寘四第張五第日六初月正年巳丁胶复
1977中學會考試葅預習專
明德社主編
數學(十六)·女長波-
Mathematics 16
Fxercise 8
Attempt All questions in
Section A and any SIX
questions in Section B..
Section A(Fach question carries 5 marks)
1. IF D and a are the roots
of the equation 5x2+2x-4-0, find the equation whose roots are 20+ and +20..
2. Find the value of k for.
which 2x3-kx2+6x-3k is exactly divisible by x+2
3. Find all solutions from
0° to 360° of tanx+cotx = 2
4. In figure, AB=BC=CD; semi
circles are drawn as shown. Show that the shaded area is one third of the area of the whole circie
5. A motorist drives for 2
hr. at 32km per hour and for half an hour at 42 km per hour; find his average SPEED for the whole journey.
6. Find the amount of wood
used to make an open box, 25cm long, 14cm wide
8cm high, external mea- surement, the wood being 5mm thick.
7. In the figure, AKC and
BID are two perpendicular chords. AK =36cm, AB 25cm Calculate KB,KD and the radius of the circles. (Geometry theoren need not be quoted when used)
D
8. In the figure, two circles intersect at P,Q and AB is the common tangent touches the circles at t the Points A,B. Find the size of the sum of LAPB and AQB (Geometry
theprem need not be, quo- ted when used.).
B
section B(Fach question car-
ries 10 marks)
0
19. The number of coins in a
bag is between 210 and 230.
Some are 10¢ coins, some
50g coins, some $1 coins. The total value of the
coins of each kind is the
same. How many coins are there altogether? 10. If the figure,shows the
graph of y=x2+ax+3, Find the least value of y the range of values x such that y0.
c) the values of D ́and a
Using the enuation of the
WAH KIU YAT PO graph and by drawing on the same figure suitable straight lines, solve
d) 2x2 4x + 1
e) 4x2- x + 4 =
11. in the figure, B,K,T,H
are concyclic, and PA AQ=AB. Prove that ZHTK = 90° ABAT.
12. Two unequal circles in- terest at 0 and 21 Straight lines AOP COT through O cut one circle at A, B, C and the other at r, S, T. AB 4ABC Trove that
AFST
BOS,
13. IF .secx=
m
1
+
S show
2m
that secx+tanx = m or
tanx?
1. What is secx
14. In figure, ABCD is a
Farallelogram, Prove that
2absinx that tane =
2 a-b
15. A box when empty weighs 10kg, it will hold 50kg of clothes or 180kg of books. What will it weigh when packed full of clothes and books if a) 20% of the volume is oc-
cupied by books and the rest by clothes
b) 20% of the weight of the
contents is made up by books and the rest by clothes?.
16. A 36 litres cask contains
301. of Spirit and 61. of water. 121. are drawn out, and the cask is then
filled up with soirit; 12 more litres are with- drawn and the cask is then filled up with water. What is the final
函來者讀
Dercentage of spirit in the cask?
新數學(十六),碁榮家
MODERN MATHEMATICS (16)
Exercise 7
Answer All the questions in
Section A and ANY STX in.
section H, AIL necessary work-
!
報日僑華
三期星
ing must be shown clearly.
Section A
日三廿月二年七七九一层公年六十六國民肇中 青教僎额
7. A person who rides à
bicycle is a
(A. motorist
B. scientist
2
X
-
1
1. One of the roots of the
+ 2k kx equation exceeds the other by 2. Find.
the values of k.
2. In the figure below, ABC-iɛ an equilateral triangle of side 6cm, A circle, centre 0, passes through 1,3 and C. Pind the radius of the circle.
A
3. Find three numbers in geom- etrical progression such that
their sum is 39 and their pro-
duct is 729.
4. In the figure below, TA and
TB are the tangents of the cle with radius 70cm. If angle
AB is 60, find the area of
the shaded part,
5. Find the set.
of real numbers satisfying the inequality
2
6. The equation.
(x −3y +5) + k(x + 2y) reqresents a family of straigh lines passing through a fixed point P. For what value of kis the line in the family pa
to the straight line x + y 2
7. Maximize 3x + y 50
under the constraints x, y N
・
≤ 102
8. Find the values of A. B
and Cir. 5x2-1 Section B
A{ x2+x+2} + { Bx÷f} {x=1}
9. If m, ʼn are the roots of
the equation 2x-4x+7=0
find the values of
22 (i) m2
(ii) m + n Also, find the equation
with roots 2mn and n m
10. In a certain college, 25%
of the students failed math- ematics, 15% of the students failed Physics, and 10% of
the students failed both ma-
thematics and physics, & atu-
dent is physics,
(1) If he
what is the probability that
he failed mathematica ? (ii) If he failed mathematics what is the probability that
he failed physics?
(11) What is the probability that he failed mathematica
ar physics?
11. In the figure, VABCD is
a right pyramid with rectang- ular base. AB = Hcm VN=12cm
BC = 6 cm Find
-
(i) angle between VA and VN (ii) angle between plane VBC
and VAD
(iii) angle between planes VAB.
and VCD.
(iv) the total surface area?!
(v), the volume .
JELER BY ME
12. ABCD is a parallelogram
with vertice 1(2,1), B(8,2) C(10,6) and D(a,b)
(1) Find the values of a and b (ii) Express the vector AE
in terms of i and j where E is the point on CD such that
CE: ED 2 1
(ii) If F is the mid-point of
BC, Rxpress the vector. AF in terms of igand.j (iv) Find the angle EAF.
13. Draw the graph of the
function f, dom f ={x:-2<x1}}
= {(x,y); y = x2-2x+2}
f=
(i) if (a,1)ef, find a (ii) if (0,b)ef, find b (iii) What is the minimum
value of f.
(iv) By drawing suitable lis
near graph on the same plane solve the equation
2
X- 20
(v) Also, by drawing suitable
straight line on the same.
graph, find the value of £3.
14 Prove, by mathematical
induction, that
n
is divisible by ̄x+y
for all even natural numbers
15. A rectangular box of in- ternal base dimensions 2r,3r and internal height Or is
fitted with spheres of radius
Find the maximum number of spheres that can be fitted into the box, giving your
reasona. What fraction of
the space is wasted ? (Ex22
1977中學入學試試題預習專欄
腰智慧社主編:
英文科
(十六)
ENGLISH (16)
Choose the best answer. write
the LETTER in the brackets.
1. Tony and San look to visiting the Ocean Fark. (A. at B. for C. after
D. forward E. over) 1.)
light
2.0)
2. Mary is fond
music. (A. to
D. with E.from)
B. of C. for
3. You had better
hia advice and work harder. (A. took E.. taken C. take
D. taking E. takes) 3.( )
4. Bill said that his lazy son.
was good nothing.
C. by D. to
(A. for
B. in E. under)
4.()
5. Miss Ho told them not to
worry
the test. 5.( ) (A. with B. by C. upon
D. against E. about)
6. I would rather watch T.V.
go to the cinema.
(A
D. than
that B. for C. and
E. but)
6.(
的大在都更式了會話,,篇
C. dentist D. artist
E. cyclist)
8. Some friends of
went
to study in England. 8.(
(A. ours B. us C. we
D. our
E. ourselves)
9. Henry doesn't like fishing
and
9.0
(A. so am I B. Bo I do
C. I also D. so have I
や E. nor do I}
10. Flease answer the door,
you ?
C. will
(A. do B. don't.
D. are E. have) Choose the answers which best complete the following passage.
If we go abroad and visit. foreign countries, we see and learn all 11.(A. sorts
B. places C. kind
D. Fieces E. pictures) of things that we can never see or learn at home, 12 ta. or B. when G. though D. and B. which) we may read about them in hooks and
and see pictures newspapers, of them 13.(A. in the garden B. at school C. at the cinema D. at work E. in the country). The best way to 14.(A. meet B. know C. have D. leam E. see) geography is to travel, and the best way to get to know and 15.(4. see
B. understand C. make D. find E. guess) the people of other countries is to meet them in their own hopes..
11-()
12.) 13
∙14.) 15.()
Read this passare carefully. Then answer Questions 16-20- which are about the passage.
Joan had often talked about their first years together twenty years ago. She was a school teacher when she first met Smith. He was a young cowboy training horses at a nearby farm.
when they decided to marry, Smith decided to save money. He stayed away from town where he knew he could srend it all quickly. Four years later she put her money with his and they tought a farm and a few cows. They thought they had the best land in the world. Smith hilt the little house with his own hands He added wooden fences to keep the cattle inside.. Often she held a light for him when he worked at night. In the soft darkness they talked about their dreams and hoped for the future.
16. when Joan first met her
boy-friend, she was a
(A. alegirl B. schoolgirl
C. nurse D. teacher E. driver)
17: Smith worked
first met. Joan.
(A. in a school
16.()
when he 217.()
B. on a
D. in a
farm C. on a bus hospital E. in a boat)
18.(
18. Smith stayed away from
town because (A. it was too crowded
B. it was too noisy C. he didn't want to see Joan
D. there were no horses
E. he wanted. to save money)
19. On their own farm they had
19.(
(A. some cOWS B. some
hors es
C. some dreams D. some cows and a house .E. some horses and a
school)
20. After they had bought the
farm, they lived there (A. diligently B. with difficulty C. lazily
D. richly E. dreaming all the time)
20.( )
ANSWERS
1.D 2.B 3.0 4.A 5.E 6.D
7.E 8.A 9.E 10.0 11.A 12.0 13.0 14.0 15.B
19.D 16.D 17.B 18.E
20.A
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一九七七年二月十音
李招坐一四的
的副如恩覽:买,最 是蕭源
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