真二第張六第日一廿月九年申庚器室 ·WAH KIU YAT PO
1981
中學會考試題預習專欄
Figure
A
新數學(四) 明德出版社魯榮家提供資料
LODERM MATHEMATIOS (4)
W.K.LO.
(SILL & DALE PRESS LTD.)
Test 2
Answer All questions in
SectionA and any SIX in Section B. Section A
1. In figure 1, 0 is the centre of the circle,
and ZADE=70°,
Wind
Figure J
Pind the set of values.
of x B such that x25x+4≤0 and x-5x+6>0.
If x2-x-4=0, find the yalue of (2x-1)2.
In figure 2.0 is the céntre of the circle OA=0B=10cm wang
Find 'the area of
shaded revion.
take 丌=3.14)
Figure 2
In figure 3, LABC-90°, LCAB=30° /CDB=450 and
AD=10.
Find the Jength of 381
If -, prove that
(a+b)(c+d)=(b+c)2
Find the value of k if
2+y2+8kx+20y+125=0 represents a point cire
8. Prove the identity.
(1+tane)2+(1-tane)2
Section B
2
COS
riangle.
報日僑華
A equilateral has a perimeter of 30cm. Another triangle is form a by joining the mid joints of the endea of the given triangle another is T.bned by: joining the mid-pointe of the sides of the 2nd sriangle and so on. Find (a) the sum of periet-
ers all triangles so formed,
(b) the sum of areas of
all triangles so
formed.
10. The cost of making to
painted ball varies partly as: the square. and partly as the cube of its radius. If the cost of a painted ball of radius 12cm is $37:5 aid that of radius Scm.
is $133, find the cost
of a ball whose radius
is 4cm.
三期墨
As shown in figure 3, from a point A: on the horizontal ground due south of a tower, the angle of elevation of the top of a tower 1日: 250.
From a point B. on the same horiz- coidal ground, due eaut
of the tower, the angle of elevation of C is 0. Find e if the distance
oints of between the observation is four times as the height of
the tower
figure 3.
12. In figure 4, ABC is a
right angled triangle with right angled at CAEC, CDB and ACB are semi-circles with diameters AC, CB and AB. Find the ratio of the area of the shaded region to the area of triangleABC.
13. Plot the raph of y=1+3x-2x?(−2≤x≤4)
(i) What is the greatest,
valve
?
(ii) By arawing suitable
linear graph, solve the equation
2x-3x-3=0.
日九廿月十年〇八九一番公年九十六國民颧中育教訊航
(iii) Aalo, by drawing
another suitable.
linear graph, find
the value of √3.
14. In figure 5, AB 18
arallel to CD, AB=BE
and CD=CE.
If AB⇒p, BE-g and
BE:ED=1:2
(1 express 45 in täims of
p and 3.
(ii) express DE in terms
ofp and d
llence, or otherwise prove that AB is perpendicular to DE.
15. 200 students took
examinatione in inglish, Chinese and Mathematics.
25 passed in Chinese
and English; 15 passed in Chinese and Mathemat. ics; 10 passed in
Mathematics and English;
30 passed in English only; 40 passed in Cninese only; 20 passed
in Mathe:atics only.
Tnere are altogether
40 passed in Nathematics.
If a student is pick- ed at rundom, find the probability that he passed in
(1) all three subjects,
(11) One subject only, ((111) no subject. (b) Te a student se
picked at random from those who passed in
English, find the
provability that he
also passed; in. Mathematics.
16. A farmer has 25 acres
of land, $1000 capital wang120 man-daya of
labour to prepare for two crops A and B. The coat per acre for sowing crop A Le $20 and that for erop is $50. Crop A takes 6 mall-days per acre, while crop B takes 3. man-daya per acre. The profit on crop Ai
11 per acre and that on crop B is $18 per acre. if the farmer spent xK acres and y acres of. land for orop A and cwop B.respectively.
(a) Write down the
constraints in terme
of x and y. (b) Write down the profit
in terms of x ad y,
(c) Using the provided
graph, find the values of x und y if he wants.
to have maximum profit.
(a) what in tids maxium
profit?
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