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H2 Math Summary Notes
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Pure Mathematics
Unit 1 Inequalities1 Question -
Unit 2 Graphing Techniques7 Questions
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Unit 3 Transformation of Graphs2 Questions
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Unit 4 Functions6 Questions
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Unit 5 APGP & Recurrence Relations6 Questions
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Unit 6 Sigma Notation6 Questions
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Unit 7 Techniques of Differentiation2 Questions
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Unit 8 Applications of Differentiation9 Questions
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Unit 9 Maclaurin Series2 Questions
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Unit 10 Techniques of Integration6 Questions
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Unit 11 Applications of Integration4 Questions
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Unit 12 Differential Equations2 Questions
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Unit 13 Vectors11 Questions
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Unit 14 Complex Numbers6 Questions
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StatisticsUnit 15 Permutation and Combinations7 Questions
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Unit 16 Probability5 Questions
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Unit 17 Discrete Random Variable4 Questions
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Unit 18 Binomial Distribution5 Questions
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Unit 19 Normal Distribution7 Questions
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Unit 20 Sampling and Estimation8 Questions
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Unit 21 Hypothesis Testing6 Questions
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Unit 22 Correlation and Linear Regression5 Questions
Lesson 5,
Question 6
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Worked Example 5
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A sequence of negative numbers is defined by \({{x}_{n+1}}=-\sqrt{8+3{{x}_{n}}}\) for \(n=1\), \(2\), \(3\), …
(i)
Show that \(-\frac{8}{3}<{{x}_{n}}<0\) for \(n=1\), \(2\), \(3\), …
(ii)
Find the exact value of \(l\), given that when \(n\to \infty \), \({{x}_{n}}\to l\).
(iii)
Show that \({{x}_{n+1}}^{2}-{{l}^{2}}=3\left( {{x}_{n}}-l \right)\).
(iv)
Show algebraically that if \({{x}_{n}}<l\) for some value of \(n\), then \({{x}_{n+1}}>l\).
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