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
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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
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Unit 12 Differential Equations
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Unit 13 Vectors
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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 2

H2 Math Summary Notes Unit 2 Graphing Techniques Worked Example 2

The curve [latex]C[/latex] has equation [latex]\frac{{{\left( x-2 \right)}^{2}}}{2}+{{\left( y-3 \right)}^{2}}=1[/latex] .

(i)

Sketch [latex]C[/latex],

[3]

(i)

Hence state the range of positive values of [latex]k[/latex] such that [latex]{{\left( x-2 \right)}^{2}}+{{\left( y+3 \right)}^{2}}={{k}^{2}}[/latex] intersects [latex]C[/latex] at twice.

[2]

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