Có bao nhiêu giá trị nguyên của tham số m để phương trình vô nghiệm

Chia sẻ

Một số câu hỏi khác cùng bài thi.

• Cho phương trình

  

  Có bao nhiêu giá trị nguyên

  

  nhỏ hơn

  

  để phương trình có nghiệm?

• Giải phương trình

  

  .

• Cho phương trình lượng giác:

  

  . Định

  

  để phương trình vô nghiệm.

• Phương trình

  

  có bao nhiêu nghiệm thuộc khoảng

  

  ?

• Số nghiệm của phương trình

  

  trong đoạn

  

  là:

• Các họ nghiệm của phương trình

  

  là:

• Nghiệm âm lớn nhất của phương trình

  

  là:

• Giải phương trình

  

  .

• Từ phương trình

  

  , ta tìm được

  

  có giá trị bằng:

• Phương trình

  

  có tập nghiệm trùng với tập nghiệm của phương trình nào sau đây?

• Nghiệmcủaphươngtrình

  

  thỏađiềukiện:

  

• Cho phương trình

  

  . Khẳng định nào dưới đây là đúng:

• Nghiêm của phương trình

  

  là:

• Biến đổi phương trình

  

  về dạng

  

  với

  

  ,

  

  thuộc khoảng

  

  . Tính

  

  .

• Tínhtổngtấtcảcácnghiệmcủaphươngtrình

  

  trongđoạn

  

  củaphươngtrình.

• Vớigiátrịnàocủa

  

  đểphươngtrình:

  

  cóđúng

  

  nghiệm

  

• Cho phương trình

  

  và các họ số thực:. I.

  

  ,

  

  . II.

  

  ,

  

  . III.

  

  ,

  

  .IV.

  

  ,

  

  . Chọn trả lời đúng: Nghiệm của phương trình là:

• Tính tổng

  

  của các nghiệm của phương trình

  

  trên đoạn

  

  .

• Số nghiệm thuộc khoảng

  

  của phương trình:

  

  là:

• Cho phương trình

  

  . Tìm m để phương trình có nghiệm.

• Phương trình nào sau đây vô nghiệm?

• Phương trình

  

  có các họ nghiệm là

• Cho

  

  thỏa mãn phương trình

  

  . Tính

  

• Tìm tham số mđể phương trình

  

  vô nghiệm.

• Nghiệm của phương trình

  

  là:

• Nghiệm của phương trình

  

  là:

• Cho

  

  thỏa mãn

  

  Giá trị

  

  bằng

• Tổng các nghiệm của phương trình

  

  trên

  

  là:

• Tổng nghiệm âm lớn nhất và nghiệm dương nhỏ nhất của phương trình

  

  là

• Gọi

  

  là tập hợp tất cả các giá trị của tham số

  

  để phương trình

  

  có đúng hai nghiệm thuộc khoảng

  

  . Hỏi

  

  là tập con của tập hợp nào dưới đây

• Giải phương trình

  

  .

• Phương trình

  

  có các nghiệm là:

• Số nghiệm của phương trình

  

  là:

• Gọi

  

  là nghiệm âm lớn nhất của

  

  . Mệnh đề nào sau đây là đúng?

• Phươngtrình

  

  cónghiệmthỏa

  

  là:

• Phương trình

  

  :

• Phương trình

  

  có nghiệm là:

• Nghiệm của phương trình

  

  là:

• Có tất cả bao nhiêu giá trị nguyên của tham số

  

  để phương trình

  

  có nghiệm?

• Số vị trí biểu diễn các nghiệm của phương trình

  

  trên đường tròn lượng giác là?

Một số câu hỏi khác có thể bạn quan tâm.

• Xét 3 tế bào sinh dục trong một cá thể ruối giấm đực có kiểu gen AB/abDe/dE. Gen A cách gen B 15cM, gen D cách gen E 20cM. Ba tế bào trên giảm phân tạo ra số loại tinh trùng tối đa có thể là:

• Một hợp tử lưỡng bội tiến hành nguyên phân, trong lần nguyên phân thứ hai, ở một tế bào có một NST ở cặp số 1 không phân li, các cặp nhiễm sắc thể khác phân li bình thường, những lần nguyên phân tiếp theo diễn ra bình thường. Hợp tử này phát triển thành phôi, phôi này có bao nhiêu loại tế bào khác nhau về số lượng nhiễm sắc thể?

• Nếu trong quá trình giảm phân ở tất cả các tế bào sinh trứng của châu chấu cái (2n=24) đều hoàn toàn bình thường, còn ở tất cả các tế bào sinh tinh của châu chấu đực đều không có sự phân li của nhiễm sắc thể giới tính thì tính theo lí thuyết, khi 2 con châu chấu này giao phối với nhau sẽ tạo ra loại hợp tử chứa 23 nhiễm sắc thể với tỉ lệ là:

• Xét một cơ thể đực có kiểu gen

  

  , trong quá trình giảm phân bình thường hình thành giao tử, có 10% số tế bào chỉ xảy ra hoán vị giữa A và a, 20% số tế bào chỉ xảy ra hoán vị giữa E và e, số tế bào còn lại không xảy ra hoán vị gen. Theo lí thuyết, trong tổng số giao tử, loại tinh trùng mang kiểu gen abde chiếm tỉ lệ là:

• Cho hình ảnh về một giai đoạn trong quá trình phân bào của một tế bào lưỡng bội 2n bình thường (tế bào A) trong cơ thể đực ở một loài và một số nhận xét tương ứng như sau:

  

  (1) Tế bào A mang có chứa ít nhất là hai cặp gen dị hợp.

  (2) Bộ NST lưỡng bội bình thường của loài là 2n = 8.

  (3) Tế bào A có xảy ra trao đổi chéo trong quá trình giảm phân 1.

  (4) Tế bào A tạo ra tối đa là 4 loại giao tử khác nhau về các gen đang xét.

  (5) Tế bào A không thể tạo được giao tử bình thường.

  Biết đột biến nếu có chỉ xảy ra 1 lần, số phát biểu đúng là:

• Tỉ lệ giao tử BBBB/BBBb/BBbb sinh ra từ cơ thể có kiểu gen BBBBBBbb là:

• Một cơ thể có kiểu gen

  

  giảm phân hình thành giao tử, trong quá trình đó một số tế bào không phân li trong giảm phân II. Số loại giao tử tối đa mà cơ thể đó có thể tạo ra là

• Một cá thể ở một lòai động vật có bộ nhiễm sắc thể 2n = 4. Khi quan sát quá trình giảm phân 2000 tế bào sinh tinh, người ta thấy 20 tế bào có cặp nhiễm sắc thế số 1 không phân li trong giảm phân I, các sự kiện khác trong giảm phân diễn ra bình thường, các tế bào còn lại giảm phân bình thường. Theo lí thuyết, trong tổng số giao tử được tạo thành từ quá trình trên thì số giao tử có 3 nhiễm sắc thể có tỉ lệ.

• Quá trình giảm phân của cơ thể có kiểu gen

  

  xảy ra hoán vị với tần số 25%. Loại giao tử hoán vị được tạo ra là

• Ở một loài thú, xét các tế bào sinh tinh của một cơ thể có kiểu gen

  

  giảm phân hình thành giao tử đã tạo ra loại giao tử AbDEXR chiếm tỉ lệ 2% trong tổng số giao tử tạo thành. Theo lí thuyết, số % tế bào đã xảy ra hoán vị gen là

Chia sẻ

Một số câu hỏi khác cùng bài thi.

• Tìm số giá trị nguyên của

  

  để phương trình :

  

  có nghiệm duy nhất

• Tìm m để phương trình

  

  có ba nghiệm phân biệt.

• Tìm

  

  để phương trình

  

  có hai nghiệm

  

  ,

  

  là độ dài các cạnh góc vuông của một tam giác vuông với cạnh huyền có độ dài bằng

  

  là

• Tìm các giá trị của tham số

  

  để phương trình

  

  vô nghiệm.

• Cóbaonhiêugiátrịnguyêncủathamsốm thuộcđoạn

  

  đểhệphươngtrình

  

  cónghiệm?

• Cho biết tập hợp tất cả các giá trị của tham số

  

  để phương trình

  

  có nghiệm là

  

  , với

  

  ,

  

  là các số nguyên dương và

  

  là phân số tối giản. Tính

  

• Hỏi có bao nhiêu giá trị

  

  nguyên trong nửa khoảng

  

  để phương trình

  

  có hai nghiệm phân biệt?

• Để phương trình sau cónghiệm duy nhất:

  

  , Giá trị của tham số

  

  là

• Với mọi giá trị dương của m phương trình

  

  luôn có số nghiệm là

• Cho phương trình

  

  

  . Với giá trị nào của

  

  thì

  

  có

  

  nghiệm

  

  ,

  

  thỏa

  

  ?

• Có bao nhiêu giá trị nguyên của m để phương trình

  

  có nghiệm?

• Cho phương trình

  

  . Phương trình có nghiệm khi

• Tìm giá trị của tham số

  

  để phương trình

  

  có hai nghiệm trái dấu.

• Để phương trình sau có 4 nghiệm phân biệt:

  

  . Giá trị của tham số

  

  là:

• Giátrịcủa

  

  đểphương trình

  

  có 4 nghiệm thực phân biệt là:

• Số giá trị nguyên của tham số thực

  

  thuộc đoạn

  

  để phương trình

  

  vô nghiệm là

• Giả sử phương trình

  

  (với

  

  là tham số) có hai nghiệm

  

  ,

  

  . Tìm giá trị nhỏ nhất của biểu thức

  

  .

• Tìm tập hợp tất cả các giá trị thực của tham số

  

  để phương trình

  

  có đúng hai nghiệm thực.

• Xác định

  

  để phương trình

  

  có ba nghiệm phân biệt lớn hơn

  

• Cho đồthịhàmsố

  

  (hìnhvẽbên).

  

  Dựavàođồthị

  

  xácđịnhsốgiátrịnguyêndươngcủam đểphươngtrình

  

  cónghiệm

  

• Để phương trình sau cónghiệm duy nhất:

  

  , Giá trị của tham số

  

  là

• Có tất cả bao nhiêu giá trị nguyên của tham số m (biết

  

  ) để hệ phương trình sau có nghiệm thực?

  

• Tìmtấtcảcácgiátrịcủathamsố

  

  đểphươngtrình

  

  cóhainghiệm

  

  ,

  

  thỏamãn

  

• Cho hệ phương trình :

  

  . Để hệ này vô nghiệm, điều kiện thích hợp cho tham số

  

  là :

• Sốcácgiátrịnguyêncủa

  

  đểphươngtrình

  

  cóhainghiệmphânbiệtlà

Một số câu hỏi khác có thể bạn quan tâm.

• Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct answer to each of the questions:

  Life originated in the early seas less than a billion years after the Earth was formed. Yet another three billion years were to pass before the first plants and animals appeared on the continents. Life’s transition from the sea to the land was perhaps as much of an evolutionary challenge as was the genesis of life. What forms of life were able to make such a drastic change in lifestyle? The traditional view of the first terrestrial organisms is based on megafossils-relatively large specimens of essentially whole plants and animals. Vascular plants, related to modern seed plants and ferns, left the first comprehensive megafossil record. Because of this, it has been commonly assumed that the sequence of terrestrialization reflected the evolution of modern terrestrial ecosystems. In this view, primitive vascular plants first colonized the margins of continental waters, followed by animals that feed on the plants, and lastly by animals that preyed on the plant-eaters. Moreover, the megafossils suggest that terrestrial life appeared and diversified explosively near the boundary between the Silurian and the Devonian periods, a little more than 400 million years ago. Recently, however, paleontologists have been taking a closer look at the sediments below this Silurian-Devonian geological boundary. It turns out that some fossils can be extracted from these sediments by putting the rocks in an acid bath. The technique has uncovered new evidence form sediments that were deposited near the shores of the ancient oceans- plant microfossils and microscopic pieces of small animals. In many instances the specimens are less than one-tenth of a millimeter in diameter. Although they were entombed in the rocks for hundreds of millions of years, many of them fossils consist of the organic remains of the organism. These newly discovered fossils have not only revealed the existence of previously unknown organisms, but have also pushed back these dates for the invasion of land by multicellular organisms. Our views about the nature of the early plant and animal communities are now being revised. And with those revisions come new speculations about the first terrestrial life-forms.

  Question:With which of the following conclusions would the author probably agree?

• Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct answer to each of the questions:

  Life originated in the early seas less than a billion years after the Earth was formed. Yet another three billion years were to pass before the first plants and animals appeared on the continents. Life’s transition from the sea to the land was perhaps as much of an evolutionary challenge as was the genesis of life. What forms of life were able to make such a drastic change in lifestyle? The traditional view of the first terrestrial organisms is based on megafossils-relatively large specimens of essentially whole plants and animals. Vascular plants, related to modern seed plants and ferns, left the first comprehensive megafossil record. Because of this, it has been commonly assumed that the sequence of terrestrialization reflected the evolution of modern terrestrial ecosystems. In this view, primitive vascular plants first colonized the margins of continental waters, followed by animals that feed on the plants, and lastly by animals that preyed on the plant-eaters. Moreover, the megafossils suggest that terrestrial life appeared and diversified explosively near the boundary between the Silurian and the Devonian periods, a little more than 400 million years ago. Recently, however, paleontologists have been taking a closer look at the sediments below this Silurian-Devonian geological boundary. It turns out that some fossils can be extracted from these sediments by putting the rocks in an acid bath. The technique has uncovered new evidence form sediments that were deposited near the shores of the ancient oceans- plant microfossils and microscopic pieces of small animals. In many instances the specimens are less than one-tenth of a millimeter in diameter. Although they were entombed in the rocks for hundreds of millions of years, many of them fossils consist of the organic remains of the organism. These newly discovered fossils have not only revealed the existence of previously unknown organisms, but have also pushed back these dates for the invasion of land by multicellular organisms. Our views about the nature of the early plant and animal communities are now being revised. And with those revisions come new speculations about the first terrestrial life-forms.

  Question:Which of the following resulted from the discovery of microscopic fossils?

• Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct answer to each of the questions:

  Life originated in the early seas less than a billion years after the Earth was formed. Yet another three billion years were to pass before the first plants and animals appeared on the continents. Life’s transition from the sea to the land was perhaps as much of an evolutionary challenge as was the genesis of life. What forms of life were able to make such a drastic change in lifestyle? The traditional view of the first terrestrial organisms is based on megafossils-relatively large specimens of essentially whole plants and animals. Vascular plants, related to modern seed plants and ferns, left the first comprehensive megafossil record. Because of this, it has been commonly assumed that the sequence of terrestrialization reflected the evolution of modern terrestrial ecosystems. In this view, primitive vascular plants first colonized the margins of continental waters, followed by animals that feed on the plants, and lastly by animals that preyed on the plant-eaters. Moreover, the megafossils suggest that terrestrial life appeared and diversified explosively near the boundary between the Silurian and the Devonian periods, a little more than 400 million years ago. Recently, however, paleontologists have been taking a closer look at the sediments below this Silurian-Devonian geological boundary. It turns out that some fossils can be extracted from these sediments by putting the rocks in an acid bath. The technique has uncovered new evidence form sediments that were deposited near the shores of the ancient oceans- plant microfossils and microscopic pieces of small animals. In many instances the specimens are less than one-tenth of a millimeter in diameter. Although they were entombed in the rocks for hundreds of millions of years, many of them fossils consist of the organic remains of the organism. These newly discovered fossils have not only revealed the existence of previously unknown organisms, but have also pushed back these dates for the invasion of land by multicellular organisms. Our views about the nature of the early plant and animal communities are now being revised. And with those revisions come new speculations about the first terrestrial life-forms.

  Question:The word “entombed” is closest in meaning to ______

• Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct answer to each of the questions:

  Life originated in the early seas less than a billion years after the Earth was formed. Yet another three billion years were to pass before the first plants and animals appeared on the continents. Life’s transition from the sea to the land was perhaps as much of an evolutionary challenge as was the genesis of life. What forms of life were able to make such a drastic change in lifestyle? The traditional view of the first terrestrial organisms is based on megafossils-relatively large specimens of essentially whole plants and animals. Vascular plants, related to modern seed plants and ferns, left the first comprehensive megafossil record. Because of this, it has been commonly assumed that the sequence of terrestrialization reflected the evolution of modern terrestrial ecosystems. In this view, primitive vascular plants first colonized the margins of continental waters, followed by animals that feed on the plants, and lastly by animals that preyed on the plant-eaters. Moreover, the megafossils suggest that terrestrial life appeared and diversified explosively near the boundary between the Silurian and the Devonian periods, a little more than 400 million years ago. Recently, however, paleontologists have been taking a closer look at the sediments below this Silurian-Devonian geological boundary. It turns out that some fossils can be extracted from these sediments by putting the rocks in an acid bath. The technique has uncovered new evidence form sediments that were deposited near the shores of the ancient oceans- plant microfossils and microscopic pieces of small animals. In many instances the specimens are less than one-tenth of a millimeter in diameter. Although they were entombed in the rocks for hundreds of millions of years, many of them fossils consist of the organic remains of the organism. These newly discovered fossils have not only revealed the existence of previously unknown organisms, but have also pushed back these dates for the invasion of land by multicellular organisms. Our views about the nature of the early plant and animal communities are now being revised. And with those revisions come new speculations about the first terrestrial life-forms.

  Question:What is the following paragraph likely to discuss?

• Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct answer to each of the questions:

  Under certain circumstances, the human body must cope with gases at greater-than-normal atmospheric pressure. For example, gas pressures increase rapidly during a drive made with scuba gear because the breathing equipment allows divers to stay underwater longer and dive deeper. The pressure exerted on the human body increases by 1 atmosphere for every 10 meters of depth on seater, so thay at 39 meters in seawater a diver is exposed to pressure of about 4 atmosphere. The pressure of the gases being breathed must equal the external pressure applied to the body, otherwise breathing is very difficult. Therefore all of the gases in the air breathed by a scuba diver at 40 meter are present at five times their usual pressure. Nitrogen, which composes 80 percent of the air we breathe, usually causes a balmy feeling of well-being at this pressure. At a depth of 5 atmosphere, nitrogen causes symptoms resembling alcohol intoxication, known as nitrogen narcosis. Nitrogen narcosis apparently results from a direct effect on the brain of the large amounts of nitrogen dissolved in the blood. Deep dives are less dangerous if helium is substituted for nitrogen, because under these pressures helium does not exert a similar narcotic effect. Asa scuba diver descends, the pressure of nitrogen on the lungs increases. Nitrogen then diffuses from the lungs to the blood, and from the blood to body tissues. The reverse occurs when the diver surfaces, the nitrogen pressure in the lungs falls and the nitrogen diffuses from the tissues into the blood, and from the blood into the lungs. If the return to the surface is too rapid, nitrogen in the tissues and blood cannot diffuse out rapidly enough and nitrogen bubbles are formed. They can cause severe pains, particularly around the joints. Another complication may result if the breath is held during ascent. During ascent from a depth of 10 meters, the volume of air in the lungs will double because the air pressure at the surface is only half of what it was at 10 meters. This change in volume may cause the lungs to distend ang even rupture. This the rise of the exhaled air bubbles, and must exhale during ascent.

  Question:It can be inferred from the passage that which of the following presents the greatest danger to a diver?

• Read the following passage and mark the letter A, B, C, or D on your answer sheet to indicate the correct answer to each of the questions:

  Under certain circumstances, the human body must cope with gases at greater-than-normal atmospheric pressure. For example, gas pressures increase rapidly during a drive made with scuba gear because the breathing equipment allows divers to stay underwater longer and dive deeper. The pressure exerted on the human body increases by 1 atmosphere for every 10 meters of depth on seater, so thay at 39 meters in seawater a diver is exposed to pressure of about 4 atmosphere. The pressure of the gases being breathed must equal the external pressure applied to the body, otherwise breathing is very difficult. Therefore all of the gases in the air breathed by a scuba diver at 40 meter are present at five times their usual pressure. Nitrogen, which composes 80 percent of the air we breathe, usually causes a balmy feeling of well-being at this pressure. At a depth of 5 atmosphere, nitrogen causes symptoms resembling alcohol intoxication, known as nitrogen narcosis. Nitrogen narcosis apparently results from a direct effect on the brain of the large amounts of nitrogen dissolved in the blood. Deep dives are less dangerous if helium is substituted for nitrogen, because under these pressures helium does not exert a similar narcotic effect. Asa scuba diver descends, the pressure of nitrogen on the lungs increases. Nitrogen then diffuses from the lungs to the blood, and from the blood to body tissues. The reverse occurs when the diver surfaces, the nitrogen pressure in the lungs falls and the nitrogen diffuses from the tissues into the blood, and from the blood into the lungs. If the return to the surface is too rapid, nitrogen in the tissues and blood cannot diffuse out rapidly enough and nitrogen bubbles are formed. They can cause severe pains, particularly around the joints. Another complication may result if the breath is held during ascent. During ascent from a depth of 10 meters, the volume of air in the lungs will double because the air pressure at the surface is only half of what it was at 10 meters. This change in volume may cause the lungs to distend ang even rupture. This the rise of the exhaled air bubbles, and must exhale during ascent.

  Question:What happens to nitrogen in body tissues if a diver ascends too quickly?

• Read the following passage and mark the letter A, B, C, or D to indicate the correct answer to each of the questions:

  Harvard University, today recognized as part of the top echelon of the world's universities, came from very inauspicious and humble beginning.

  This oldest of American universities was founded in 1636, just sixteen years after the Pilgrims landed at Plymouth. Included in the Puritan emigrants to the Massachusetts colony during this period were more than 100 graduates of England's prestigious Oxford and Cambridge universities, and these universities graduates in the New Word were determined that their sons would have the same educational opportunities that they themselves had had. Because of this support in the colony for an institution of higher learning, the General Court of Massachusetts appropriated 400 pounds for a college in October of 1636 and early the following year decided on a parcel of land for the school; this land was in an area called Newetowne, which was later renamed Cambridge after its English cousin and is the site of the present-day university.

  When a young minister named John Harvard, who came from the neighboring town of Charlestowne, died from tuberculosis in 1638, he willed half of his estate of 1,700 pounds to the fledgling college. In spite of the fact that only half of the bequest was actually paid, the General Court named the college after the minister in appreciation for what he had done. The amount of the bequest may not have been large, particularly by today's standard, but it was more than the General Court had found it necessary to appropriate in order to open the college.

  Henry Dunster was appointed the first president of Harvard in 1640, and it should be noted that in addition to serving as president, he was also the entire faculty, with an entering freshmen class of four students. Although the staff did expandsomewhat, for the first century of its existence the entire teaching staff consisted of the president and three or four tutors.

  Question: The passage indicates that Harvard is ____________.

• Read the following passage and mark the letter A, B, C, or D to indicate the correct answer to each of the questions:

  Harvard University, today recognized as part of the top echelon of the world's universities, came from very inauspicious and humble beginning.

  This oldest of American universities was founded in 1636, just sixteen years after the Pilgrims landed at Plymouth. Included in the Puritan emigrants to the Massachusetts colony during this period were more than 100 graduates of England's prestigious Oxford and Cambridge universities, and these universities graduates in the New Word were determined that their sons would have the same educational opportunities that they themselves had had. Because of this support in the colony for an institution of higher learning, the General Court of Massachusetts appropriated 400 pounds for a college in October of 1636 and early the following year decided on a parcel of land for the school; this land was in an area called Newetowne, which was later renamed Cambridge after its English cousin and is the site of the present-day university.

  When a young minister named John Harvard, who came from the neighboring town of Charlestowne, died from tuberculosis in 1638, he willed half of his estate of 1,700 pounds to the fledgling college. In spite of the fact that only half of the bequest was actually paid, the General Court named the college after the minister in appreciation for what he had done. The amount of the bequest may not have been large, particularly by today's standard, but it was more than the General Court had found it necessary to appropriate in order to open the college.

  Henry Dunster was appointed the first president of Harvard in 1640, and it should be noted that in addition to serving as president, he was also the entire faculty, with an entering freshmen class of four students. Although the staff did expandsomewhat, for the first century of its existence the entire teaching staff consisted of the president and three or four tutors.

  Question: It can be inferred from the passage that the Puritans who traveled to the Massachusetts colony were ______________.

• Mark the letter A, B, C or D on your answer sheet to indicate the correct answer to each of the following question.

  If_____, the Xmas tree would look more impressive.

• Harvard University, today recognized as part of the top echelon of the world's universities, came from very inauspicious and humble beginning. This oldest of American universities was founded in 1636, just sixteen years after the Pilgrims landed at Plymouth. Included in the Puritan emigrants to the Massachusetts colony during this period were more than 100 graduates of England's prestigious Oxford and Cambridge universities, and these universities graduates in the New Word were determined that their sons would have the same educational opportunities that they themselves had had. Because of this support in the colony for an institution of higher learning, the General Court of Massachusetts appropriated 400 pounds for a college in October of 1636 and early the following year decided on a parcel of land for the school; this land was in an area called Newetowne, which was later renamed Cambridge after its English cousin and is the site of the present-day university. When a young minister named John Harvard, who came from the neighboring town of Charlestowne, died from tuberculosis in 1638, he willed half of his estate of 1,700 pounds to the fledgling college. In spite of the fact that only half of the bequest was actually paid, the General Court named the college after the minister in appreciation for what he had done. The amount of the bequest may not have been large, particularly by today's standard, but it was more than the General Court had found it necessary to appropriate in order to open the college. Henry Dunster was appointed the first president of Harvard in 1640, and it should be noted that in addition to serving as president, he was also the entire faculty, with an entering freshmen class of four students. Although the staff did expand somewhat, for the first century of its existence the entire teaching staff consisted of the president and three or four tutors.

  The main idea of this passage is that ______________ .