真二第張六第日九初月正年己饜夏 WAH KIU
報日僑華
二期星
L
文中學會考試題預習
數學科
(十七)
歐陽络交
EXAMPLE
SOLUTION
MATHEMATICS (17)
LESSON 17 GRAPHS & SIMPLE
ICATION
cyclist Starts from A at noon and rides steadily at 12 mph towards B. 60 miles away At 2 pm a motorist leaves:
A and travels at 36 mph. Find from graph when the two meet and their ance from A at this time Find also the times at which they are 12 miles apart
a
the max.
alue.
dis from the graph, ishen (z+X}{3~x)=2;
MOTE: If a function gradually increases (or decreases )
Hill it reaches a certain value te, which is alg
shrically greater than (ar less than ) all neighbo
values
lues on both sides, then ★ is called a maximum
(« minimum) value of the function
As in the fig. the continuous
are ABC represents the
graph of y=f(x). In which Rx) is o max. at A. C f(x)
a min
EXAMPLE 4 Without making a table,
rough figures of the graphs of
which of the equations
has no root
SOLUTION
(a)
y=12-17 is a parabola
y=
the point t
日五廿月二年九六九一圈公年八十五國民奉中,有教僑审
璇,有
肉粉
封迎者
明白了與直就像樓,就應該上跟時,常供為,亦足以有傳樂病一般,散播至他同學。所 扶序,簡直也就没有抗非有你的可愛了,我們, 但足以破壞宮的良好秩序,同時他們的影响力 一举說話,玩耍,甚至經開座位或高聲嘈吵。湛室,爲處理。因爲把內有數個證類的兒童,就不
一波子決博士加班。字 同太太及批同姑爺歸寧, 友换就波周壓抽獎,由當是我愛叔,校友機 一點、米表菜等主持,傑,擁有有。
筑特別濃厚, 香江學院教育學會就職禮 春節聯歡大會同時舉行 新春歡樂氣文精要,更動。目 、绞牙筷子、冠實雙奶,當致逡「剁事】時一個小遊撒,將課文內容,用隈跳方式演出,以 封,由前校長分别致上的活動。例如 - 做一些與交有關的小活動,出問題的癥。
熱門產、
雅酒擞尤樓南部全陳語嵩、用舫、李、張定、梁解達、帽
,甚至在遊戲時也模仿老師 3一秒,由財
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·第三項就是「搬帼」和「燃說」的運用。过
的是前,開發以較多的用殖方面的活動,例如,受用,少用意著。不過,不為任际成交额,都不
群腦筋思治等,上述的所說,也就解釋了,何 選擇一些與跳改有關,而又有趣的問題,使他們
常的誘導和發洩,自必然不但對秩序無用, 些活利的原因。而見资們的活力,無然得到了正常營找些機會,對小組團體,給以戴國,對 「結及育界人士,除極力子帶我們隨能給兒放多,跌到麼勵方面,有一點不可忽限的,就是隨
·但能酇促進聽合作,開學生互相勉,使無
博士,潮站長凌子逃 一戰群有:梅校長錢酒瓶、馮瓠、趙球、楊紹、脚葵、柯君、洪 人的禮貌、假人的、深宅方面,滿足以爲
(精) 幾個原則 陳允才,就蓋懿、医、清秀、吳少良、吳;校方網訂了包羅萬有的宗豬校規,作用還是说乎(乙)謝淼的活麼·兒死的天性方面,還有一數衆多的學生,得到滿足,同時又可希除一般向人 名得、黎志街、陳赫雄一四族、曾秀英、梁節頸而易被離本對见危的影响稠度了。所為, 「 而且,也有效地把舌力用於巴因东餓了」,「學生而翁,高體進,收效,是非党鉅大的。它不 ,多少都騰右一個人娶勵所奈生作做氣,以及引起其他同學的舾
「大會。. 日壽會者:致·湼發、陳光、減壓熤·奥离玲、何添市,北微的。可是,如果甜食政道宫要、不止、生理上的時又帶,得他人,忌等。
健康
主珍、子卿、陳經質的話,也就是等於把許多許多的拒絕,實體地的注意以及與他人作競爭寧。如果还积魏需要,
至紫懲抗面,激然不可隨便施用。
一台,阮子平,丘學,
維盡、衛安齊、世
秋生,葉宗洲、黃、堿凌子郭博士竪 先 、梁國館、會駹、潘 別合照留念。
貞、潘志光、花綻兒,創職典禮開始,斷 陳經國,張,李光·鄭文文、任佑成、蔡田
然不可影日而語。 、余館長、陳層資等, 有·馬祖莢,周圍漢,、朱慧、伍談象、何一博士分別致詞,後由全 肏,把兒童的活力,作正強的發喪的話,他們 ,激俊英,胡椒作,曹·翠紅、李瑚玲、李翠影 的職員,會員,校友分,婆迫將自己找茶會,活動一下。一條估中,所謂 ,英讽刺,梁君佐,融 任少芳、吳鉅慈等、同一台詞,除由眾憂錢有一師的,硬件指定全級的小學生,不斷地際坐幾個 下午七時正,眾投 第一百四十餘人, 鑲有:王艾文in 朱志苔、腾博士及创堂長凌子娑一小時,簡直是沒有可能的。假如激師不聽一些機 馮熱形,尖庄,活在一芬、戴竹薇、李天基、 由主席原家齐同携致開·奥在肌來,,是喜愛活動的。所以,如果想教 ,既得到源足,也就不女新明課金的秩序了。 身心兼 高雄元,將國中,一圈、陶世耶、術家岸、一個好、將戶婉、妙、沙糖然動了。這比修桀架不休地監督低,當 面,例如牢守秩序,甚至與別入爭吵,以吸引他,即切不可,因為,假如學生知道了改們斯怨過的 惡女花開,二果。一,確認將,所一頑皮的小朋友,如很響易十多人,如果示斑內的秩序被圓氛良好的器,歉,本入所迷熱,如有不影晝之處,敬希各位提供,
·適當誘邁一個學生活動時,表現出始們個人方面的報導才能,並且更有 相信大家都知道,每一個兒業機會,與他人作出公平的競爭,他們的天晚需求 第一項就是慕 多些關所 亦會對教師,對無後,深深喜愛的,就是所謂
織,兒裔們便有了足够的機會,滋綱性生活,同 ·最後,本入想特別的,號4日所深站 除了上述的外,還有無個,做到上逃的解響工作的。如果各位能合近中的學
人對他的注意力,剛才我所說的正破黃染途徑,經前,都不會執行的話,他自後對延師勸告, 「织按出特別的時間,或做許多額外的工作才可以
·生循蹈矩,然學上黑篇易,而嚴生方面】
例行工作時,稍露留案,即可以娩行-而把母 角點,都著重於一般小學數師,可於執行他們
來然
幾個要點
·特別留意
衖或一項,願上
阿好生多
下生做织
臺灣 、吴拙邁、路幹生、鑠,並有幸團抽獎,由伍區 不守狭隘起來。最常見的現象,就是和脚座的同一師就必須先行艳娜遂常爲財苦少的有問題兒眾,加以椒-
。(琳)
their speeds are unifam, .. their trant
As found from the graphs
are linear
can They meet at 2:45
<b>. They are 12 mi apart
33 miles from 2:30pm and
XAMPLE & Sohne grophically, 52*- 8x = 36
SOLUTION,
Let
+(8x+36)
x+36)
which is again differ units in
the same shape as graph in
units
Darson one cas
the graph c3 does not
but diffe
axes)
Hence, as solution
equation
Solve graphically the
allowing par
simaltanėnas eoaati
The roots of the given equatio
y=5(82+36)
12 136
(3X=36: are thi values of ⋆ which satisfy the above pair of simuthaneza equations From the graphs as shown, we find
NOTE
X=
3.6.
above problem can also be solved by dra the graph y=
8X-36 Fhe inferseethin of the graph and the x-axis (ie, the line goo) are the solutions
EXAMPLE 3 Draws the graph of y=(2+x}{3−x),
und find the maximum value of (2+2)(3-x) Find, olio, as accurately as possible, the values of x for which (2+x)(3-2)B. equal to 2
SOLUTION
。
.0
±18 ±9 #6 ±45
from the graphs, the bit of intersection are ‚3) (-5 -6)
the solutions are
NOTE: The curve xy =18 is known
a rectangular hyperbola Any equation of the form
xy=ks. h = csmod,
will give a smilar graph as
the right hand side figure.
HINTS & ANS TO EX 16
)+2()+3. 6(4)+5
then x=aR
(54) −5(24) + 2(3k) = 8:
fence,
26. 2=16]
Let x, y be the lengths of the sides of the Cudes, then, ratio ef volume =(3)3
33.52
Ratio of their surfaces = (*) =(2/3,52)
2.114:1
abb
F. b =ac
Rigd to prove (a+b)(b+0= (Nab +Nbc )2
L. S. =(a+b)(b+c)=ab+ac+b2+be+ab+rbe + 2 b2 R.S. = (JAb + [[ S= ab+zb@ctbs=ab+25+bc NOTE :(1) If a;b=c=d then the quantities are
said to be in proportion, and d is called. the fourth
proportion a, b, c,a and are called the extremes while b Care called the means. (a) If a b = bic the three
uan tities quar are said to be in continued proportion c is said to be the third proportional to a and b
. and bus called the mean proportional between a and
v=F13
$(18)2 = 5852p
=13.8247
= 137
37P
=1136) =46 6567
=XERCISE_17
I've graphically the equations.
号
PE=
3x + y =
man travels from A to B at the rate
mpt und
man start
ako min.
from
after his start a second
孽
•s to B at 36 mph and reaches
his distinaton 8
graphically
was this graf
after the first man. Find distance from A to B
of gex and xy=6x+ an: the same diagram for values of x from to +3 From the graphs, solve 5X*
6x+4 Also find out roughly from the graphs, by drawing approximate parallel line, for what value of a the equation tX*=6x+a will have equal roster Draw roughly the graphs of the six trigonomet- mical functions from
At noon
A starts
to 275
to walk at 6 mph, and at 1:30pm. B follows on hørse back at 8 mph. When will & overtake A ↑ Also find
(a) when A is 5 miles ahead of B (b) when A is 3 miles ahead of