Integers
S33
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Ordering integers
Add / Sub Mathematically
Letters and Numbers
Multiplying Integers
Dividing Integers
2-Dec-11 Created by Mr. Lafferty Maths Dept
Starter Questions
S33
Q1. Explain why 30% of £270 = £81
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Q2. How many Euros do I get for £20 if
exchange rate is £1 1.5 €
Q3. The answer to the question is 90. What is the
question.
2-Dec-11 Created by Mr. Lafferty Maths Dept
Integers
S33
Learning Intention Success Criteria
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1. To understand how to add 1. To be put integers in
positive and negative
numbers using the order of size.
thermometer as an aid.
2-Dec-11 Created by Mr. Lafferty Maths Dept
Integers
Temperature Sea Level
S33
Definition : An INTEGER is a negative or positive
whole number, including 0.
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e.g. -2, -1, 0, 5, 100
Note : -2.5, -1.2, 23.5 Are NOT INTEGERS
Write down 3 places where negative numbers are used
Coordinate Profit and
Grid Loss
2-Dec-11 Created by Mr. Lafferty Maths Dept
12
S33
Integers 10
11
9
8
7
Integers can be represented 6
on a thermometer or number line. 5
4
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The further to the top a number is 3
the bigger it is. 2 Positive +
Greater 1
than 0
-1
12 > 4 -2
-3
-4 Negaive -
-5
Less -2 > -3 -6
than -7
-8
-9
-4 < -1 -10
-11
-3.5 < -2.8 -12
2-Dec-11 Created by Mr. Lafferty Maths Dept
S33
Integers
Coordinate Grid
y - axis Plot the point
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(3,2)
3
2 x-coordinate is 3
1 y-coordinate is 2
origin
-4 -3 -2 -1 0 1 2 3 4 x - axis
-1
(-2,2)
-2
-3 (-4,-2)
Plot the point that makes
1 2 3 4 5 shape a parallelogram.
2-Dec-11 Created by Mr. Lafferty Maths Dept
S33
Integers
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Now try Exercise 2.1
Ch2 (page 23)
2-Dec-11 Created by Mr. Lafferty Maths Dept.
Starter Questions
S33
Q1. Is 7 + 6x2 = 26 or 19
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Q2. How many euros do I get for £10 if
exchange rate is £1 1.4 €
Q3. The answer to the question is 30. What is the
question.
2-Dec-11 Created by Mr. Lafferty Maths Dept
S33
Negative Numbers
Addition & Subtraction
Learning Intention Success Criteria
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1. To explain how to write 1. To be able to write down
down mathematically mathematically the
addition and subtraction addition and subtraction
of negative integers. of both positive and
negative integers.
2-Dec-11 Created by Mr. Lafferty Maths Dept
Negative 12
11
Numbers 10
9
S33
8 “+ -” side by
6
7 side replace
(a) 12 + 4 = 16 5 by single “-”
4
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3
2
Start Go up 1
at 12 4 0
-1
(b) 10 + ( - 8) = -2
-3
-4
10 - 8 = 2 -5
-6
-7 “- -” side by
-8
(c) -7 – (- 10) = -9 side replace
-10
-7 + 10 = 3 -11 by single “+”
-12
2-Dec-11 Created by Mr. Lafferty Maths Dept
Negative Numbers
S33
Examples
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(1) 3-7 = -4
Remember
(2) 4 + (-9) = -5
(3) -7 – (- 8) =1 “+ -” = -
(4) -2 + (-12) = -14 “- -” = +
(5) -5 – (-25) = 20
(6) 8 + (-9) = -1
2-Dec-11 Created by Mr. Lafferty Maths Dept
S33
Integers
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Now try Ex 3.1 to
4.2
Ch2 (page 26)
2-Dec-11 Created by Mr. Lafferty Maths Dept.
Starter Questions
S33
1. 21% of £300
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2. True or false :
(a) -1 - (-1) = 2 (b) - 3 - (5 - (-4)) = - 6
(c) - 6 + 10 - ( - 3) = 7
3. Does 3.5 10-2 = 0.35
2-Dec-11 Created by Mr. Lafferty Maths Dept
Substitution
S33
Learning Intention Success Criteria
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1. To explain the process of 1. Understand process of
working out expressions by substitution.
substitution method.
2. Solving expressions
showing working.
2-Dec-11 Created by Mr.Lafferty Maths Dept
Substitution
S33
1 If a = 2 and b = 14 evaluate
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a+b
Sub in a=2
= 2 + 14 Sub in b=14
= 16
2-Dec-11 Created by Mr.Lafferty Maths Dept
Substitution
S33
2 If a = 3 and b = -9 evaluate
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a-b
= 3 - (-9) Remember “- -” replace by “+”
= 3 + 9
= 12
2-Dec-11 Created by Mr.Lafferty Maths Dept
Substitution
S33
3 If a = 3 and b = 9 evaluate
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b2 – a2
9x9 – 3x3 Remember b2 means b x b
= 81 - 9
= 72
2-Dec-11 Created by Mr.Lafferty Maths Dept
Substitution
S33
If a = 5 and b = 6 evaluate
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1. a + b =11 4. b - a =1
2. ab =30 5. 4b =24
3. 3a =15 6. 3ab =90
2-Dec-11 Created by Mr.Lafferty Maths Dept
Substitution
S33
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Now try Exercise 5.1
Ch2 (page 28)
Q1 – Q4
2-Dec-11 Created by Mr. Lafferty Maths Dept
Tidying Up Like Terms
S33
Learning Intention Success Criteria
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1. To explain the process of 1. Understand the term like
tidying up expressions. terms.
2. Be able to tidy up like
terms.
2-Dec-11 Created by Mr.Lafferty Maths Dept
Tidying Terms
S33
WE CAN ONLY TIDY UP “LIKE TERMS”
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1, 3 , 5, -6, 8 are like terms simple numbers
x, 3x , -2x are like terms in x
x2, 3x2, -2x2 are like terms in x2
x is NOT the same as x2
2-Dec-11 Created by Mr.Lafferty Maths Dept
Tidying Terms
S33
Examples
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3a2 – 2a2 = a2
3x – 4y – x – 2y = 2x – 6y
4x2 – x – y + 6x2 = 10x2 – x - y
6p2 – q – 3q + 6p2 = 12p2 – 4q
2-Dec-11 Created by Mr.Lafferty Maths Dept
Starter Questions
S33
1. Share 36 in the ratio 3 : 9
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1 1
2. Calculate of
2 2
1 3 1
3. Does 1 Explain ?
2 4 4
4. Explain how we solve - 3x + 9 27
2-Dec-11 Created by Mr. Lafferty Maths Dept.
S33
Integers
Multiplication
Learning Intention Success Criteria
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1. Understand how to
1. Explain how to multiply
multiply positive and
positive and negative
negative integers.
integers.
2-Dec-11 Created by Mr. Lafferty Maths Dept.
S33
Integers
Multiplication
Multiplying Integers Rules
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1 x (-2) = -2 (-2) x (-1) = 2 Multiplying Integers
(-4) x 5 = -20 (- 2) x (-5) = 10
+ve x -ve = -ve
-ve x +ve = -ve
(-3) x 3 = -9 (-5) x (-5) = 25
5 x (-8) = -40 (-4) x (-8) = 32 -ve x -ve = +ve
+ve x +ve = +ve
2-Dec-11 Created by Mr. Lafferty Maths Dept.
Remember
S33
BODMAS Integers
Multiplication
Multiplying Integers Rules
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1 + (-2) x (-10) = 21 Multiplying Integers
3+ (-5)2 = 28
+ve x -ve = -ve
-ve x +ve = -ve
8 – (-3)2 = -1
5 x (-2)2 + 5 - 19= 6 -ve x -ve = +ve
+ve x +ve = +ve
2-Dec-11 Created by Mr. Lafferty Maths Dept.
Integers
S33
Multiplication
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Now try MIA Ex 6.1
Ch2 (page 31)
2-Dec-11 Created by Mr. Lafferty Maths Dept.
Starter Questions
S33
1. Share 63 in the ratio 2 : 5
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2. Decide which are true or false
(a) a a = 2a (b) 3b 5f = 8bf
(c) 2w w = 2w2 (d) 2xy × 4y = 8 xy
1 3 16
3. Does Explain ?
3 7 21
4. Write in scientific notation and to 2 sig. fig.
(a) 0.03465 (b) 4960000
2-Dec-11 Created by Mr. Lafferty Maths Dept.
S33
Integers
Division
Learning Intention Success Criteria
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1. Understand how to divide
1. Explain how to divide
positive and negative
positive and negative
integers.
integers.
2-Dec-11 Created by Mr. Lafferty Maths Dept.
S33
Integers
Division
Dividing Integers Rules
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8 ÷ (-4) = -2 (-22) ÷ (-2) =11 Multiplying Integers
(-24) ÷ 6 =-4 (- 56) ÷ (-7) = 8
+ve ÷ -ve = -ve
-ve ÷ +ve = -ve
(-3) ÷ 3 = -1 (-15) ÷ (-5) = 3
16 ÷ (-2) = -8 (-4) ÷ (-8) = 0.5 -ve ÷ -ve = +ve
+ve ÷ +ve = +ve
2-Dec-11 Created by Mr. Lafferty Maths Dept.
Remember
S33
BODMAS Integers
Division
Division Integers Rules
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1 + (-20) ÷ (-10) = 3 Multiplying Integers
100 ÷ (-5)2 = 4
+ve ÷ -ve = -ve
-ve ÷ +ve = -ve
100 - 36 ÷ (-3)2 = 96
-48 ÷ (6 - 2)2 + 5 = 2 -ve ÷ -ve = +ve
+ve ÷ +ve = +ve
2-Dec-11 Created by Mr. Lafferty Maths Dept.
Integers
S33
Division
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Now try MIA Ex 8.1
Ch2 (page 31)
2-Dec-11 Created by Mr. Lafferty Maths Dept.