2016 A-level H2 Mathematics (9740) Paper 2 Suggested Solutions

2016 A-level H2 Mathematics (9740) Paper 2 Suggested Solutions

JC Mathematics

All solutions here are SUGGESTED. KS will hold no liability for any errors. Comments are entirely personal opinions.

Numerical Answers (click the questions for workings/explanation)

Question 1: 0.0251 \text{~m/min}
Question 2: \frac{x^2}{2} \text{sin}nx + \frac{2x}{n^2} \text{cos}nx - \frac{2}{n^3} \text{sin}nx + C;~ a = 2 \text{~or~} 6;~ \pi (\frac{2}{5} - \text{ln} \frac{3}{\sqrt{5}})
Question 3: a + \frac{3}{4} - \text{sin}a - \text{cos}a + \frac{1}{4} \text{cos}2a;~ \frac{1}{4}(\pi + 1)^2
Question 4: z = 2.63 + 1.93i, ~ 3.37 + 0.0715i ;~8^{\frac{1}{6}}e^{i(-\frac{\pi}{12})}, ~8^{\frac{1}{6}}e^{i(-\frac{3 \pi}{4})}, ~8^{\frac{1}{6}}e^{i(\frac{7\pi}{12})};~ n=7
Question 5: \frac{11}{42};~ \frac{4}{11};~ \frac{4}{1029}
Question 6: 60;~ 10;~ \{ \bar{x} \in \mathbb{R}, 0 \textless \bar{x} \le 34.8 \};~ \{ \alpha \in \mathbb{R}, 0 \textless \alpha \le 8.68 \}
Question 7: 24;~ 576;~ \frac{1}{12};~ \frac{5}{12}
Question 8: r = -0.980;~ c = -17.5;~ d = 91.8;~ y = 85.9
Question 9: a = 7.41;~ p = 0.599 \text{~or~} 0.166;~ 0.792
Question 10: 0.442;~ 0.151 ;~ 0.800;~ \lambda = 1.85

 

Relevant materials

MF15

KS Comments

2015 A-level H2 Mathematics (9740) Paper 2 Question 11 Suggested Solutions

JC Mathematics

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
Number of ways = \frac{8!}{2!2!} = 10080 ways

(ii)
Number of ways = 10080 -1 = 10079 ways

(iii)
Number of ways = 6! = 720 ways

(iv)
Case 1: 2 A’s together and B’s separated
5! \times ^6 C_2 = 1800
Case 2: 2 B’s together and A’s separated
5! \times ^6 C_2 = 1800
Case 3: 2 A’s together and 2 B’s together
720

Number of ways =10080 – 1800 – 1800 – 720 = 5760 ways

2015 A-level H2 Mathematics (9740) Paper 2 Question 8 Suggested Solutions

JC Mathematics

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

Let X denote the mass of pineapple tarts and \mu denote the population mean mass of pineapple tarts.

H_0: \mu = 0.9

H_1: \mu ~ \textless ~ 0.9

Unbiased estimate of population mean = 0.8825

s^2 = 0.0747854073^2 \approx 0.00559 (3 SF)

Under H_0, \bar{X} \sim \mathrm{N} (\mu, \frac{s^2}{n})

Test Statistic, T = \frac{\bar{X}- \mu}{\frac{s}{\sqrt{n}}} \sim t(7) at 10% level of significance.

Using GC, p-value = 0.264619 > 0.1

\Rightarrow, do not reject H_0

There is insufficient evidence at 10% significance level to reject the stall owner’s claim.

2015 A-level H2 Mathematics (9740) Paper 2 Question 6 Suggested Solutions

JC Mathematics

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
Let X denote the number of red sweets in a small packet of 10 sweets.

X \sim \mathrm{Bin} (10, 0.25)

\mathrm{P}(X \ge 4) = 1 - \mathrm{P}(X \le 3) \approx 0.224 (3 SF)

(ii)
Let Y denote the number of red sweets in a large packet of 100 sweets.

Y \sim \mathrm{Bin} (100, 0.25)

Since n is large, np = 25 > 5, n(1-p) = 75 > 5

Y \sim \mathrm{N}(25, 18.75) approximately

\mathrm{P}( Y \ge 30) = \mathrm{P}(X > 29.5) by continuity correction
\approx 0.149 (3 SF)

(iii)
Let W denote the number of packets out of 15 packets that contain at least 30 red sweets.

Y \sim \mathrm{Bin}(15, 0.1493487984)

\mathrm{P}( W \le 3) \approx 0.825 (3 SF)

2015 A-level H2 Mathematics (9740) Paper 2 Question 5 Suggested Solutions

JC Mathematics

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
Manager is unable to obtain an appropriate sampling frame.

(ii)
Manager can consider taking equal number of respondents from adults and aged first. Then, he can stand outside the supermarket, interview whoever walks in, based on his personal preferences until he obtains the number of respondents he require.

(iii)
As he samples based on his own preferences, there might be selection bias.