2023 A-level H1 Mathematics (8865) Paper 2 Suggested Solutions

(a)

(b)

(c)
mean
standard deviation

(a)
Case 1: 3 odd digits

Case 2: 2 even digit and 1 odd digit

Required probability

(b) We consider the complement where A and B do not have any number in common.
Required probability

(a)

(b)

(a)

(b) Using GC, Product moment correlation coefficient

(c) Using GC,

(d) When . The population is estimated to be 2.22 millions with area 36. This estimate is reliable since is within the data range of and the product moment correlation correlation is close to 1, which suggests a strong positive linear correlation.

(e) The scientist should not include this data as this data is an outlier.

(a)

(b)
Required probability

(c)
Required probability

(d)
Required probability

(e)

Required probability

(a)
Sample mean

Let be the distance of the ball thrown by children and be the population mean distance thrown.
Test vs at 5% level of significance.
Under , since is sufficiently large, by central limit theorem, approximately.
p-value
Since , we do not reject at 5% level of significance and conclude with insufficient evidence the mean distance has increased.

(b)
Test vs at 5% level of significance.
Under , since is sufficiently large, by central limit theorem, approximately.
For to be rejected,

Solving,
Thus required set of values is

(a) Let be the masses of small, medium, and large candles respectively.

Required probability

(b)

(c)
Let
Required probability

(d) 0.02 dollars per gram means we have 20 dollars per kilogram
Let
Required probability