高等数学 英文试题A
英文 高数题
英文高数题Mathematics has always been a subject that challenges and intrigues students around the world. From the basic arithmetic operations to the complex theories and formulas, mathematics is a language of its own, requiring a unique set of skills and understanding. One particular aspect of mathematics that has captured the attention of many students is the realm of English mathematics problems.English mathematics problems, also known as word problems, are a unique and often perplexing subset of mathematical challenges. These problems present a scenario or a real-world situation and require the solver to translate the given information into mathematical terms and then apply appropriate mathematical operations to arrive at the solution.The appeal of English mathematics problems lies in the fact that they not only test one's mathematical abilities but also their language comprehension and problem-solving skills. Unlike traditional numerical problems, where the focus is solely on the application of mathematical concepts, English mathematics problems demand adeeper understanding of the problem statement, the ability to extract the relevant information, and the skill to construct a mathematical model that accurately represents the given scenario.One of the primary challenges in solving English mathematics problems is the need to interpret and understand the problem statement. Often, these problems are written in a way that can be ambiguous or confusing, requiring the solver to carefully read and analyze the information provided. This process of deciphering the problem statement is crucial, as it lays the foundation for the subsequent steps in the problem-solving process.Another significant challenge in English mathematics problems is the ability to translate the given information into mathematical terms. This process, known as "mathematization," involves identifying the relevant variables, formulating the appropriate equations or expressions, and establishing the relationships between the different elements of the problem. This step requires a deep understanding of mathematical concepts and the ability to apply them in a practical context.Once the problem has been translated into mathematical terms, the solver must then apply the appropriate mathematical operations to arrive at the solution. This step can be particularly challenging, as the complexity of the problem and the interplay between the variousmathematical concepts can make it difficult to determine the correct approach.Despite these challenges, the benefits of solving English mathematics problems are numerous. By engaging with these types of problems, students not only improve their mathematical skills but also develop critical thinking, problem-solving, and language comprehension abilities. These skills are highly valuable not only in the academic setting but also in the professional world, where the ability to tackle complex problems and communicate effectively is highly sought after.Moreover, the practice of solving English mathematics problems can also help students develop a deeper appreciation for the practical applications of mathematics in the real world. By connecting mathematical concepts to real-life scenarios, students can better understand the relevance and importance of mathematics in various fields, from engineering and science to finance and economics.In conclusion, English mathematics problems are a unique and challenging aspect of the mathematical landscape. While they may present significant obstacles, the rewards of mastering these problems are substantial, both in terms of academic achievement and the development of essential life skills. As students continue to engage with these problems, they will not only improve theirmathematical abilities but also gain a deeper understanding of the world around them and the role that mathematics plays in shaping it.。
高中数学英文试题及答案
高中数学英文试题及答案High School Mathematics English Exam Questions and AnswersQuestion 1:Solve the following quadratic equation for x:\[ 2x^2 - 7x + 3 = 0 \]Answer 1:To solve the quadratic equation \( 2x^2 - 7x + 3 = 0 \), we can use the quadratic formula:\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]where \( a = 2 \), \( b = -7 \), and \( c = 3 \). Plugging in the values, we get:\[ x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4(2)(3)}}{2(2)} \]\[ x = \frac{7 \pm \sqrt{49 - 24}}{4} \]\[ x = \frac{7 \pm \sqrt{25}}{4} \]\[ x = \frac{7 \pm 5}{4} \]So, the solutions are \( x = 3 \) and \( x = \frac{1}{2} \).Question 2:Find the derivative of the function \( f(x) = 3x^4 - 2x^3 + x^2 + 5 \).Answer 2:To find the derivative of the function \( f(x) = 3x^4 - 2x^3 + x^2 + 5 \), we apply the power rule for derivatives:\[ f'(x) = 4 \cdot 3x^3 - 3 \cdot 2x^2 + 2 \cdot x + 0 \]\[ f'(x) = 12x^3 - 6x^2 + 2x \]Question 3:Evaluate the definite integral of the function \( g(x) = 4x - 3 \) from \( x = 1 \) to \( x = 4 \).Answer 3:To evaluate the definite integral of \( g(x) = 4x - 3 \) from \( x = 1 \) to \( x = 4 \), we integrate the function and then subtract the value of the integral at the lower limit from the value at the upper limit:\[ \int_{1}^{4} (4x - 3) \, dx = \left[ 2x^2 - 3x\right]_{1}^{4} \]\[ = (2 \cdot 4^2 - 3 \cdot 4) - (2 \cdot 1^2 - 3 \cdot 1) \] \[ = (32 - 12) - (2 - 3) \]\[ = 20 - (-1) \]\[ = 21 \]Question 4:Simplify the expression \( \frac{2x^2 - 4x + 2}{x - 1} \) by factoring.Answer 4:To simplify the expression \( \frac{2x^2 - 4x + 2}{x - 1} \), we factor out the greatest common factor from the numerator: \[ \frac{2(x^2 - 2x + 1)}{x - 1} \]Notice that the numerator is a perfect square trinomial:\[ \frac{2(x - 1)^2}{x - 1} \]Now, we can cancel out the common factor \( (x - 1) \) from the numerator and denominator:\[ 2(x - 1) \]So, the simplified expression is \( 2x - 2 \).Question 5:Determine the equation of the line that passes through the points \( (2, 3) \) and \( (-1, -2) \).Answer 5:To find the equation of the line passing through the points \( (2, 3) \) and \( (-1, -2) \), we first find the slope \( m \) of the line:\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 3}{-1 - 2} = \frac{-5}{-3} = \frac{5}{3} \]Now, using the point-slope form of a line equation \( y - y_1 = m(x - x_1) \), we can plug in one of the points and the。
高考数学英语真题试卷
高考数学英语真题试卷Part I: Multiple Choice QuestionsInstructions: For each of the following questions, choose the best answer from the options given.1. If x + 5 = 9, what is the value of x?A. 14B. 4C. 9D. -42. Find the value of y in the following equation: 2y - 3 = 11A. 10B. 7C. 5D. 93. What is the slope of the line passing through the points (2, 4) and (6, 10)?A. 2B. 3C. 4D. 54. Solve the following inequality: 3x + 7 < 16A. x < 3B. x > 3C. x < 9D. x > 95. If the volume of a cube is 27 cubic centimeters, what is the length of one side of the cube?A. 3 cmB. 4 cmC. 5 cmD. 6 cmPart II: Short Answer QuestionsInstructions: Answer each of the following questions with a concise and clear response.6. If the equation of a line is y = 2x + 3, what is the slope of the line and the y-intercept?7. Find the roots of the quadratic equation x^2 - 5x + 6 = 0.8. The shape of a triangle has angles measuring 30 degrees, 60 degrees, and 90 degrees. What type of triangle is it?9. Simplify the expression: (2x^2 - 3x + 5) - (x^2 + 2x - 1).Part III: Long Answer QuestionsInstructions: Answer each of the following questions in detail, showing all work and calculations.10. A quadratic equation is given by x^2 - 4x - 5 = 0. Use the quadratic formula to find the roots of the equation.11. A circle has a radius of 5 centimeters. Calculate the area and circumference of the circle.12. Given the equation of a line as y = 3x + 2, find a point on the line and determine the x-intercept.13. A rectangular garden has dimensions of 8 meters by 12 meters. Find the perimeter and area of the garden.14. Solve the system of equations:3x - 2y = 42x + y = 1015. A ball is thrown into the air with an initial velocity of 20 m/s. The height h of the ball at time t is given by the equation h = -5t^2 + 20t. How long does it take for the ball to reach its maximum height?End of ExamNote: This practice exam is intended for review purposes only. Good luck with your preparation for the upcoming math and English exams!。
高一数学英文考试卷
高一数学英文考试卷High School Mathematics Exam for Grade 10 - English VersionInstructions:- Answer all questions in English.- Show all your working out in your answer sheet.- Use the back of the page if necessary.Section A: Multiple Choice Questions (20 marks)1. What is the value of \( x \) in the equation \( 3x + 5 =20 \)?A) 3B) 4C) 5D) 62. The sum of two numbers is 10. If one number is 4, what is the other number?A) 6B) 5C) 4D) 33. Which of the following is not a quadratic equation?A) \( x^2 + 3x + 2 = 0 \)B) \( 2y^2 - 3y + 1 = 0 \)C) \( 5z + 7 = 0 \)D) \( 4w^2 + 6w + 2 = 0 \)4. The graph of the function \( f(x) = x^2 \) is:A) A straight lineB) A parabola opening upwardsC) A parabola opening downwardsD) A hyperbola5. What is the slope of the line represented by the equation \( y = 2x + 3 \)?A) 2B) 3C) -2D) -3... (Continue with 15 more multiple choice questions) ...Section B: Short Answer Questions (30 marks)1. Simplify the expression \( \frac{3x^2 - 7x + 2}{x - 1} \) by factoring.2. Solve the system of equations:\[\begin{cases}x + y = 5 \\2x - y = 1\end{cases}\]3. Find the vertex of the parabola given by the equation \( y= -3(x - 2)^2 + 5 \).4. Convert the decimal 0.75 to a fraction in simplest form.5. Determine the equation of the line that passes through the points (2, 3) and (-1, -2).... (Continue with 5 more short answer questions) ...Section C: Long Answer Questions (50 marks)1. A rectangular garden is to be enclosed with a fence. If the length of the garden is 10 meters more than twice its width, and the perimeter is 56 meters, find the dimensions of the garden.2. A company produces two types of widgets. The cost to produce one widget of type A is $3, and the cost to produce one widget of type B is $5. If the company has a budget of $250 to spend on production and they want to produce at least 20 widgets of type A, how many of each type should they produce to minimize costs?3. A ball is thrown vertically upwards with an initial velocity of 20 meters per second. The height \( h \) of the ball after \( t \) seconds can be modeled by the equation\( h(t) = -5t^2 + 20t \). Find the time it takes for the ball to reach its maximum height and what that height is.4. A sequence is defined by the recursive formula \( a_n =4a_{n-1} - 3 \) with the first term \( a_1 = 1 \). Find thefirst 5 terms of the sequence.5. Prove that the square of any odd integer can be expressed as the sum of two consecutive even numbers.... (Continue with 5 more long answer questions) ...Section D: Essay Questions (Bonus - 10 marks)1. Discuss the importance of mathematical literacy in everyday life and how it can be beneficial in various professions.2. Explain how mathematical models are used in predicting natural phenomena, such as weather patterns or population growth.End of ExamPlease ensure you have answered all questions and handed in your completed answer sheet. Good luck!。
高等数学 英文试题A
西南大学课程考核《高等数学IA 》课程试题 【A 】卷(1) The function 414)(-=x x f at x = 4 is ( ). A. not continuous, f (4) does not exist and )(lim 4x f x → does not exist. B. continuous.C. not continuous, )(lim 4x f x → exists but f (4) does not existD. not continuous, )(lim 4x f x → and f (4) exist but )4()(lim 4f x f x ≠→.(2) For the function y = arcsin x , we have the assert ( ).A ．'y is undefined at x = -1 and x = 1, so its graph has not tangent lines at ⎪⎭⎫⎝⎛2π,1 and ⎪⎭⎫ ⎝⎛--2π,1.B ．since its graph has not tangent lines at ⎪⎭⎫ ⎝⎛2π,1 and ⎪⎭⎫ ⎝⎛--2π,1,'y is undefined at x = -1 and x = 1.C ．'y is defined at x = -1 and x = 1, and its graph has tangent lines at ⎪⎭⎫ ⎝⎛2π,1 and ⎪⎭⎫ ⎝⎛--2π,1.D ．'y is undefined at x = -1 and x = 1, and its graph has tangent lines at ⎪⎭⎫ ⎝⎛2π,1 and ⎪⎭⎫ ⎝⎛--2π,1.(3)=⎰x x x d )(ln 15( ) .A. C x x +-4)(ln 41 B.C x +-6)(ln 61. C. C x +-4)(ln 41 D. C x x +-6)(ln 61. (4) The definite integral=+⎰-x x xd 131132( ).A.334 B. 324. C. 423 D. 433 (5) Area of shaded region in the following figure is ( ).西南大学课程考核(试题【A】卷) ——————————————密————————————封————————————线——————————————A.332B.364. C.3128D. 323. Find the solutions for following problems by computing (8 points each，40 points in all)(1) Find the limitxxx2lnlim+∞→(2) Evaluate )0('+f, )0('-f and )0('f for⎩⎨⎧≥<-=,,)(2xxxxxf.Figure 2《高等数学IA 》课程试题 【A 】卷(3) Use the implicit differentiation to find xy d d for the equation xy y x 1833=+.(4) Find ⎪⎪⎭⎫ ⎝⎛⎰223d )sin(d d x t t x x .(5) Find the definite integral x xd e1⎰.西南大学课程考核(试题【A】卷)——————————————密————————————封————————————线——————————————4. Solve the following comprehensive problems (10 points each，30 points in all) (1) Evaluate the indefinite integral xx dln⎰.(2) Sketch the graph of 104)(34+-=xxxf using the detailed steps of the graphing procedure.《高等数学IA 》课程试题 【A 】卷(3) Show that the area of an ellipse defined by 12222=+by a x is ab π.Hint x x x 22sin 211cos 22cos -=-=。
高一英语高等数学基础概念练习题40题
高一英语高等数学基础概念练习题40题1.She has a beautiful _____.A.voiceB.soundC.noiseD.whisper答案解析：A。
“voice”通常指人的嗓音；“sound”泛指各种声音；“noise”是噪音；“whisper”是低语声。
这里说她有美丽的，应该是嗓音，所以选A。
2.The book is very _____.A.interestingB.interestedC.interestD.interestingly答案解析：A。
“interesting”表示“令人感兴趣的”，通常修饰物；“interested”表示“感兴趣的”，通常修饰人；“interest”是名词或动词；“interestingly”是副词。
这里书很有趣，修饰书用“interesting”，所以选A。
3.He is a _____ student.A.hard-workingB.work-hardC.hard-workD.working-hard答案解析：A。
“hard-working”是合成形容词，表示“勤奋的”；“work-hard”和“working-hard”不是正确的表达；“hard-work”是名词短语。
这里说他是一个勤奋的学生，用“hard-working”，所以选A。
4.There are many _____ in the park.A.peopleB.peoplesC.personD.persons答案解析：A。
“people”表示“人，人们”，是集合名词，本身就是复数形式；“peoples”表示“民族”；“person”是个体名词，单数形式；“persons”是“person”的复数形式，但通常较少使用。
这里说公园里有很多人，用“people”，所以选A。
5.The food tastes _____.A.goodB.wellC.badlyD.beautifully答案解析：A。
微积分 高等数学 英文练习题以及答案(1)
lim
n
sin n 0. n
(n 1, 2, ) 。
n
n
(4) xn sin
n ； 2
1 证：因为 sin x 1，所以 sin n n1 有界，而 lim 0 ，根 n n
据题目已知的结论有：
则 xn 1,
(n 1, 2, ) ，lim xn 1 ， 但是 lim xn 不存在。
3
Exercise 1-2 Limits of Sequences 1. Observe the behavior of the general term of each of the following sequences as n increases infinitely, determine the sequences that have limits and write out the limit if it exists: (1) xn
(7) xn cos
1 ； n
极限存在，为 1。
n 4 n 4 n 4 4 1 2 0.1 2 n n n( n 4 n) 2n
2 2
只要 n 20或n 5 即可。
2
xn a n .
(8) xn ln
1 . n
所以取 N 5 ， 则当 n N ， xn a 即 成立。
Xi’an Jiaotong-Liverpool University
Subgroup
Name
ID No.
1
Preliminaries: Functions 1. Find the natural domains of the following functions: (1)
英语高考数学试卷及答案
Section I: Listening Comprehension (25%)Part A: Short Conversations (5 questions, 5 points each)1. What is the man's problem?A. He can't find his wallet.B. He is late for work.C. He needs to buy a new phone.D. He lost his keys.2. What does the woman suggest the man do?A. Take a taxi.B. Wait for the bus.C. Walk to the office.D. Call his boss.3. How much is the shirt on sale for?A. $30.B. $40.C. $50.D. $60.4. What time does the train leave?A. 9:00 am.B. 10:00 am.C. 11:00 am.D. 12:00 pm.5. What is the woman's profession?A. Teacher.B. Nurse.C. Lawyer.D. Engineer.Part B: Long Conversations (5 questions, 5 points each)6. What is the main topic of the conversation?A. Travel plans.B. Health issues.C. Education.D. Career choices.7. Why does the man want to study abroad?A. To improve his English.B. To gain more work experience.C. To learn about different cultures.D. To earn more money.8. What are the woman's concerns about studying abroad?A. Language barriers.B. Cultural differences.C. Financial difficulties.D. Health problems.9. How does the woman plan to overcome these concerns?A. By taking language courses.B. By living with a local family.C. By saving money.D. By joining a study group.10. What advice does the woman give to the man?A. To be patient and persistent.B. To focus on his studies.C. To travel as much as possible.D. To seek help from his teachers.Section II: Use of English (15%)Part A: Vocabulary (10 questions, 10 points each)11. Choose the word that best completes the sentence.A. AdaptB. AdaptedC. AdaptingD. Adaptation12. Choose the word that best completes the sentence.A. CanceledB. CancelC. CancellationD. Canceledly13. Choose the word that best completes the sentence.A. AttitudeB. AttitudesC. AttitudinallyD. Attitudinally14. Choose the word that best completes the sentence.A. BenefitB. BenefitingC. BenefitedD. Beneficial15. Choose the word that best completes the sentence.A. ClarifyB. ClarifiedC. ClarifyingD. ClarificationPart B: Grammar (5 questions, 5 points each)16. Choose the correct form of the verb.A. I am going to __________ (be) late for the meeting.B. She __________ (go) to the store yesterday.C. They __________ (do) their homework last night.D. He __________ (have) a good time at the party.17. Choose the correct form of the verb.A. She __________ (be) a teacher for ten years.B. He __________ (go) to the gym every morning.C. They __________ (do) their best to win the game.D. I __________ (have) a lot of friends.18. Choose the correct form of the verb.A. They __________ (go) to the movies last night.B. She __________ (be) in the library.C. We __________ (do) our homework.D. You __________ (go) to the party?19. Choose the correct form of the verb.A. I __________ (do) my homework now.B. She __________ (be) a doctor.C. They __________ (go) to school.D. He __________ (have) a lot of friends.20. Choose the correct form of the verb.A. They __________ (do) their homework.B. She __________ (be) a teacher.C. I __________ (go) to the gym every morning.D. He __________ (have) a lot of friends.Section III: Reading Comprehension (30%)Passage 1 (5 questions, 5 points each)Read the following passage and answer the questions below.The importance of exercise cannot be overstated. Regular physicalactivity is essential for maintaining good health and preventing diseases. According to the World Health Organization (WHO), at least 150 minutes of moderate-intensity aerobic exercise or 75 minutes ofvigorous-intensity aerobic exercise per week is recommended for adults.Exercise has numerous benefits, including improving cardiovascular health, reducing the risk of chronic diseases such as heart disease, stroke, and diabetes, and improving mental health. Regular exercise canalso help with weight management, improve sleep quality, and boost overall well-being.However, despite the well-known benefits of exercise, many people still struggle to incorporate physical activity into their daily routine. Some common barriers to exercise include lack of time, lack of motivation, and lack of knowledge about the benefits of exercise.Questions:21. What is the main idea of the passage?A. Exercise is beneficial for physical and mental health.B. Regular exercise is essential for maintaining good health.C. Exercise can help prevent chronic diseases.D. Lack of exercise is a significant barrier to good health.22. According to the passage, how many minutes of exercise per week is recommended for adults?A. 30 minutesB. 60 minutesC. 90 minutesD. 150 minutes23. What are some of the benefits of regular exercise mentioned in the passage?A. Improved cardiovascular health and reduced risk of chronic diseases.B. Improved mental health and better sleep quality.C. Weight management and overall well-being.D. All of the above.24. What are some common barriers to exercise mentioned in the passage?A. Lack of time and motivation.B. Lack of knowledge about the benefits of exercise.C. Physical disabilities and health conditions.D. All of the above.25. What is the author's main purpose in writing this passage?A. To encourage people to exercise regularly.B. To inform readers about the benefits of exercise.C. To discuss the barriers to exercise.D. To compare different types of exercise.Section IV: Writing (20%)Task 1: Short Answer Questions (10 points)26. What is the main idea of the following sentence?"Regular exercise is essential for maintaining good health and preventing diseases."27. What is the purpose of the following sentence?"According to the World Health Organization (WHO), at least 150 minutes of moderate-intensity aerobic exercise or 75 minutes of vigorous-intensity aerobic exercise per week is recommended for adults."Task 2: Writing (10 points)Write a short essay on the following topic:"Exercise: Its Benefits and Challenges"You should write at least 100 words. Use the following outline as a guide:- Introduction: Briefly introduce the topic of exercise and its importance.- Body: Discuss the benefits of regular exercise, such as improved physical and mental health, weight management, and disease prevention.- Challenges: Identify some of the challenges people face when trying to incorporate exercise into their daily routine.- Conclusion: Summarize the main points and emphasize the importance of exercise in maintaining good health.。
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西南大学课程考核
《高等数学IA 》课程试题 【A 】卷
(1) The function 4
14
)(-=
x x f at x = 4 is ( ). A. not continuous, f (4) does not exist and )(lim 4
x f x → does not exist. B. continuous.
C. not continuous, )(lim 4
x f x → exists but f (4) does not exist
D. not continuous, )(lim 4
x f x → and f (4) exist but )4()(lim 4
f x f x ≠→.
(2) For the function y = arcsin x , we have the assert ( ).
A ．'
y is undefined at x = -1 and x = 1, so its graph has not tangent lines at ⎪⎭⎫
⎝⎛2π,
1 and ⎪⎭⎫ ⎝
⎛
--2π,1.
B ．since its graph has not tangent lines at ⎪⎭⎫ ⎝⎛2π,
1 and ⎪⎭⎫ ⎝
⎛
--2π,1,'y is undefined at x = -1 and x = 1.
C ．'
y is defined at x = -1 and x = 1, and its graph has tangent lines at ⎪⎭⎫ ⎝⎛2π,
1 and ⎪⎭⎫ ⎝⎛
--2π,1.
D ．'
y is undefined at x = -1 and x = 1, and its graph has tangent lines at ⎪⎭⎫ ⎝⎛2π,
1 and ⎪⎭⎫ ⎝
⎛
--2π,1.
(3)
=⎰x x x d )(ln 1
5( ) .
A. C x x +-
4
)(ln 41 B.
C x +-6)(ln 61
. C. C x +-
4)(ln 41 D. C x x +-6
)
(ln 61
. (4) The definite integral
=+⎰-x x x
d 131
1
32
( ).
A.
334 B. 324. C. 423 D. 4
33 (5) Area of shaded region in the following figure is ( ).
西南大学课程考核(试题【A】卷) ——————————————
密————————————
封
————————————
线——————————————
A.
3
32
B.
3
64
. C.
3
128
D. 32
3. Find the solutions for following problems by computing (8 points each，40 points in all)
(1) Find the limit
x
x
x2
ln
lim
+∞
→
(2) Evaluate )0('+f, )0('-f and )0('f for
⎩
⎨
⎧
≥
<
-
=
,
,
)
(
2x
x
x
x
x
f.
Figure 2
《高等数学IA 》课程试题 【A 】卷
(3) Use the implicit differentiation to find x
y d d for the equation xy y x 183
3=+.
(4) Find ⎪⎪⎭
⎫ ⎝⎛⎰2
23d )sin(d d x t t x x .
(5) Find the definite integral x x
d e
1
⎰.
西南大学课程考核(试题【A】卷)
——————————————
密————————————
封————————————
线——————————————4. Solve the following comprehensive problems (10 points each，30 points in all) (1) Evaluate the indefinite integral x
x d
ln
⎰.
(2) Sketch the graph of 10
4
)
(3
4+
-
=x
x
x
f usin
g the detailed steps of the graphing procedure.
《高等数学IA 》课程试题 【A 】卷
(3) Show that the area of an ellipse defined by 122
22=+b
y a x is ab π.
Hint x x x 2
2
sin 211cos 22cos -=-=。