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This is answers for H2 Mathematics (9740). H2 Mathematics (9740), click here.

Numerical Answers (click the questions for workings/explanation)

Question 1: 2 \sqrt{15}; xy=6
Question 2: d = 1.5;~ r \approx 1.21 \text{~or~} r \approx -1.45;~n=42
Question 3: (\frac{1}{2}a, 0), (0,b);~ (a+1, 0,);~ (\frac{a+1}{2}, 0);~ (0, a), (b, 0);~ a = 1;~ gg(x) = x, x \in \mathbb{R}, x \neq 1  , ~ g^{-1}(x) = 1 - \frac{1}{1-x}, x \in \mathbb{R}, x \neq 1;~b= 2 \text{~or~}0
Question 4: 15.1875;~ \frac{\pi}{2a(a-1)};~ b = \frac{1}{2} + \frac{1}{2}\sqrt{1-a+a^2}
Question 5: \frac{5}{12}, \frac{5}{14}, \frac{5}{28}, \frac{1}{21};~ \mathbb{E}(T) = \frac{20}{7}, \text{Var}(T) = \frac{75}{98};~ 0.238
Question 6: 955514880;~ 1567641600;~ \frac{1001}{3876}
Question 7: 31.8075, 0.245;~ p = 0.0139; Do not reject h_0, Not necessary.
Question 8: Model (D); a \approx 4.18, b \approx 74.0;~ r \approx 0.981
Question 9: 0.632;~ 1.04 \times 10^{-4};~ 0.458;~ 0.421;~ 0.9408
Question 10: 0.345;~ 0.612;~ \mu = 12.3, \sigma = 0.475;~ k \approx 55.7

 

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