Transcript GCSE Mathematics - STEM CPD Module

Lecture: Introductory maths
Arithmetic and Algebra
Dr Sathish Nammi & Terence James Haydock
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Module Leaning Outcome
To achieve this unit a learner must:
1.
Determine the fundamental algebraic laws and apply
algebraic manipulation techniques to the solution of
problems involving algebraic functions, formulae and
graphs
Algebraic
Graphs
Formulae
Function
2. Use this very basic math topic to solve simple problems of a
real-life engineering testing application
Application
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Session Learning objectives
• After this session you should be able to:
 Compute numeric expressions using BIDMAS
 Evaluate numeric expressions in standard and
engineering form
 Solve simple linear equations inc those involving
fractions
 Transpose simple formulae
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Recommended Reading
Algebra Workbook for Dummies
Mary Jane Sterling
Have a look
Foundation Mathematics
KE Stroud & DJ Booth
Have a look
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Recap: Arithmetic operations
KEY: Provide spaces either
side of + , – and = e.g. 4 + 1 =
5, however do nor provide
spaces for x and / (4x4 = 16 or
6/2 = 3)
• Addition (+)
5+6=
Answer
• Multiplication (x)
3x4=
• Subtraction (-)
7–5=
Answer
• Commutative
4+5=
5
• Division (÷ or / )
16/4 =
Answer
Answer
• Associative
• Distributive
A
3 + (4 + 5) =
A
3(4 + 5) =
A
a+b=
A
a + (b + c) =
A
(a + b)/c =
A
ab =
A
a(bc) =
A
a(b + c) =
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A
Recap:
Remove the brackets
• 4(5a - b) - 2(3a - b - c)
=
• 5(2a - 5c) =
A
A
A
A
A
A
A
A
A
=
• 3(a + b) =
A
A
• 6 (-3a + 2b - 5c)
=
6
A
A
A
• 4(2a - 3b) - 5(a - 6b)
=
A
A
A
A
A
=
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A
A
A
Introduction
Formulae are used in many Science, Technology,
Engineering and Maths (STEM) problems to relate
certain quantities.
F  Force
m  mass
a  acceleration
Often it becomes necessary to
transpose a formulae in order to make
other variables as the subject of that
formulae
F  ma
F
a
m
F
m
a
Subject
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Try this: make F the subject
Example 1
C
F  32

100
180
Multiply both sides by 180 to
allow for cancellation
C
F  32
180 
180
100
180
9C
 F  32
5
9C
 32  F
5
9C
F
 32
5
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Simplify both sides
Add 32 to both sides to allow for
cancellation
Re-write new subject on the left
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Try this: make x the subject
Example 2
4x 12  4
4x 12 12  4
A

A

A
9
4

Add 12 to both sides
A
A
A
4
Cancel out the -12 and +12 on
The left hand side
Divide both sides by 4
Your answer is
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Expand brackets; value of x=?
Example 3
3( x  1)  2  8
Expand brackets (slide 6)
Simplify
A
Add +1 on both sides to
allow for cancellation
A
A
Divide both sides by 3
3x 9

3
3
A
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Try this: make y the subject
Example 4
4 x  12  9 y  18
Add 18 to both sides
Cancel – 18 and +18 and
also calculate for -12 +18
A
A
Divide both sides by 9
to allow for cancelation
4x  6
y
9
4x  6
y
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Re-write new subject on
the left
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F  Force
m  mass
Example 5
F = ma
a  acceleration
a=
m=
Subject
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Please use F, m and a as your
inputs (with spaces in between)
Transpose for F
Answer
Transpose for m
Answer
Transpose for a
Answer
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 Stress
 Strain
Example 6
E  Young ' s Modulus
E=
a=
m=
Subject
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Please use Stress, Strain and
Young’sModulus as your inputs
(with or without spaces in
between)
Transpose for E
Answer
Transpose for σ
Answer
Transpose for ε
Answer
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Summary
• An equation is an assertion and it may not always be true. whereas,
formulae is always true.
• Equations may not be applicable to many situations or problems.
• Formulae is a method to achieve result.
• Procedures involving changing the subject of an equations is same
as that used for formulae.
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End Lecture