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

As these workings and answers are rushed out asap, please pardon me for my mistakes and let me know if there is any typo. Many thanks.

I’ll try my best to attend to the questions as there is H2 Math Paper 2 coming up.

Question 1

(i)

(ii)

Question 2

(rejected since ) or

Question 3

(i)

(ii)

Using GC, required answer (3SF)

(iii)

When

(3SF)

(iv)

Question 4

(i)

Let

When

When

Coordinates

(ii)

When . So is a minimum point.

When . So is a maximum point.

(iii)

x-intercept

(iv)

Using GC,

Question 5

(i)

Area of ABEDFCA

(ii)

Perimeter

When (rejected since )

When

Question 6

(i)

The store manager has to survey male students and female students in the college. He will do random sampling to obtain the required sample.

(ii)

Stratified sampling will give a more representative results of the students expenditure on music annually, compared to simple random sampling.

(iii)

Unbiased estimate of population mean,

Unbiased estimate of population variance,

Question 7

(i)

[Venn diagram to be inserted]

(ii)

(a)

(b)

(iii)

Question 8

(i)

Required Probability

(ii)

Find the probability that we get same color. then consider the complement.

Required Probability

(iii)

Question 9

(i)

Let X denote the number of batteries in a pack of 8 that has a life time of less than two years.

(a)

Required Probability

(b)

Required Probability

(ii)

Let Y denote the number of packs of batteries, out of 4 packs, that has at least half of the batteries having a lifetime of less than two years.

Required Probability

(iii)

Let W denote the number of batteries out of 80 that has a life time of less than two years.

Since n is large,

approximately

Required Probability

by continuity correction

Question 10

(i)

Let X be the top of speed of cheetahs.

Let be the population mean top speed of cheetahs.

Under

Test Statistic,

Using GC, is rejected.

…

(ii)

For to be not rejected,

(round down to satisfy the inequality)

Question 11

(i)

[Sketch to be inserted]

(ii)

Using GC, (3SF)

(iii)

Using GC,

(3SF)

(iv)

When (3SF)

Time taken minutes

Estimate is reliable since is within the given data range and is close to 1.

(v)

Using GC, (3SF)

(vi)

The answers in (ii) is more likely to represent since is close to 1. This shows a strong positive linear correlation between x and y.

Question 12

Let X, Y denotes the mass of the individual biscuits and its empty boxes respectively.

(i)

(ii)

(iii)

Let and