真二第張七第一日二月正年午戊复
WAH KIU YAT PO
報日僑華
育教僑華
yim x + 150 is the required additional linear graph
From the groph, 66 students
(55
二期星
11
2. If
find the values
of students) have marke below 36.
ab ̈a+
日八廿月二年八七九一展公年七十六國民華中 華
14.
the shadow of the shorter
Find
pole is 4im Long.
the bearing of the shadow
cast by the rope.
A
MHI & Dale Prest
1978
P U S Š.81 27
新數學 廿二 魯榮家
MODERN HATHEMATICS (22) Answers to Exercise 8 (cont.) 10.(1) Let the height of the conical vessel' be h. cm, vol-
ume of water contained be V. Since, for similar solids, (volume ratio)
= (corresponding side ratio)3.
120 : V h3: (*h)?
·V 15 cm (Ang.)
(11) Let the sum of volume of
water contained and the total
volume of the spheres be V!
Since depth of water
From the graph, there is no. intersection between the
curve and the linear graph. Therefore, there is no such value of x which gives the area of the rhombus 6cm2.
Note: Since the area of the
rhombus is:
Area =3x(5
the pass mark required = 36. (Ans.)
(b) The pass percentage is
45%%
(o) From the graph,114students (95% of the students) with marks less then 54, there
fore the range for grade "A 18
marks greater or equal to 54.
15. (a) E
The maximum value of the.
expression
AD =2
2BC
2(c-b)
26 + 20
20+ 20
26 +
(Ans.)
(b) AC-AB
19 3.125.
Therefore, the maximum area of a rhombus with sum of
lengths of diagonals equal to 5om 1s 3.125 cm
(AC) (AB)008 LBAC
thx 1.1
11
120 VI
b3 (1) 3
1331
•
x 120
it is impossible that the area is 6 cm2
and therefore.
(AB) (AC COB L BAC)
no solution is obtained from the graph.
=
(AB)2
of +5
3. Three pieces of string, the length of which are
4
gem, 6cm and 33cm respectively, are cut into pieces which are all of the same length. Find in cm the greatest length that these pieces can have, und how many of them the re
are,
4. A hemispherical bowl,
diameter 6cm full of water, is emptied into an empty cylindricel glass of radius 4cm both measurements being internal. Find the depth of water in the glass.
5. Simplify
(1-tanx) +(1
(1-cotx) +(1+cotx)"
10cm B
8cm
15.
In the figure, ZABC-61",
ZACR=35. ·Find the ratio Bir -26-
.CD
In the figure, ABPC is cyclic quadrilateral. PXLAB; PYLBC, PZLAC, Prove that ⠀;
(a) 4PX 4PCA
(b)X, Y, Z are collinear.
16.
8000
19.965 cm
Let the radius of each sphe
be r att
Total volume of the spheres
=19.965 15 = 4.965
3(Tr3) = 4.965
= 0.3951
0.7338 cm (Ans.)
11. (a) Slope of PA
00m
= 100 (ins.)
(0)
Since BFFE ED = DC
DF 1 F3 21
AT
2AB+ AD
3
2AB+ AD = 3AF
(1) In rt. A ABC-
Slope of PB =
BC AC
2013 + 5AD
COS LACB.
PA is perpendicular
BC 100 x coв 53
5(2AB 25AP
AD) (Ans.)
= 60 cm
16.
(b)Since
to FB
( - )2 + 1) - -1
+y -
25.
Hence, it is a circle with
centre at (0,0) and radius
255
(0)
From (1)
4x + 3y
2
13.
2
= 25
J4 or -4
Substitute into` (1)
3 or 3
C, D are the points (-3,4), (3,-4)
(a) The mid-point of OD is
(2244)
(0,0).
the centre of the circle
1. CD is one of the diameters
12.(a) Let the lengths of the diagonala of the rhombus be respectively.
x cm and y C
x + y = 5
or y 5 x
Area of the Tombus
≈ 4x ()()(dy)
G
dxy = x(5 - x)
.. Area 與
ст "(Año)
*x(5 - x) on2
(b) If area of the rhombus is
*
6 cm
cm2 then
•
6
ax(5 - x).
6 m
52 + 12 = 0
Since the given graph is
y = x 4x - 3
-
2
y = x + 15
- X
*
In rt. A BCF
FC
=tan 30°
FC = 60 x ten 30°
60 x 0.5773 = 34.64cm.
In rt. A FAC
tan
FC FACC
4 FAC.=
=
34.64 100
= 0.3464
1967
(ii) Aren or ABCF
30 x CF
≈ x 60 x 34,64
2 =1039.2 cm
Volume of the solid
(Ans.)
CD x Area of ▲ BCF
AB
sin ACB = 0.8
AB AC x 0.8 = 80cm = CD
Volume 80 x 1039.2
03136 cm3 (Ans.)
14.(1) From the given graph
Larks
988988
Number of students with marks below
C
30
140
50
As shown in the Venn diagram, M set of students taking
mathematics.
7- set of students taking
physics.
n(K) 70, n(P) 50.
n(MAP) = 30, n(Ṁ v P)=90 (1) Number of students taking neither mathematics nor physics = 50 (Ane.)
(11) Number of students tak- ing eithèr mathematics or
physios but not both.
= 90 - 30, 60 (Ans.) (iii) The probability that a student picked at random and that he is teking physics but not mathematics
20
H
140
(Ans.)
(iv) Among the students not
taking physics, the probability
that a student takes matha.
40
140-50
this mart
10
14
20
30
30
48
40
78
(Ane.)
50
110
60
120
數學
二十二女長波
(11)(a)
Mathematics 22
Exercise 10
Attempt all questions in Section A and any six questions in Section B. Section A
1. If the equation
(m−1)x2+2(m+1)x-1=0` have two unequal real roots, find the values of mi
In the figure, ABCB is. square, Calculate LDPC.
Ө
The radii of the circular
arcs in the given figure
are equal and their centres
lie on AR If AB-10cm
CD-4cm, calculate the
radius of each arc.
(Geometry Theorem need not
be quoted when used,
the figure, AT and BP are the tangents of the circle at A and B.. If
LATO=35, 4TOR-115, find ZBPO (Geometry Theorem need not be quoted when used.)
Section B
9. The total cost of making
a certain article consista partly of a constant sum independent of the size of the article and partly of a sum which varies as the cube of the length of the article. If the cost is $25 when the length is len and 851 when the length is 3cm,
what will it be when the length iá 8cm?
a 3b * 3b+2c £c+a 8+56 show that x must equal either or −1,
10. If x
11. Two towns X and Y are 40 km apart. A car leaves X at 9a.m. travelling towards. Y at an average "speed of 30km/hr. 30min.
later a car leaves Y travelling towards X art an average speed of 45km 45km/lir.. When the cars meet the drivers talk for 10min., then each returns to his starting- point, both arriving back at 10:20a.. Find graphically.
(a)The time at which the
cars meet.. (b)The distance from X
when the cara meet. (c)The average speed at
which each car travels on the return journey. 12.An estate was bought by a man for $240,000. He sold of the estate at a gain of 20% and of it
5
at a loss of 15%. At what gain percent must be sell the remainder so as to make a profit of 10% on the whole.
13.Two vertical poles 6n, 10m high stand on level ground 5m apart on the East-West linei a tight rope connec connects their tops;
when the sun is due South
In the figure, BC is the
diameter of the circle..
AD//BC and CE the tangent
of the circle at C.
Prove that: BC-AE-BD2.
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