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TRANSCRIPT
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1.1 Functions and mappings
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Transformation of graphs
Example 1
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Example 2 Combined Transformations
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1.2 Composite functions
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1.3 Inverse functions
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The inverse trig functions
The inverse trig functions only exist when we restrict the domain of the original functions. So that they become 1:1 mappings
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1.4 The modulus function and inequalities
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Curve Sketching
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Laws of Logarithms
2.1 Definitions, equations & graphs
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Definitions & Graphs
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2.2 Modelling with exponential functions
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3.1 The Reciprocal Functions
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3.2 The Compound & Double Angle Formulae
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Double Angle Formula
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3.3 The forms r cos(x +/- y), r sin(x +/- y)
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4.1 The Chain Rule
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4.2 The Product Rules
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4.3 The Quotient Rules
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Inverse Functions
Exponentials & Logs
Further example
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Further example
5.1 Integration by substitution
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Integration by inspection
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Integration of Exponentials & Logarithms
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5.2 Volumes of revolution
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Change of Sign Methods
To find the root of a function f(x), if
f(a) > 0f(b) < 0
and the function is continuous, then there is a root between a and b.
We can narrow this down by successively halving the size of the interval, until we get an answer to the required accuracy.
Example
6.1 Numerical Methods
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We can continue this method indefinitely, to whatever accuracy we require
This method is useful for confirming the existence of a root between two given values. It can be unreliable however, sometimes failing to find a
root(s) when they are very close together, or ‘finding’ a root that doesn’t exist.
Iterative Methods
(there are many other re-arrangements you could have done)
Then start at any value (it will be given in the question; here we use x=0, and show 3 iterations)
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This method continues until it converges on the solution x = 0.276 (to 3 dp)
Iterative methods will often fail to find the root for given re-arrangements. If this is the case, you must try a different re-arrangement.
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In this example, yn = y8
1.1 Transformations 1 Question 1
6.2 Numerical Integration
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(5)Question 1 insert
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Question 2
Total / 10 �1.2 Composite Functions 1
Question 1
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Question 2
Total / 10 �1.3 Inverse Functions 1
Question 1
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Question 2
Total / 10 �
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1.4 Modulus function & inequalities 1
Question 1
Question 2
Total / 10 �2.1 Log Equations & Graphs 1
Question 1
Question 2
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Total / 10 �2.2 Modelling 1
Question 1
Question 2
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Total / 14 �3.1 The Reciprocal Functions 1
Question 1
Question 2
Total / 10 �
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3.2 Compound & Double-angle formulae 1
Question 1
Question 2
Total / 10 �
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3.3 The forms rcos(x+/-y), rsin(x+/-y) 1
Question 1
Question 2
Total / 12 �4.1 The Chain Rule 1
Question 1
Question 2
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Question 3
Total / 15 �4.2 The Product Rule 1
Question 1
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Question 2
Total / 10 �4.3 The Quotient Rule 1 Question 1
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(3)
Question 2
Total / 10 �5.1 Integration by Substitution 1
Question 1
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Question 2
Total / 11 �5.2 Volumes of revolution 1 Question 1
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Question 2
Total / 10 �6.1 Numerical Methods 1
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Question 1
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Question 2
Total / 10 �6.2 Numerical Integration 1 Question 1
Question 2
Total / 8 �
1.1 Transformations 1 Solutions Question 1
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(5)Question 1 insert
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Question 2
Total / 10 �1.2 Composite Functions 1 Solutions
Question 1
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Question 2
Total / 10 �
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1.3 Inverse Functions 1 Solutions Question 1
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Question 2
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Total / 10 �
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1.4 Modulus function & inequalities 1 Solutions
Question 1
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Question 2
Total / 10 �2.1 Log Equations & Graphs 1 Solutions Question 1
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Question 2
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Total / 10 �2.2 Modelling 1 Solutions Question 1
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Question 2
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Total / 14 �3.1 The Reciprocal Functions 1 Solutions Question 1
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Question 2
Total / 10 �3.2 Compound & Double-angle formulae 1 Sols Question 1
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Question 2
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Total / 10 �3.3 The forms rcos(x+/-y), rsin(x+/-y) 1 Solutions Question 1
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Question 2
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Total / 12 �
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4.1 The Chain Rule 1 Solutions Question 1
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Question 2
Question 3
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Total / 15 �
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4.2 The Product Rule 1 Solutions
Question 1
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Question 2
Total / 10 �4.3 The Quotient Rule 1 Solutions Question 1
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(3)
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Question 2
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Total / 10 �
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5.1 Integration by Substitution 1 Solutions
Question 1
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Question 2
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= 3.5 + 4ln2
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Total / 11 �5.2 Volumes of revolution 1 SolutionsQuestion 1
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Question 2
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Total / 10 �
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6.1 Numerical Methods 1 Solutions Question 1
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Question 2
Total / 10 �6.2 Numerical Integration 1 Solutions Question 1
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Question 2
Total / 8