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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Unit 3 Transformation of Graphs
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Unit 4 Functions
Conceptual Video
How to Use GC to Plot an Inverse Graph
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Unit 5 APGP & Recurrence Relations
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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
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Unit 13.2 Worked Example 1
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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 5

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

A sequence of negative numbers is defined by [latex]{{x}_{n+1}}=-\sqrt{8+3{{x}_{n}}}[/latex] for [latex]n=1[/latex], [latex]2[/latex], [latex]3[/latex], …

(i)

Show that [latex]-\frac{8}{3}<{{x}_{n}}<0[/latex] for [latex]n=1[/latex], [latex]2[/latex], [latex]3[/latex], …

(ii)

Find the exact value of [latex]l[/latex], given that when [latex]n\to \infty [/latex], [latex]{{x}_{n}}\to l[/latex].

(iii)

Show that [latex]{{x}_{n+1}}^{2}-{{l}^{2}}=3\left( {{x}_{n}}-l \right)[/latex].

(iv)

Show algebraically that if [latex]{{x}_{n}}<l[/latex] for some value of [latex]n[/latex], then [latex]{{x}_{n+1}}>l[/latex].

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