Download - Math (F4) Math Reasoning 4.1, 4.2
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MATHEMATICAL REASONING
CHAPTER
4
MATHEMATICS FORM 4
STATEMENT AND QUANTIFIERS
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LEARNING OUTCOMES
By the end of the lesson, student should be able to:
(a)Determine whether a given sentence is statement and that statement is true or false.
(c) Construct true or false statements using given numbers and mathematical symbol.
(d) Construct statement using quantifier all and some.
(e) Determine whether a statement that contains the quantifier “all” is true or false.
(f) Construct a true statement using the quantifier “all” or “some” given an object and a property.
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A statement is a sentence that is either TRUE or FALSE but not both.
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Look at these Lemang! They are baked in bamboo. Lemang is made up of rice and water. Am I right, uncle?
No, it is made up of glutinous rice and coconut milk. Is it your favourite dish on Hari Raya?
Yes, I love to eat Lemang very much.
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STATEMENT NOT STATEMENTThey are baked in bamboo.
Look at these Lemang!
Lemang is made up of rice and water.
Is it your favourite dish on Hari Raya?
No, it is made up of glutinous rice and coconut milk.
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Yes, I love to eat Lemang very much.
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STATEMENTSTATEMENT
TRUETRUE FALSEFALSE
WORDS
WORDS + NUMBERS
NUMBERS + MATH SYMBOL
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Five is greater than three
5 is greater than 3
5 > 3
Statement can be written in 3 ways
Words
Numbers Words Numbers
Numbers Mathematical symbol Numbers
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Singapore is an island
6 is greater than 7
23 = 32
Malaysia is an island
The third significant figure of 1.079 is 7
15 > -15
True statement
True statement
True statement
False
statement
False statement
False statement
WordsNumbers & Words
Numbers & Symbols
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x + 3 = 5
x2 – y2 = 3BOTH ARE NOT STATEMENT!
Because it can either be true of false depending on the value of x
and y
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•Come here!
•How old are you?
•X + 2 = 5• y + 3x
COMMAND
QUESTION
EQUATIONS
NOT STATEMENT
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Construct statement using numbers and mathematical symbol
4 , 7, >True
7 > 4
15 ÷ 5 = 3
-5 x 2 < 1 x 8
True
True
False
False
False
4 > 7
15, 5, 3, ÷, = 5 ÷ 15 =
3
1, 8, -5, 2, x, <
1 x 8 < -5 x 2
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All animals have legs
All birds can fly
Quantifiers ‘ALL’ and ‘SOME’Specify quantity or number of objects
FALSE
TRUE
FALSE
All positive numbers are
greater than 0Some of us have been selected to join PLKN
TRUE
Some empty sets have elementsFALSE
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MORE QUANTIFIERSEach
ALL
Most
Many Every
None
A lot of
A few
Several
Any
Part of
SOME
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Any positive numbers are greater than 0
Any positive numbers are greater than 0
All positive numbers are
greater than 0
Some of us have been selected to join PLKN
USING MORE QUANTIFIERS
Only a few or several has been selected to join PLKN
Only a few or several has been selected to join PLKN
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OBJECT PROPERTY TRUE STATEMENT
Construct a true statement using the quantifier “all” or “some” given an object and a property
Trapezium
Diagonals of squares
Months
A pair of parallel sides
Bisect each other at 90o
Have 30 days
All trapeziums have a pair
of parallel sidesAll diagonals of Squares bisect each other at 90o
Some monthshave 30 days
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A statement is a sentence that is either true or false but not both simultaneously.
Example:
8 x 2 = 16
4 – 2 = 3
4x + 5
Statement is true
Statement is false
Not a statement
STATEMENT
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Quantifiers are used to indicate the number of cases there are in a statement.
• “ALL” indicates each and every one
• “SOME” indicates at least one or several.
Example:
1) All octagons have 8 sides.
2) Some triangles have equal sides.
QUANTIFIERS [“ALL” or “some”]
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