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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 5
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Worked Example 4
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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 \(5\) terms of the sequence starting from the initial value provided.
(i)
\({{x}_{n+1}}=\sqrt{{{x}_{n}}+5}\), \({{x}_{0}}=1\).
(ii)
\({{u}_{n+1}}=0.5{{u}_{n}}+8\), \({{u}_{1}}=4\).
(iii)
\({{a}_{n}}={{a}_{n-1}}+k\), \({{a}_{0}}=3\).
(iv)
\({{u}_{n}}=-2{{u}_{n-1}}\), \({{u}_{0}}=3\).
(v)
\({{T}_{n}}={{T}_{n-1}}+{{T}_{n-2}}\), \({{T}_{1}}=0\), \({{T}_{2}}=1\).
Responses