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 4

H2 Math Summary Notes Unit 4 Functions Worked Example 4

It is given that [latex]\text{f}\left( x \right)=\left\{ \begin{matrix}4-2x\text{   for   }0<x\le 2,  \\-{{(x-4)}^{2}}+4\text{    for   }2<x\le 4,  \\\end{matrix} \right.[/latex]

and [latex]\text{f}\left( x \right)=\text{f}\left( x +4 \right)[/latex] for all real values of [latex]x[/latex].

(i)

Evaluate [latex]\text{f}\left( 17 \right)+\text{f}\left( -8 \right)[/latex].

(ii)

Sketch the graph of [latex]y=\text{f}\left( x \right)[/latex] for [latex]-10\le x\le 7[/latex].

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