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Maths
YEAR 10
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Powers and roots
Exponentiation求幂: base (a) , power (n) a^n
How to read it? Read as: a raised to the n-th
power, a raised to the power of n, or possibly
a raised to the exponent of n, or more briefly
as a to the n. Some exponents have their own
pronunciation: for example, a^2 is usually read
as a squared and a^3 as a cubed.
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Example:
5^2=25 (5 raised to the power of 2 equal to
25) 25 is a power of 5, 5 is a root of the power
( square root or perfect square)
4^3=64 ( 4 raised to the power of 3 or 4 cubed)
64 is a cube number.
4 is said to be the cube root of 64
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Directed number (integers)
Positive Zero Negative
Number line can be either horizontal （水平）
or vertical （垂直）
The rules：
 ++ makes +
 -+ makes –
 - - makes +
Sea level (P16)
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Fractions
b/a
numerator / denominator
Equivalent fractions (equal in value)
Simplest form: numerator and denominator
have no common factors
90/120=? SIMPLEST FORM
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Operations on fractions
 Adding or subtracting fractions:find the LCM of the
denominators
 What is LCM?
 Lowest common multiple
 How to find LCM? 2 WAYS
 1) list the multiples of each number and then pick out
 2) express each of the numbers as a product of prime
factors and then work out
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Continue
Dividing fractions
reciprocal (multiplicative inverse)
The product of reciprocals is always 1
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Decimals
5.268
Decimal point: the union end and fractions
begin.
Changing (transform) fractions to decimals
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Recurring decimals (Repeating)
Dot
Recurring decimals are rational numbers (why)
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Rounding numbers
Rounding to the nearest ten
Rounding to the nearest unit
Rounding to decimal places (e.g. 1 decimal
place. 2 decimal places)
Rounding to significant figures
Work out the answer to one more place than
you need. If the extra number is 5 or more,
add 1 to the number before it. If the extra
number is less than 5, leave the number
before it as it is.
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Significant figures
 1,2,3,4,5,6,7,8,9 All non-zero digits are counted as
significant figures
 ZERO (0) ??? Significant or not significant?
 Zero appearing anywhere between 2 non-zero digits
are significant e.g. 100002
 Leading zeros are not significant e.g. 0.00052
 A zero to the left of a decimal point is significant if
there is a non-zero digit to its right. e.g. 10000.02
 A zero to the right of a decimal point is significant if
there is a non-zero digit to its left. E.g. 120.2300
 Zeros in a number not containing a decimal point can
be ambiguous e.g. 12000
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Ratio and proportion
 Ratio: a comparision between two or more amounts.
Usually expressed as "a to b" or a:b
 a:b a being the antecedent [ˌæntɪˈsi:dnt] and b being the
consequent
 Hotdogs and pies are sold in a ratio of 3:4 at a local
football match. If 840 pies and hotdogs were sold. How
many of them were pies?
 Solution:
 ①Determine the ratio ( the ratio is 3:4);
②Determine the total number of parts (3+4=7)
③Calculate the value of each part (each part:840/7=120)
④Determine the number of parts needed (Number of pies
sold=4×120=480)
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Map scale
 The map of Deutschland
[ˈdɔitʃlənd]
 Map scale is 1:1 500 000
 This means that 1 unit of
measurement on the
map must be multiplied
by 1 500 000 to get the
distance in real life.
 Express these map
scales in the form 1:n
 5cm to 2km
 To do Unit conversion
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Proportion
 Show the relationship of two
variables whose ratio is
constant
 a and b are proportional
if the ratio a/b is constant
 E.g. Ivan-make a cake. The
proportions of sugar or egg is
always given
 Direct proportion
 Inverse proportion: density Vs.
Volume ( certain mass: m=ρ
×V)
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Rate
Rate: compare 2 different quantities that are
measure in different units. E.g. velocity =s/t
Rate Vs. Proportion
Rate: the most common type of rate is "per
unit time" which can be expressed as a
percentage ( %)
Proportion: a:b
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Percentages
Percentage is a fraction that has a
denominator of 100
X%=X/100
Percentages of a given quantity
E.g. 14% VAT on $100 (in China VAT is 17%
or 13%) means if you buy a computer, the
price tag says $100, but the store charged you
for $114. $14 is VAT( value added tax)
VAT=100×(14/100)=14
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Profit and loss
Make money: the difference between the
purchase price and the costs of bringing to
market
GOAL for businessmen is profit maximization
(利润最大化）
E.g. the box you made in your economic
lesson
COST: glue+paper+time=￥1 =$ 0.15
Price：$ 5
Robber！！！
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Continue
 Profit=Price-Cost
 Loss=Cost-Price
You buy an air ticket cost
$ 1000
 Percentage profit
 Percentage loss
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Discount
 Reduced price
 Pay=original price ×（1discount）
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Money
 Foreign currency：Dollar Pound Euro Yen
 Exchange
e.g. ＄A AUD ＄100=￥680.98 -> ＄1=￥6.8098
Cappuccino ＄5 =？RMB
 The influence of RMB appreciation
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Time
12-hour and 24-hour system
ante meridiem [ˈænti meˈridiem] (a.m.,
"before midday") and post meridiem (p.m.,
"after midday")
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New words in questions
Find the value of
Evaluate
Work out
Express fractions in its simplest form
The product of (X)
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