule', there may be 2 possible angle
solutions (a and 180-a).
- Always
find both angles and then check to see if the larger one is possible:
- check
that (180-a) plus the other 2 angles does not exceed 180. If it does
exceed 180, then the only possible solution is 'a'. If it does not
exceed 180, then 'a' and '180-a' are both possible solutions.
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What is the 'cosine rule'?
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a2 = b2 + c2 - 2bc.cosA
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How do you solve an equation in the form f(x) = n, where n is a
number, by a graphical method?
|
Draw the
graphs of y = f(x) and y = n.
The
solution(s) are the 'x' value where the two graphs cross.
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what does f(x) mean?
|
It means
'the function of x'.
It means
'f' is an expression using 'x'
eg if f(x)
= 2x + 3
then the
expression '2x + 3', is called 'f'.
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if f(x) = 2x + 3, what does f(n) mean, where 'n' is a number?
|
Substitute
x with the number.
eg if f(x)
= 2x + 3
then, f(5)
= 2x5 + 3
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What are congruent shapes?
|
Shapes that are identical in every respect.
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What is the formula for the volum of a cone?
|
∏r2h/3
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What is the formula for the volume of a sphere?
|
4∏r3/3
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What is the formula for the curved surface area of a cone?
|
∏rL
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What is the formula for the total surface are of a cone?
|
∏r(L + r2)
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What is the formula for the surface area of a sphere?
|
4∏r2
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What are the 2 formalae for area of a triangle?
|
A = bh/2
or
A =
absinθ/2
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