2022 DSE 數學 試後討論
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題目衰 marking 補救
有年唔係指名道性用某條 outc 公式無分咩
有年唔係指名道性用某條 outc 公式無分咩
39 96 係咪*頭
係
祝樓主考1
其實呢題完全唔需要cyclic quad,cyclic quad係將成件事複雜左
條題目本身已經幫你plan左(b),(c),(d)都係用中三知識去做,let x=<PAM
用sin(x)同cos(x)去計就完成,最重要係睇到邊隻角係90度
(b) GA=125(distance formula),GP=radius=75(都係distance formula)
PA=100(pyth. thm)
cos(x)=4/5 sin(x)=3/5
PQ垂直於GA(chord property或congruent triangle),所以<M=90度
MA/100=cos(x)=4/5, MA=80,全條125所以GM=45
最尾section formula, M=(110,76)
由此至終無理過PA定QA係vertical,甚至唔重要唔需要知
(c) AM is angle bisector of <PAQ(chord property或congruent triangle)
Let X be centre of inscribed circle, X must be on AM and M must lie on inscribed circle(by defination of in-centre and inscribed circle)
Let P' on PA and Q' on QA tangent to inscribed circle
Let MX=XP'=r (radius)
XA=80-r
XP'/XA=sin(x), r/(80-r)=3/5, r=30
MX=30, XA=50
最尾section formula X=(128,52)
無假設過inscribed circle 穿過M,而係因為AM係angle bisector所以M一定要on inscribed circle及X一定on MA
(d) Let circumcentre be Y,
AM is perpendicular bisector(chord property或congruent triangle)
Y must be on AM
Let P'' on PA such that YP'' is perpendicular bisector of PA
因為PA=100(proved),所以P''A=50
YA=radius of circumcircle
P''A/YA=cos(x)=4/5
50/YA=4/5
YA=62.5
無假設circumcircle touch G,亦唔需要知,因為YA明顯係radius of circumcircle
因為r:YA=30:62.5=/=1:2
所以area ratio is not 1:4
條題目本身已經幫你plan左(b),(c),(d)都係用中三知識去做,let x=<PAM
用sin(x)同cos(x)去計就完成,最重要係睇到邊隻角係90度
(b) GA=125(distance formula),GP=radius=75(都係distance formula)
PA=100(pyth. thm)
cos(x)=4/5 sin(x)=3/5
PQ垂直於GA(chord property或congruent triangle),所以<M=90度
MA/100=cos(x)=4/5, MA=80,全條125所以GM=45
最尾section formula, M=(110,76)
由此至終無理過PA定QA係vertical,甚至唔重要唔需要知
(c) AM is angle bisector of <PAQ(chord property或congruent triangle)
Let X be centre of inscribed circle, X must be on AM and M must lie on inscribed circle(by defination of in-centre and inscribed circle)
Let P' on PA and Q' on QA tangent to inscribed circle
Let MX=XP'=r (radius)
XA=80-r
XP'/XA=sin(x), r/(80-r)=3/5, r=30
MX=30, XA=50
最尾section formula X=(128,52)
無假設過inscribed circle 穿過M,而係因為AM係angle bisector所以M一定要on inscribed circle及X一定on MA
(d) Let circumcentre be Y,
AM is perpendicular bisector(chord property或congruent triangle)
Y must be on AM
Let P'' on PA such that YP'' is perpendicular bisector of PA
因為PA=100(proved),所以P''A=50
YA=radius of circumcircle
P''A/YA=cos(x)=4/5
50/YA=4/5
YA=62.5
無假設circumcircle touch G,亦唔需要知,因為YA明顯係radius of circumcircle
因為r:YA=30:62.5=/=1:2
所以area ratio is not 1:4
105/105 43/45
都幾難1
都幾難1
買卷睇下係咪105
我就覺得今年唔易滿分
我就覺得今年唔易滿分
好
但mc 錯2題好柒
但mc 錯2題好柒人開始老啦 轉數冇咁快
每年都有一次反老返童既感覺
我已經好滿足
加上我淨係教core, 考m 又冇乜意思
每年都有一次反老返童既感覺
我已經好滿足
加上我淨係教core, 考m 又冇乜意思
唔講又真係似2016 個年又係出左頻數分布表，估唔到今年捲土重來圓個條估唔到撈圓的方程同畢氏定理
如果考生只識操past paper 唔了解原理就仆直
如果考生只識操past paper 唔了解原理就仆直
可能考試局想比人汁分？
應該因為疫情調淺左，2021 年個份世界級來，多頂式個part 似2019/2020 年咁。
負責人無變，應該係疫情想照顧d考生唔好出太難
即係其實要學生知除法算式點做，唔識除法算式寫唔到橫式就無得做
搞到條題目有一堆out-c formula可以用
之後嗰幾屆嘅考生真係多得佢唔少
之後嗰幾屆嘅考生真係多得佢唔少
「無講有分別 所以就無所謂」呢一個講法本身唔成立
without the loss of generality 嘅意思其實係話
「就算有分別都唔影響以下嘅討論」
而唔係直程話無分別
而且 without the loss of generality 呢樣課入面無 又咁多年都無喺 marking 出現過嘅嘢
就同 out-c 方法一樣 風險自負
without the loss of generality 嘅意思其實係話
「就算有分別都唔影響以下嘅討論」
而唔係直程話無分別
而且 without the loss of generality 呢樣課入面無 又咁多年都無喺 marking 出現過嘅嘢
就同 out-c 方法一樣 風險自負
原來可以咁樣搵radius
好易醒唔起 剩係做啱a b
啲運算途中value 好大 好易以為計錯
c d呢兩題真係好難
好彩我唔係考生
好易醒唔起 剩係做啱a b
啲運算途中value 好大 好易以為計錯
c d呢兩題真係好難
好彩我唔係考生