MTH 314a MTH 315a MTH 315b. Algebra. Tidying up terms. Number Machine. Working with Expressions. Solving Simple Equations. www.mathsrevision.com. Solving Harder Equations. Understanding Inequalities. Solving Simple Inequalities. MTH 314a MTH 315a MTH 315b. Starter Questions.
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MTH 315a
MTH 315b
Q1. Calculate
Q2. Convert 60% to fraction and simplify.
to a percentage.
Q3. Convert
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Q4. What is the time difference 09:28 and 10:50
Q5. The answer to the question is 90. What is the
question.
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MTH 315a
MTH 315b
Tidying Terms
a+2b+3a+b
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MTH 314a
MTH 315a
MTH 315b
+
+
=
First Row :
+
+
2c
c
4c
= 7c
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+
+
=
2nd Row :
+
+
2d
2d
3d
= 7d
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MTH 314a
MTH 315a
MTH 315b
+
+
=
3rd Row :
+
+
3f
f
2f
= 6f
CANNOT
TIDY UP
ANYMORE
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In Total we have
7c + 7d + 6f
WE CAN ONLY TIDY UP “LIKE TERMS”
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MTH 314a
MTH 315a
MTH 315b
WE CAN ONLY TIDY UP “LIKE TERMS”
Tidy up the following:
Q1. 2x + 4x + 5y 3y + 18 =
Q2. 4a + 3b + 5a + 6 – b =
6x + 2y + 18
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9a + 2b + 6
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MTH 314a
MTH 315a
MTH 315b
Your turn !
Page 46 Exercise 1
Q1 and Q2
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MTH 315a
MTH 315b
Q1. Tidy up the expression
Q2. Calculate
Q3. Round to 1 decimal place.
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(a) 2.34 (b) 10.25 (c) 3.23
Q4. 12.5 % as a fraction
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MTH 315a
MTH 315b
Number Machine
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7m
Number Machine
MTH 314a
MTH 315a
MTH 315b
To build an expression from the number machine
simply follow the rules given:
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MTH 314a
MTH 315a
MTH 315b
To build an expression from the number machine
simply follow the rules given:
20
23
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3b
3b+9
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MTH 314a
MTH 315a
MTH 315b
Your turn !
Page 93 Exercise 2
Q1
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UNDO
Number Machine
MTH 314a
MTH 315a
MTH 315b
To UNDO the number machine
simply do the opposite of the rules given:
+8
x2
18
36
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UNDO
Number Machine
MTH 314a
MTH 315a
MTH 315b
To UNDO the number machine
simply do the opposite of the rules given:
9
x4
5
20
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MTH 314a
MTH 315a
MTH 315b
Your turn !
Page 93 Exercise 2
Q3 and Q4
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MTH 314a
MTH 315a
MTH 315b
Learning Intention
Success Criteria
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MTH 314a
MTH 315a
MTH 315b
1
If a = 3 and b = 9 evaluate
a + b
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Sub in a=3
=
3
+
9
Sub in b=9
=
12
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MTH 314a
MTH 315a
MTH 315b
2
If a = 3 and b = 9 evaluate
ab
a x b
Remember ab means a x b
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Sub in a=3
=
3
x
9
Sub in b=9
=
27
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MTH 314a
MTH 315a
MTH 315b
3
If a = 3 and b = 9 evaluate
4b
4 x b
Remember 4b means 4 x b
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=
4
x
9
Sub in b=9
=
36
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MTH 314a
MTH 315a
MTH 315b
If a = 5 and b = 6 evaluate
1. a + b
=11
4. b  a
=1
2. ab
=30
5. 4b
=24
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3. 3a
=15
6. 3ab
=90
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MTH 314a
MTH 315a
MTH 315b
If a = 5 and b = 3 evaluate
4
2a + 4b
2xa + 4xb
=
Remember 2a means 2 x a
Sub in a=5
4x
3
=
2x
5
+
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Sub in b=3
=
10
12
+
=
22
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MTH 314a
MTH 315a
MTH 315b
5
If a = 5 and b = 3 evaluate
a
2
a x a
=
Remember a2 means a x a
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Sub in a=5
=
5
x
5
=
25
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b
Substitution
MTH 314a
MTH 315a
MTH 315b
6
If a = 15 and b = 3 evaluate
a
15
=
b
3
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Sub in a=15
=
5
Sub in b = 3
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a
Substitution
MTH 314a
MTH 315a
MTH 315b
If a = 2 and b = 6 evaluate
1) 4a + 3b
=26
4) 5b – 3a
=24
2) a2
=4
5) 4a2
=16
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3) b2
=36
=3
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MTH 314a
MTH 315a
MTH 315b
Your turn !
Page 94 Exercise 3
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MTH 314a
MTH 315a
MTH 315b
Level E Solving Equations
The rule we use to solve equations is
The rule “change side change sign”
Write down the opposite of the following :
+
+


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opposite is
opposite is
x
x
÷
÷
opposite is
opposite is
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Check to see if correct !
Equations
MTH 314a
MTH 315a
MTH 315b
Level E Solving Equations
The rule “change side change sign”
+8 opposite is 8
5 opposite is +5
Examples
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Check to see if correct !
Equations
MTH 314a
MTH 315a
MTH 315b
Level E Solving Equations
The rule “change side change sign”
times by 8 opposite is divide by 8
times by 3 opposite is divide by 3
Examples
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MTH 314a
MTH 315a
MTH 315b
Level E Solving Equations
Now try Exercise 4
Ch8 (page 96)
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MTH 315a
MTH 315b
Level E Harder Equations
Learning Intention
Success Criteria
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Created by Mr.Lafferty Maths Dept
MTH 314a
MTH 315a
MTH 315b
Level E Harder Equations
The rule we use to solve equations is
The rule “change side change sign”
Write down the opposite of the following :
+
+


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opposite is
opposite is
x
x
÷
÷
opposite is
opposite is
Created by Mr.Lafferty Maths Dept
Equations
MTH 314a
MTH 315a
MTH 315b
Level E Harder Equations
The rule “change side change sign”
+1
opposite is 1
Examples
times by 2
opposite is divide by 2
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Equations
MTH 314a
MTH 315a
MTH 315b
Level E Harder Equations
The rule “change side change sign”
6
opposite is +6
Examples
times by 4
opposite is divide by 4
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MTH 314a
MTH 315a
MTH 315b
Level E Harder Equations
Now try Exercise 5
Ch8 (page 97)
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MTH 315a
MTH 315b
Level E Solving Inequalities
Learning Intention
Success Criteria
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MTH 314a
MTH 315a
MTH 315b
Level E Solving Inequations
The equations you were solving were called
equations because they contained an “=“ sign.
There are 4 other Mathematical symbols
They are called inequalities :
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greater than or equal to
greater than
less than or equal to
less than
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MTH 314a
MTH 315a
MTH 315b
Arrow ALWAYS points to the smallest number
Level E Solving Inequalities
Examples : Write in words what each mean.
5 > 3
means 5 is greater than 3
7 < 6
means 7 is less than 6
means x can take the value
2 or greater
x ≥ 2
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y ≤ 5
means y can take the value
5 or less
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MTH 314a
MTH 315a
MTH 315b
Level E Solving Inequalities
Examples : Write out an inequality for the numbers
(a) 14 and 6
14 > 6
(b) 2 and 1
2 < 1
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(c) 3 and 7
3 > 7
(d) 34 and 35
34 > 35
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MTH 314a
MTH 315a
MTH 315b
Level E Solving Inequalities
Examples : Choosing from 3, 2, 1, 0 , 1, 2, 3
(a) y < 0
3, 2, 1
(b) y > 2
3
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(c) y ≤ 2
3, 2
(d) y > 3
No solution
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MTH 314a
MTH 315a
MTH 315b
Level E Solving Inequalities
Now try Exercise 6
Ch8 (page 99)
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MTH 315a
MTH 315b
Level E Inequalities
Learning Intention
Success Criteria
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MTH 314a
MTH 315a
MTH 315b
Level E Inequalities
The Good News
Same rule as solving equations
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The rule “change side change sign”
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Check to see if correct !
Inequalities
MTH 314a
MTH 315a
MTH 315b
Level E Solving Inequalities
The rule “change side change sign”
+10 opposite is 10
9 opposite is +9
Examples
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Check to see if correct !
Inequalities
MTH 314a
MTH 315a
MTH 315b
Level E Solving Inequalities
The rule “change side change sign”
times by 9 opposite is divide by 9
times by 7 opposite is divide by 7
Examples
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MTH 314a
MTH 315a
MTH 315b
Level E Inequalities
Now try Exercise 7
Ch8 (page 101)
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