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內容節錄：

Instructions of Section B

La Salle College

Final Examination 2017-2018

Mathematics

Compulsory Part

Time allowed: 2 hours 15 minutes

Question Answer Book

3. Attempt ALL questions. Write your answers in the spaces

provided in this Question-Answer Book. The last page is a

supplementary answer sheet.

All working must be clearly shown.

Unless otherwise specified, numerical answers should be either

exact or correct to 3 significant figures.

The diagrams in this paper are not necessarily drawn to scale.

Use the calculator which is pad-printed with the

"HKEAA APPROVED" or with "HKEAA APPROVED" label.

Write your examination number in the spaces

provided on the top right corner of this cover page.

This section consists of five questions. The total mark of this

section is 35.

2017-18 Final F.5 Math I Section B

Question No.

2017-18 Final F.5 Math I Section B

Fifteen dots are evenly spaced on the circumference of a circle.

(a) Tim claims that it is impossible to form a right angled triangle by picking 3 dots from these 15

dots. Do you agree with him? Explain your answer briefly.

(b) How many combinations of three dots can we pick from the 15 dots so that an isosceles triangle

can be formed?

(c) How many combinations of three dots can we pick from the 15 dots so that an acute angled

triangle can be formed?

2017-18 Final F.5 Math I Section B

End of Section B

Question No.:

2017-18 Final F.5 Math I Section B

Supplementary Answer Sheet

Section B (35 marks)

15. In the figure, ABCD is a circle. AB and DC are produced to meet at E. It is given that AC = CE and B

is the mid-point of AE.

(a) Is AC a diameter of the circle? Explain your answer.

A rectangular coordinate system is introduced in the figure so that DE is parallel to the x-axis

and the coordinates of A are (-1, 0). It is given that the equation of the circle is

y²- 6x6y-7= 0. Find

2017-18 Final F.5 Math I Section B

(i) the coordinates of C,

(ii) the equation of the straight line passing through B and C.

2017-18 Final F.5 Math I Section B

It is given that f(x) is the sum of two parts, one part varies as x² and the other part varies as x.

Suppose that f(1) = −25 and ƒ(7) = 35.

Solve f(x) = -40.

A(a, -40), B(b, -40) and C(c, 0) are points on the graph of y = f(x), where c = 0.

Find the area of the quadrilateral OABC, where O is the origin.

2017-18 Final F.5 Math I Section B

2017-18 Final F.5 Math I Section B

The stem-and-leaf diagram below shows the distribution of the weekly working time (in hours) of

employees in a company.

Stem (tens)

Leaf (units)

2017-18 Final F.5 Math I Section B

It is given that the mean and the range of the above distribution are 41 and 29 respectively.

Find the standard deviation of the above distribution.

Janice is one of the employees in the company.

A new employee is joined to the company whose weekly working time is 41 hours.

Explain briefly how Janice's standard score will change.

2017-18 Final F.5 Math I Section B

Ada invites John and eight other friends to join a party. All have to bring along with a present for

exchange. Each participant will draw a present randomly without replacement.

(a) Find the probability that John will get his own present but Ada will not.

Given that Ada does not get her own present, find the probability that John will get his own

2017-18 Final F.5 Math I Section B

2017-18 Final F.5 Math I Section B