下載連結︰
https://drive.google.com/file/d/1soFx68ukF1Mf5mqpD_xgp308yoMKjhRv/view?usp=sharing
最近做緊中三的練習
因為想溫翻再基本 d 的技巧,出左一 d 關於因數的練習
例如︰12的因數係咩? 答︰1, 2, 3, 4, 6, 12 (即係可以將12整除的正整數) 共有 6 個
但之後我再出深少少的題目,我要列齊所有因數好似有少少困難
例如︰ 113400 的因數係有幾多個呢?
我諗左一陣,發現呢個問題其實 DSE 的 permutation and combination 排列與組合 的題目黎
我講講我的諗法
先用12做例子,12 = 2^2*3^1
因數就係於 2^2 中抽多少出黎、3^1 中抽多少出黎
Step A : 2^2︰您可以抽 0, 1, 2 個 "2"
Step B : 3^1 : 您可以抽 0, 1 個 "3"
Step A 有 3 個選擇、Step B 有 2 個選擇,過關就係 (3x2) = 6 個組合
包括有 (2^0*3^0), (2^1*3^0), (2^2*3^0), (2^0*3^1), (2^1*3^1), (2^2*3^1)
即 1, 2, 4, 3, 6, 12
相同的諗法去諗 113400
我地先用質數分解 113400 = 2^3 * 3^4 * 5^2 * 7^1
接著做因數時就會從中選擇
Step A : 2^3︰您可以抽 0, 1, 2, 3 個 "2"
Step B : 3^4︰您可以抽 0, 1, 2, 3, 4 個 "3"
Step C : 5^2︰您可以抽 0, 1, 2 個 "5"
Step D : 7^1︰您可以抽 0, 1 個 "7"
Step A 有 4 個選擇、Step B 有 5 個選擇,Step C 有 3 個選擇、Step D 有 2 個選擇,
過關就係 (4x5x3x2) = 120 個組合
包括有
2^0 * 3^0 * 5^0 * 7^0 = 1
2^1 * 3^0 * 5^0 * 7^0 = 2
2^2 * 3^0 * 5^0 * 7^0 = 4
2^3 * 3^0 * 5^0 * 7^0 = 8
2^0 * 3^1 * 5^0 * 7^0 = 3
2^1 * 3^1 * 5^0 * 7^0 = 6
2^2 * 3^1 * 5^0 * 7^0 = 12
2^3 * 3^1 * 5^0 * 7^0 = 24
2^0 * 3^2 * 5^0 * 7^0 = 9
2^1 * 3^2 * 5^0 * 7^0 = 18
2^2 * 3^2 * 5^0 * 7^0 = 36
2^3 * 3^2 * 5^0 * 7^0 = 72
2^0 * 3^3 * 5^0 * 7^0 = 27
2^1 * 3^3 * 5^0 * 7^0 = 54
2^2 * 3^3 * 5^0 * 7^0 = 108
2^3 * 3^3 * 5^0 * 7^0 = 216
2^0 * 3^4 * 5^0 * 7^0 = 81
2^1 * 3^4 * 5^0 * 7^0 = 162
2^2 * 3^4 * 5^0 * 7^0 = 324
2^3 * 3^4 * 5^0 * 7^0 = 648
2^0 * 3^0 * 5^1 * 7^0 = 5
2^1 * 3^0 * 5^1 * 7^0 = 10
2^2 * 3^0 * 5^1 * 7^0 = 20
2^3 * 3^0 * 5^1 * 7^0 = 40
2^0 * 3^1 * 5^1 * 7^0 = 15
2^1 * 3^1 * 5^1 * 7^0 = 30
2^2 * 3^1 * 5^1 * 7^0 = 60
2^3 * 3^1 * 5^1 * 7^0 = 120
2^0 * 3^2 * 5^1 * 7^0 = 45
2^1 * 3^2 * 5^1 * 7^0 = 90
2^2 * 3^2 * 5^1 * 7^0 = 180
2^3 * 3^2 * 5^1 * 7^0 = 360
2^0 * 3^3 * 5^1 * 7^0 = 135
2^1 * 3^3 * 5^1 * 7^0 = 270
2^2 * 3^3 * 5^1 * 7^0 = 540
2^3 * 3^3 * 5^1 * 7^0 = 1080
2^0 * 3^4 * 5^1 * 7^0 = 405
2^1 * 3^4 * 5^1 * 7^0 = 810
2^2 * 3^4 * 5^1 * 7^0 = 1620
2^3 * 3^4 * 5^1 * 7^0 = 3240
2^0 * 3^0 * 5^2 * 7^0 = 25
2^1 * 3^0 * 5^2 * 7^0 = 50
2^2 * 3^0 * 5^2 * 7^0 = 100
2^3 * 3^0 * 5^2 * 7^0 = 200
2^0 * 3^1 * 5^2 * 7^0 = 75
2^1 * 3^1 * 5^2 * 7^0 = 150
2^2 * 3^1 * 5^2 * 7^0 = 300
2^3 * 3^1 * 5^2 * 7^0 = 600
2^0 * 3^2 * 5^2 * 7^0 = 225
2^1 * 3^2 * 5^2 * 7^0 = 450
2^2 * 3^2 * 5^2 * 7^0 = 900
2^3 * 3^2 * 5^2 * 7^0 = 1800
2^0 * 3^3 * 5^2 * 7^0 = 675
2^1 * 3^3 * 5^2 * 7^0 = 1350
2^2 * 3^3 * 5^2 * 7^0 = 2700
2^3 * 3^3 * 5^2 * 7^0 = 5400
2^0 * 3^4 * 5^2 * 7^0 = 2025
2^1 * 3^4 * 5^2 * 7^0 = 4050
2^2 * 3^4 * 5^2 * 7^0 = 8100
2^3 * 3^4 * 5^2 * 7^0 = 16200
2^0 * 3^0 * 5^0 * 7^1 = 7
2^1 * 3^0 * 5^0 * 7^1 = 14
2^2 * 3^0 * 5^0 * 7^1 = 28
2^3 * 3^0 * 5^0 * 7^1 = 56
2^0 * 3^1 * 5^0 * 7^1 = 21
2^1 * 3^1 * 5^0 * 7^1 = 42
2^2 * 3^1 * 5^0 * 7^1 = 84
2^3 * 3^1 * 5^0 * 7^1 = 168
2^0 * 3^2 * 5^0 * 7^1 = 63
2^1 * 3^2 * 5^0 * 7^1 = 126
2^2 * 3^2 * 5^0 * 7^1 = 252
2^3 * 3^2 * 5^0 * 7^1 = 504
2^0 * 3^3 * 5^0 * 7^1 = 189
2^1 * 3^3 * 5^0 * 7^1 = 378
2^2 * 3^3 * 5^0 * 7^1 = 756
2^3 * 3^3 * 5^0 * 7^1 = 1512
2^0 * 3^4 * 5^0 * 7^1 = 567
2^1 * 3^4 * 5^0 * 7^1 = 1134
2^2 * 3^4 * 5^0 * 7^1 = 2268
2^3 * 3^4 * 5^0 * 7^1 = 4536
2^0 * 3^0 * 5^1 * 7^1 = 35
2^1 * 3^0 * 5^1 * 7^1 = 70
2^2 * 3^0 * 5^1 * 7^1 = 140
2^3 * 3^0 * 5^1 * 7^1 = 280
2^0 * 3^1 * 5^1 * 7^1 = 105
2^1 * 3^1 * 5^1 * 7^1 = 210
2^2 * 3^1 * 5^1 * 7^1 = 420
2^3 * 3^1 * 5^1 * 7^1 = 840
2^0 * 3^2 * 5^1 * 7^1 = 315
2^1 * 3^2 * 5^1 * 7^1 = 630
2^2 * 3^2 * 5^1 * 7^1 = 1260
2^3 * 3^2 * 5^1 * 7^1 = 2520
2^0 * 3^3 * 5^1 * 7^1 = 945
2^1 * 3^3 * 5^1 * 7^1 = 1890
2^2 * 3^3 * 5^1 * 7^1 = 3780
2^3 * 3^3 * 5^1 * 7^1 = 7560
2^0 * 3^4 * 5^1 * 7^1 = 2835
2^1 * 3^4 * 5^1 * 7^1 = 5670
2^2 * 3^4 * 5^1 * 7^1 = 11340
2^3 * 3^4 * 5^1 * 7^1 = 22680
2^0 * 3^0 * 5^2 * 7^1 = 175
2^1 * 3^0 * 5^2 * 7^1 = 350
2^2 * 3^0 * 5^2 * 7^1 = 700
2^3 * 3^0 * 5^2 * 7^1 = 1400
2^0 * 3^1 * 5^2 * 7^1 = 525
2^1 * 3^1 * 5^2 * 7^1 = 1050
2^2 * 3^1 * 5^2 * 7^1 = 2100
2^3 * 3^1 * 5^2 * 7^1 = 4200
2^0 * 3^2 * 5^2 * 7^1 = 1575
2^1 * 3^2 * 5^2 * 7^1 = 3150
2^2 * 3^2 * 5^2 * 7^1 = 6300
2^3 * 3^2 * 5^2 * 7^1 = 12600
2^0 * 3^3 * 5^2 * 7^1 = 4725
2^1 * 3^3 * 5^2 * 7^1 = 9450
2^2 * 3^3 * 5^2 * 7^1 = 18900
2^3 * 3^3 * 5^2 * 7^1 = 37800
2^0 * 3^4 * 5^2 * 7^1 = 14175
2^1 * 3^4 * 5^2 * 7^1 = 28350
2^2 * 3^4 * 5^2 * 7^1 = 56700
2^3 * 3^4 * 5^2 * 7^1 = 113400
Chapter 1 - Note (word version)
Chapter 2 - Note (word version)
Chapter 3A - Note (word version)
Chapter 3B - Note (word version)
Chapter 3C - Note (word version)
Chapter 3D - Note (word version)
Chapter 3E - Note (word version)
Chapter 3F - Note (word version)
Chapter 4 - Note (word version)
Chapter 5 - Note (word version)
Chapter 6 - Note (word version)
Chapter 7 - Note (word version)
Chapter 8 - Note (word version)
遺傳物質 Genetic material
遺傳物質是親代與子代之間傳遞遺傳信息的物質。
除一部分病毒的遺傳物是RNA外,其餘的病毒以及全部具典型細胞結構的生物的遺傳物都是DNA。
進化是指種群裡的遺傳性狀在世代之間的變化,性狀指是遺傳物質的表現。人類進化的實質是種群遺傳物質的改變。
Genetic material is the material that transmits genetic information between parents and offspring.
Except for some viruses whose genetic material is RNA, the genetic material of other viruses and all organisms with a typical cell structure are DNA.
Evolution refers to the change of genetic traits in a population between generations, and traits refer to the performance of genetic material. The essence of human evolution is the change of population genetic material,
昆明魚 Myllokunmingia
昆明魚是迄今已知的地球生命出現早期的最高等的脊椎動物,它有由軟骨構造的頭顱骨及骨骼。
昆明魚的發現,不僅將包括人類在內的整個脊椎動物演化史向前推進了5000萬年,而且改變並完善了脊椎動物早期演化理論。
Myllokunmingia is known to date as the highest vertebrate in the early stage of life on earth. It has a skull and skeleton made of cartilage.
The discovery of Myllokunmingia has not only advanced the entire history of vertebrate evolution including humans by 50 million years, but also rewritten and perfected the theory of early vertebrate evolution.
提塔利克魚 Tiktaalik
提塔利克魚是最早擁有頸部的魚類,強狀的肋骨可以讓它們離開水域,讓它們在狩獵時擁有更多的自由,不論是在陸地上或是淺水中。
提塔利克魚擁有可以在堅硬地面支撐自身重量及呼吸空氣的構造,這是頭骨演化一個關鍵的改變,促使我們的遠祖可以適應陸地上的生活。
Tiktaalik is the first fish to have a neck. The strong ribs allow them to leave the water and allow them to have more freedom when hunting, whether on land or in shallow water.
The Tiktaalik has a structure that can support its own weight and breathe air on a hard ground. This is a key change in the evolution of the skull, allowing our distant ancestors to adapt to life on land.
始組單弓獸 Archaeothyris
始組單弓獸的體型較大,頜部強壯,且能張得比其他早期爬行動物還大,具有較大的犬齒,顯示它們是肉食性動物。
始組單弓獸是所有單弓動物的祖先,包括哺乳類。
The Archaeothyris was larger in size, had strong jaws, and could expand larger than other early reptiles, and had larger canine teeth, indicating that they were carnivorous animals.
The Archaeothyris is the ancestor of all single how animals, including mammals.
大帶齒獸 Megazostrodon
大帶齒獸長相酷似老鼠,大小如同鼬鼠,行為也類似鼬鼠,是最早的哺乳類。它是穴居動物,在夜間捕食。
大帶齒獸過著穴居的生活,擁有和人類一樣的膈,被認為是人類的祖先。
The Megazostrodon looks exactly like a mouse, is the size of a weasel, and behaves like a weasel. It is the earliest mammal. It is a burrowing animal and hunts at night.
The Megazostrodon lives a burrowing life, has the same diaphragm as humans, and is considered to be the ancestor of humans.
更猴 Plesiadapis
更猴是已知最早似靈長目的哺乳動物其中之一屬,外觀有點像松鼠。更猴仍保有爪,但和現代的靈長類動物相差很遠,這類動物有四支爪子,不能彎曲的那種,很不靈活。
有觀點認為更猴的發現給靈長類的進化過程帶來了新的發現,但也有觀點認為更猴形類群和現代靈長類不屬於一個隊伍。
The Piesiadapis is one of the earliest known genus of primate mammals and looks a bit like squirrels. Plesiadapis still have claws, but they are very different from modern primates. These animals have four claws, which cannot bend and are very inflexible.
Some believe that the discovery of Plesiadapis has brought new discoveries to the evolution of primates, but there are also opinions that the Plesiadapis-shaped groups and modern primates do not belong to the same team.
南方古猿 Australopithecus
南方古猿已經能直立行走,使用天然工具,生活方式可能為群體生活,共同尋找食物,共同防止其他猛禽野獸的攻擊。
南方古猿被認為是從猿到人轉變的第一階段,是整個人屬的祖先。
Australopithecus has been able to walk upright, use natural tools, and may live in groups, seek food together, and jointly prevent attacks from other raptors and beasts.
Australopithecus is considered to be the first stage of the transition from ape to man, and is the ancestor of the entire Homo genus.
智人 Homo sapiens
智人是人屬下的唯一現存物種,大腦的發達與複雜化可能有利於聚群的社會生活,群居生活十分有利於以協作方式獲取獵物、採集食物和交流信息等,因而使智人在生存競爭中佔優勢。
智人分為早期智人和晚期智人,晚期智人在體質特徵上和現代人已沒有明顯差異,能精製石器和骨器,懂得繪畫、雕刻等藝術。
Homo sapiens is the only existing species in the genus Homo sapiens. The development and complexity of the brain may be conducive to social life in groups. Living in groups is very conducive to obtaining prey, collecting food and communicating information in a collaborative manner, thus.
Homo sapiens are divided into early Homo sapiens and late Homo sapiens. The physical characteristics of the late Homo sapiens have no obvious differences from modern people. They can refine stone and bone tools, and know the arts such as painting and carving.
資料來源︰生命簡史 古生物放置 遊戲的資料
___________________________________
HKDSE Chemistry 化學 的電子書 :
Chemistry - Calculation Training A
Type 1: Isotopes 同位素
Type 2: Relative atomic masses 相對原子質量
Type 3: Avogadro’s number 亞佛加德羅數
Type 4: Percentage of mass 質量百分比
Type 5: Number of atoms / ions / molecules 原子/離子/分子的數目
Type 6: Empirical formula / Chemical formula 實驗式 / 化學式
Type 7: Mass of reactant / product 反應物 / 生成物的質量
Chemistry - Calculation Training B
Chemistry - Calculation Training C
Chemistry - Calculation Training D
HKDSE Chemistry (Compulsory Part) 化學 (必修部分) 天書
___________________________________
___________________________________
HKDSE Physics 臨考前 吃到飽 系列 (Question & Suggested Solution)
DSE M1 臨考前 吃到飽 系列 (Question & Suggested Solution)
楯齒龍 Placodus
生存年代︰ 2.5 至 2.3 億年前
體長︰ 1
至 3 米
分佈區域︰ 中生代海洋 Mesozoic Ocean
目Order︰ 盾齒龍目 Placodontia
楯齒龍用突出的前齒,將水底無脊椎動物的堅硬外殼拉扯出來,並用後方的平坦牙齒,將獵物外殼壓碎。
楯齒龍是陸地動物,但到海中尋找軟體動物、腕足動物和甲殼類作為食物。
Placodus
used their protruding front teeth to pull out the hard shells of underwater
invertebrates, and crushed the shells of prey with the flat teeth at the back.
Placodus
is a land animal, but it goes to the sea to find molluscs, brachiopods and
crustaceans as food.
幻龍 Nothosaurus
生存年代︰ 2.3 至 2 億年前
體長︰ 3
米
分佈區域︰ 中生代海洋 Mesozoic Ocean
目Order︰ 幻龍目 Nothosauroidea
幻龍緩慢跟踪獵物,利用針狀牙齒的長頜部捕抓魚類與其他海中動物。
幻龍是半海生動物,它們可能過著類似現代海豹的生活。
Nothosaurus
slowly follows its prey, using its long jaws with needle-like teeth to catch
fish and other sea animals.
Nothosaurus
are semi-sea animals, and they may live a life similar to modern seals.
海龍 Thalattosaurus
生存年代︰ 2.3 至 2 億年前
體長︰ 4
米
分佈區域︰ 中生代海洋Mesozoic Ocean
目 Order︰ 海龍目Thalattosauria
海龍類外表似大型蜥蝪,有長而側向平坦的尾巴,適合生存於海中環境。
海龍擁有大眼睛,可讓它們的深水中視力更好,而眼睛周圍有骨環,可防止眼睛在深水中遭巨大水壓壓碎。
Thalattosaurus
resemble large lizards with long and laterally flat tails, which are suitable
for living in the sea.
Thalattosaurus
have big eyes, allowing them to have better vision in deep water, and there are
bone rings around the eyes to prevent the eyes from being crushed by huge
pressure in deep water.
海鱷 Pelagosaurus
生存年代︰ 1.9 至 1.45 億年前
體長︰ 7
米
分佈區域︰ 中生代海洋Mesozoic Ocean
目Order︰ 海鱷亞目Thalattosuchia
海鱷性情兇猛,四肢演化成了鰭肢狀,尾巴的形狀像魚鰭,在海中的行動相當敏捷。
海鱷從其出現開始,就一直受到魚龍、上龍、滄龍等天敵的威脅,直至滅亡也沒能翻身。
Pelagosaurus
has a fierce temperament. Its limbs have
evolved into flippers, and its tail is shaped like a fin, it moves very quickly
in the sea.
Since its
emergence, Pelagosaurus has been threatened by natural enemies such as
Temnodontosaurus, Pliosaurus and Mosasauroidea, and has not been able to turn
over till its extinction.
魚龍 Temnodontosaurus
生存年代︰ 2.5 至 0.9 億年前
體長︰ 2至23 米
分佈區域︰ 中生代海洋Mesozoic Ocean
目Order︰ 魚龍目Lchthyosauria
魚龍的遊速可以達到每小時40公里,鯺狀的四肢可能被用來起穩定以及控制轉向的作用,魚龍的主食可能是魚類。
雖然魚龍的外表看似魚類,但它們並不屬於魚類。
The
swimming speed of Temnodontosaurus can reach 40 kilometers per hour. The fin-like limbs may be used to stabilize
and control steering. The staple food of
ichthyosaurs may be fish.
Although
Temnodontosaurus look like fish, they are not fish.
蛇頸龍 Plesiosaurus
生存年代︰ 2 至 0.9 億年前
體長︰ 3至20 米
分佈區域︰ 中生代海洋Mesozoic Ocean
目Order︰ 蛇頸龍亞目 Plesiosauroidea
蛇頸龍以U形的嘴部、銳利的牙齒捕抓獵物,它們以兩對鰭腳推動身體,尾巴因為太短而不能推動身體前進。 在水中游泳時,頸部可能有控制制方向的功能。
蛇頸龍的頸椎骨基本不能活動,只能做極小弧度的擺動和升降,幾乎不能抬高脖子。
Plesiosaurus
uses a U-shaped mouth and sharp teeth to catch prey. They are two pairs of fins to push the
body. The tail is too short to push the
body forward.
When
swimming in the water, the neck may have the function of controlling direction.
The
cervical vertebrae of Plesiosaurus are basically unable to move, and can only
swing and lift in a very small arc, and they can hardly raise the neck.
上龍 Pliosaurus
生存年代︰ 2 至 0.7 億年前
體長︰ 4至15 米
分佈區域︰ 中生代海洋Mesozoic Ocean
目Order︰ 上龍亞目 Pliosauroidea
上龍特徵是短頸部、長頭部、體型大、呈流線型、行動快速且兇猛。
上龍類是肉食性動物,長而強壯的頜部有多排銳利的牙齒,可能獵食魚龍或蛇頸龍。
Pliosaurus
is characterized by a short neck, a long head, a large body, a streamlined shape,
fast action and fierceness.
Pliosaurus
are carnivorous animals, with long and strong jaws with multiple sharp teeth, which
may hunt Temnodontosaurus or Plesiosaurus.
滄龍 Mosasauroidea
生存年代︰ 0.7 至 0.65 億年前
體長︰ 3至15 米
分佈區域︰ 中生代海洋Mesozoic Ocean
科Family︰ 滄龍超科 Mosasauroidea
滄龍有雙鉸鏈狀的頜部、頭顱骨,能將獵物整個吞下,身體形狀類似現代巨蜥,但更為修長、流線性。
滄龍類在白堊紀晚期的大海中迅速擴張,成為頂級掠食者,在很短的時間內完全取代了上龍的生態位並導致其完全滅絕。
Mosasauroidea
has a double-hinged jaw and skull, which can swallow its prey whole. Its body shape is similar to modern monitor
lizards, but it is more slender and streamlined.
Mosasauroidea
expanded rapidly in the sea in the late Cretaceous and became top predators,
completely replacing the niche of Pliosaurus within a short period of time and
leading to its complete extinction.
資料來源︰生命簡史 古生物放置 遊戲的資料
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