H2 Math Summary Notes

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

H2 Math Summary Notes Unit 11 Applications of Integration Worked Example 3

Region [latex]A[/latex] is bounded by [latex]y=\sqrt{x}[/latex], [latex]y[/latex]-axis and [latex]y=2-{{x}^{2}}[/latex].

Region [latex]B[/latex] is bounded by [latex]y=\sqrt{x}[/latex], [latex]x[/latex]-axis and [latex]y=2-{{x}^{2}}[/latex].

Find

(i)

volume of [latex]A[/latex] rotated through [latex]2\pi [/latex] about [latex]y[/latex]-axis;

(ii)

volume of [latex]B[/latex] rotated through [latex]2\pi [/latex] about [latex]x[/latex]-axis;

(iii)

volume of [latex]B[/latex] about through [latex]2\pi [/latex][latex]y[/latex]-axis.

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