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Form 3 Mathematics

LA SALLE COLLEGE

FINAL EXAMINATION 2019-2020

Time allowed: 105 minutes

Question - Answer Book

Instructions

Write your examination number in the spaces provided on this

cover page.

3. Attempt ALL questions in this section.

Write your answers in the spaces provided in this Question-

Answer Book. Page 11 is a supplementary answer sheet.

The total mark of this section is 40.

All working must be clearly shown. You will receive no

marks for answers without working steps.

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.

7. Use of HKEAA approved calculator is allowed.

A hunter is stationing at the location A, targetting at a horse running from the location B

to the location C in a straight line as shown in the figure. It is known that B is due south

of A and C is S64°W from A. The distances of AB and AC are both 100 m.

What is the compass bearing of B from C?

The hunter is about to discharge the arrow from the bow such that the horse is hit

at the shortest distance from the hunter. The speeds of the horse and the arrow are

12 m/s and 80 m/s respectively.

(i) What is the shortest distance between the horse and the hunter?

Find the time the hunter has to wait for discharging the arrow when the horse

starts moving from B.

Supplementary Answer Sheet

- End of Paper -

Section C (40 marks)

17. The frequency distribution table and the cumulative frequency distribution table below

show the distribution of the heights of the students in a class.

(a) Complete the tables below.

Height (cm)

Height less

Find an estimate of the mean of the distribution.

If a student is randomly selected, find the probability that the height of the selected

student is less than 170.5 but not less than 155.5.

18. In the figure, the straight line L₁: 3x - 4y - 24 = 0 cuts the x-axis at A and y-axis at B.

The straight line L2 is the perpendicular bisector of AB which cuts the x-axis at C and y-

axis at D. M is the intersecton of L₁ and L2.

Find the coordinates of A and B.

Find the area of AAMC.

L1:3x-4y-24=0

Find the equation of L2 in the form of y = mx + c.

In the figure, M and N are the mid-points of AD and BC respectively with AB // MN.

BD intersects AC and MN at P and Q respectively. AC intersects MN at R.

Prove that AB // DC.

Prove that A ABP ~ ACDP.

If PR = 6, BP =10, DP = 18, find AP.

A closed vessel in form of a right pyramid contains liquid to a depth of 4.5 cm as

shown in the figure. The bases of the frustum formed by the liquid are squares with

area 16 cm² and 256 cm² respectively. It is given that VX = x cm and PQ = y cm.

Find the values of x and y.

Show that h

Find the total surface area of the frustum.

The vessel is turned upside down such that the liquid forms a pyramid with

square base r cm and a depth of h cm.

(ii) Hence, find the value of r.