solve the following quadratic equations using the …...taster day 2017 lesson notes.notebook 1 july...
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![Page 1: Solve the following quadratic equations using the …...TASTER DAY 2017 lesson notes.notebook 1 July 05, 2017 Jun 16 09:59 A level Maths Taster Session Introduction to A level Maths](https://reader033.vdocuments.net/reader033/viewer/2022042117/5e94bec4b15892729b05caae/html5/thumbnails/1.jpg)
TASTER DAY 2017 lesson notes.notebook
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July 05, 2017
Jun 1609:59
Alevel Maths Taster Session
Introduction to Alevel Maths
So good choice, but only if you really enjoy doing Maths, as you will be spending a lot of time on it!
Jun 1608:21
Solve the following quadratic equations using the methods given:Factorise Quadratic formula
(leave in surd form)
Complete the square
(find exact solutions)
![Page 2: Solve the following quadratic equations using the …...TASTER DAY 2017 lesson notes.notebook 1 July 05, 2017 Jun 16 09:59 A level Maths Taster Session Introduction to A level Maths](https://reader033.vdocuments.net/reader033/viewer/2022042117/5e94bec4b15892729b05caae/html5/thumbnails/2.jpg)
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July 05, 2017
Jun 1608:28
The quadratic formula proof:The formula is derived from the general quadratic equation, by completing the square.
Jun 1608:28
How Alevel maths works!4 lessons per week a mixture of:
• Pure Maths topics
• Statistics
• Mechanics
Examined by:
3 x 2 hour papers at the end of Y13
1. Pure Maths topics only
2. Pure Maths and Mechanics
3. Pure Maths and Statistics
![Page 3: Solve the following quadratic equations using the …...TASTER DAY 2017 lesson notes.notebook 1 July 05, 2017 Jun 16 09:59 A level Maths Taster Session Introduction to A level Maths](https://reader033.vdocuments.net/reader033/viewer/2022042117/5e94bec4b15892729b05caae/html5/thumbnails/3.jpg)
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July 05, 2017
Jun 2515:22
A: Proof
B: Algebra and functions
C: Coordinate geometry in the (x,y) plane
D: Sequences and series
E: Trigonometry
F: Exponentials and logarithms
G: Differentiation
H: Integration
I: Numerical methods
J: Vectors
K: Statistical sampling
L: Data presentation and interpretation
M: Probability
N: Statistical distributions
O: Statistical hypothesis testing
P: Quantities and units in mechanics
Q: Kinematics
R: Forces and Newton’s laws
S: Moments
Jun 1608:29
A new topic LogarithmsInvestigate with your log button:
log10
log100
log1000
log1
log0.1
What theories do you have can you make any predictions?
![Page 4: Solve the following quadratic equations using the …...TASTER DAY 2017 lesson notes.notebook 1 July 05, 2017 Jun 16 09:59 A level Maths Taster Session Introduction to A level Maths](https://reader033.vdocuments.net/reader033/viewer/2022042117/5e94bec4b15892729b05caae/html5/thumbnails/4.jpg)
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July 05, 2017
Jun 1609:19
What about...?log5
log50
log500
log4
log3
log2
What do you notice?
Jun 1609:21
The notation 'log' is dedicated to base 10 logarithms and can also be written as log10
log1010 = 1
log10100 = 2
log101000 = 3
log100.1 = 1
because...
![Page 5: Solve the following quadratic equations using the …...TASTER DAY 2017 lesson notes.notebook 1 July 05, 2017 Jun 16 09:59 A level Maths Taster Session Introduction to A level Maths](https://reader033.vdocuments.net/reader033/viewer/2022042117/5e94bec4b15892729b05caae/html5/thumbnails/5.jpg)
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July 05, 2017
Jun 1610:02
So, the logarithm (to base 10) of any number, is the power of ten needed to obtain that number.
This can be extended to other bases to give a general rule:
If
thenlogaN = x
N = ax
'log to base a of N = x'
Here, a is still called the base
So x is the power of a needed in order to get N
Jun 1610:13
So, to evaluate different logs, we can use this process:
1) log24 2) log381
![Page 6: Solve the following quadratic equations using the …...TASTER DAY 2017 lesson notes.notebook 1 July 05, 2017 Jun 16 09:59 A level Maths Taster Session Introduction to A level Maths](https://reader033.vdocuments.net/reader033/viewer/2022042117/5e94bec4b15892729b05caae/html5/thumbnails/6.jpg)
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July 05, 2017
Jun 1610:14
We can find x as the base:
logx125 = 3
Jun 1610:15
Try these:
Write in the form y = ax
logmc = d logbp = q log s = t
Evaluate:log264 log464 log55 log21
![Page 7: Solve the following quadratic equations using the …...TASTER DAY 2017 lesson notes.notebook 1 July 05, 2017 Jun 16 09:59 A level Maths Taster Session Introduction to A level Maths](https://reader033.vdocuments.net/reader033/viewer/2022042117/5e94bec4b15892729b05caae/html5/thumbnails/7.jpg)
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July 05, 2017
Jun 1610:22
Solve:
logx8 = 3 logx16 = 0.5
Jun 1610:01
So logarithms are powers...Just like the rules for powers/indices, there are a set of rules for logs, that allow us to manipulate expressions algebraically.
We have
logaa = 1 loga1 = 0Also (remember the base 10 logs)
1
2
3
![Page 8: Solve the following quadratic equations using the …...TASTER DAY 2017 lesson notes.notebook 1 July 05, 2017 Jun 16 09:59 A level Maths Taster Session Introduction to A level Maths](https://reader033.vdocuments.net/reader033/viewer/2022042117/5e94bec4b15892729b05caae/html5/thumbnails/8.jpg)
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July 05, 2017
Jun 1610:29
These rules allow us to combine, simplify and solve where necessary.
Eg: We know that log5 = 0.699 (3 sf)
So log50 =
Jun 1610:41
Express as a single logarithm
7loga2 3loga12 + 5loga3
1
2
3
![Page 9: Solve the following quadratic equations using the …...TASTER DAY 2017 lesson notes.notebook 1 July 05, 2017 Jun 16 09:59 A level Maths Taster Session Introduction to A level Maths](https://reader033.vdocuments.net/reader033/viewer/2022042117/5e94bec4b15892729b05caae/html5/thumbnails/9.jpg)
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July 05, 2017
Jun 1610:43
Try these:
2loga5 loga15 - loga3 loga4 + loga3
2loga5 + loga4 - loga10
1
2
3
Jun 1611:05
2loga5 + loga4 - loga10
![Page 10: Solve the following quadratic equations using the …...TASTER DAY 2017 lesson notes.notebook 1 July 05, 2017 Jun 16 09:59 A level Maths Taster Session Introduction to A level Maths](https://reader033.vdocuments.net/reader033/viewer/2022042117/5e94bec4b15892729b05caae/html5/thumbnails/10.jpg)
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July 05, 2017
Jun 1610:47
And finally - try using the rules in reverse.
Express each of these in terms of log a, log b, log c
log(abc) log(a2bc) log(a√b)
Jun 2515:47
Getting ready for September:
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Jun 2516:20
Jun 2516:21
![Page 12: Solve the following quadratic equations using the …...TASTER DAY 2017 lesson notes.notebook 1 July 05, 2017 Jun 16 09:59 A level Maths Taster Session Introduction to A level Maths](https://reader033.vdocuments.net/reader033/viewer/2022042117/5e94bec4b15892729b05caae/html5/thumbnails/12.jpg)
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Jun 2516:22
Good luck and welcome to A‐level maths!