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

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: $0.647;~ 0.349;~k=2.56$
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: $0.632;~ 1.04 \times 10^{-4};~ 0.472;~ 0.421;~ 0.9408$
Question 10: $0.345;~ 0.612;~ \mu = 12.3, \sigma = 0.475;~ k \approx 55.7$

### Relevant materials

MF26

• Jia

Hi. Can you upload question 5 and 9iv/vii. These are the questions that differ from the other paper. Thankyou.

• i dont have that paper. can send me at +65 9815 6827. I’ll do it.

• Jia

Hello. I’ve sent you the papers. Please check 🙂

• thank you

• Kay

Hi! Do you still need the paper?

• rainbow

for 5 i got 0.647, 0.350 and some decimal for the k.
for 9iv i got 0.472 i think x>=19.5 by c.c
for 9vi is conditional prob and i said something about the margin of error being less than the probability of fault 0.08.

• Haizz

Hi, wondering for the hypothesis testing question, is the left tail test accepted? Because in the real world context, the most important thing is u<32? Because if they overstated their claim, they can get sued but if they understated it then it doesnt matter? Well thats my logic but i regretted overthinking and changing my answer during the exam

• rainbow

doubt it. It’s not about the company being sued, it’s about testing if the claim holds true. And since it’s two-tailed the critical region changes also.

• Jan

Will there be ‘error carry forward’ marks?? For eg if part (iii) needs (ii) answers, but my answer for part (ii) was wrong??

• Andrew

Sorry is there any error for 9iii? When i key into GC i get approx 0.47154

• yes, i made a mistake. sorry! Thank you 🙂

• rainbow

dont think the 9iv is correct? from gc value gives 0.472

• yes, my bad. so sorry. typed wrongly. Thank you 🙂

• Jay

Hi, is it okay for you to show the working for 4bi) using the substitution u= a-y^2? Thanks so much for your help! 🙂

• Definitely. So Long as answer is correct 🙂

• Depressed

I’m so sorry. This may seem very pessimistic but I would just like to know, what do u think are the cutoffs for grades C and D? It would be really helpful.