H2 Math Summary Notes

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Pure Mathematics
Unit 1 Inequalities
Basics of Test Point Method
Unit 2 Graphing Techniques
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Worked Example 7
Unit 3 Transformation of Graphs
Worked Example 1 (i)
Worked Example 1 (ii)
Unit 4 Functions
Conceptual Video
How to Use GC to Plot an Inverse Graph
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Worked Example 4
Unit 5 APGP & Recurrence Relations
Conceptual Video
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Unit 6 Sigma Notation
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Unit 7 Techniques of Differentiation
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Unit 8 Applications of Differentiation
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Unit 9 Maclaurin Series
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Unit 10 Techniques of Integration
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Unit 11 Applications of Integration
Conceptual Video
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Unit 12 Differential Equations
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Unit 13 Vectors
Conceptual Video
Unit 13.1 Worked Example 1
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Unit 13.1 Worked Example 3
Unit 13.1 Worked Example 4
Unit 13.1 Worked Example 5
Unit 13.2 Worked Example 1
Unit 13.2 Worked Example 2
Unit 13.2 Worked Example 3
Unit 13.2 Worked Example 4
Unit 13.2 Worked Example 5
Unit 14 Complex Numbers
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Statistics
Unit 15 Permutation and Combinations
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Unit 16 Probability
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Unit 17 Discrete Random Variable
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Unit 18 Binomial Distribution
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Unit 19 Normal Distribution
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Unit 20 Sampling and Estimation
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Unit 21 Hypothesis Testing
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Unit 22 Correlation and Linear Regression
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Worked Example 4

H2 Math Summary Notes Unit 5 APGP & Recurrence Relations Worked Example 4

For each of the following recurrence relations, explain how to obtain the next term in the sequence based on the given formula, describe the relationship represented by the recurrence relation, and calculate and write down the first [latex]5[/latex] terms of the sequence starting from the initial value provided.

(i)

[latex]{{x}_{n+1}}=\sqrt{{{x}_{n}}+5}[/latex], [latex]{{x}_{0}}=1[/latex].

(ii)

[latex]{{u}_{n+1}}=0.5{{u}_{n}}+8[/latex], [latex]{{u}_{1}}=4[/latex].

(iii)

[latex]{{a}_{n}}={{a}_{n-1}}+k[/latex], [latex]{{a}_{0}}=3[/latex].

(iv)

[latex]{{u}_{n}}=-2{{u}_{n-1}}[/latex], [latex]{{u}_{0}}=3[/latex].

(v)

[latex]{{T}_{n}}={{T}_{n-1}}+{{T}_{n-2}}[/latex], [latex]{{T}_{1}}=0[/latex], [latex]{{T}_{2}}=1[/latex].

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