14. Find the Maclaurin series of the function and its radius of convergence. (10%)

10. Find to the 1-st decimal place by the Newton's method with an initial guess of x0 =4. (5%) 

Ⅲ、11. Calculatc the itegmdxdzdy (10%)

12. Find the volume of the given solid under the surface z = xy and above the triangle with vertices (1, 1), (4, 1), and (1, 2). (10%)

13. Find the volume of the parallelepiped determined by vectors a =i+ j-k, b=i-j+k, c=i+j+k. (10%)

15. Evaluate the integral for by making an appropriate change of variables, where R is given by the inequality |xl+ly |≤1.(10%) 

Part A. Question Design (15%) Attention : You DON’T need to paraphrase or summarize the following passages. 1. Cloze (5 %) Directions : 1. Design a multiple-choice cloze test with FIVE blanks. Each question should have four answer options, with one correct answer and three distractors.2. Underline the part of speech if you want to leave it blank.3. Circle the correct answer to each question.       The Great Sphinx in the Giza desert is a mythological creature with the body of a lion and the head of a human being. This monumental statue is often regarded as a national symbol of Egypt, having guarded the famous Egyptian pyramids for 4,000 years. Nevertheless, the stone creature does not look like it did 4,000 years ago; wind, water, pollution, and human contact have slowly aged the rock. Scientists are now trying to restore it. They not only want it to look like it did when it was first built but also are looking for ways to keep it from deteriorating more than it has.      Fixing the Sphinx is not an easy job. It takes several years of planning before the work begins. Each stone in the Sphinx is carefully measured. Scientists use computers to help figure out the size and shape of each stone. Each old stone is given a number. Then, one by one, replacement stones are carved by hand, just like people did long ago, in the exact sizes and shapes as the ones they are replacing. When the new stones are ready, they are installed and the worn ones are removed.       Scientists are also worried about how to keep the Sphinx from falling apart again. However, there is no easy solution to the problem, not to mention a solution that is agreeable to all parties. The one thing that is agreed upon is that something needs to be done to protect this ancient sculpture.

2. Mixed Question (10%) Directions : 1. Design FIVE mixed questions. Provide correct answers. 2. Incoporate multiple-choice questions and other types of exam questions into your test design.         Of all the social mistakes, none is perhaps more common than meeting a new person, exchanging names and promptly forgetting theirs — forcing you to either swallow your pride and ask again, or languish in uncertainty forever.        Why do we forget? The simplest explanation: you’re just not that interested, says Charan Ranganath, the director of the Memory and Plasticity Program at the University of California, Davis. “People are better at remembering things that they’re motivated to learn. Sometimes you are motivated to learn people’s names, and other times it’s more of a passing thing, and you don’t at the time think it’s important.”        But this isn’t always the case. Often you really do want to remember, and find yourself forgetting anyway, Ranganath says. This may be because you underestimate the work necessary to remember something as seemingly simple as a name.A common name may be forgettable because it doesn’t strike your mind as interesting, or because you know multiple people with that name already. On the other hand, a rare name may be easy to recognize but harder to recall. And any name, common or not, has to fight for space in your already-crowded brain. Given all these factors, it takes more effort than you think to lock down a name.        “You’re not only remembering the name, but you’re remembering the name in relation to a face. Even if you get the information in, which we call encoding, you might not be able to find the information because there’s so much competition between other names and other faces in your memory,” Ranganath says. “People are often overconfident, and they underestimate how hard it will be later on.”          So, how do we remember? Mnemonic devices can be helpful, Ranganath says. He recommends finding something distinctive about the person or their appearance, and relating it back to their name. Remembering a common name like John might be difficult, for example, but if you can mentally categorize someone as John the Jogger, it may stick out more. Meanwhile, finding ways to test yourself, even as the conversation is ongoing, may also be helpful, he adds. Take note of the person’s name when they say it, then quiz yourself on it a few minutes, or even seconds, later. “Try to recall the information immediately or soon after you learn it,” Ranganath says. “The act of actually testing yourself on the name will help you retain it better in the long term.”        Repeating the person’s name after they say it may also trigger a more powerful effect than listening alone. “If you generate something, it’s actually easier to remember than if you just passively take it in,” he says. “You’re actually learning to immediately see that face and then produce this name.”And if you do forget, envision the moment you met somebody — the setting, other things you talked about and so on — to try to cognitively retrace your steps, Ranganath says.       But if all else fails, know that forgetting names is a very common problem, even among memory researchers. “When you think about all these factors,” Ranganath says, “it’s really a miracle that we can remember anybody’s name.”

Part B. Composition Instruction (10%) Directions :1. Review and evaluate the following composition based on its content, organization, vocabulary, and grammar. The total score will be 20 points. 2. Give constructive feedback

Part C. Activity Design (15%) Directions: 1. Based on the following passage , design one teaching activity that is aimed at 35 eleventh-grade students. 2. Explain in detail how this activity will help students improve their four basic language skills and critical thinking skills.        Healthy disagreement is the ability to openly, honestly and respectfully present an opposing opinion, instead of simply going along with what’s presented. A culture of healthy disagreement improves the quality of a team’s work by exposing flaws in singular ways of thinking.Healthy disagreement also promotes innovation and help teams avoid group think.        To keep disagreement healthy, teammates must remain respectful.Without mutual respect, disagreement can easily become toxic and devolve into personal attacks, destroying the culture of a team or the atomsphere in a home.        Heathy disagreement can be difficult to achieve for two reasons.       The first is that some people have personalities that are simply more agreeable.This isn’t necessarily a bad thing ; highly agreeable people typically display a high degree of empathy and are natural peacekeepers. But taken too far, agreeableness can also become a weakness. It can tempt you to say things you don’t really mean or to resist speaking up when needed, like when it comes to giving constructive criticism.This can prove toxic in the long run.        The second reason healthy disagreement is difficult to achieve has to do with the way people tend to act in groups. People feel social pressure to agree with others, even when they don’t understand the reasons—or even when those reasons don’t make sense.        Put simply, people are often afraid to be different.        For example, a series of experiments by psychologist Solomon Asch showed that a large percentage of people (up to 75%) tend to go along with the decisions of a group, even when the decision doesn’t make any sense.This has to do with what we call “ social conformity” , or , in more simple terms, peer pressure. Interestingly. Asch found in his experiments that when just one person spoke up to give a correct answer, the number of subjetcs willing to conform dramatically lowered. In other words, by simply voicing your opinion, not only can you gain confidence to do the right thing when surrounded by others who don’t, you can actually help others do the right thing, too.        There are a few things you can do to promote a culture of healthy disagreement. First of all, don’t disagree just for the sake of disagreeing. But if you lean far on the “agreeable” spectrum, you have to learn how to speak up when needed. One way to do this is to ask yourself : If I don’t say this, will I regret it later? Remember, though, when you do speak up, do so respectfully. Often, it’s not what you say that people take the wrong way; rather, it’s how you say it. So, strive to really understand your teammates’ position before countering it.        If you are the type who isn’t afraid to speak up even when everyone else agrees, keep doing so respectfully. Or, if you are the opposite ,the next time someone speaks up or starts to rock your boat, resist the urge to dismiss them as “ difficult.” Remember the value they bring and the power of those two emotionally-intelligent words: healthy disagreement.

Part D. Essay (10%)        With the implementation of the 108 curriculum, students are required to provide learning portfolios as references when they apply to universities. As an English teacher, and, a potential homeroom teacher in CHSH, what’s your role in helping students build and enrich their learning portfolios? What might be the problems or obstacles you may encounter? How would you deal with them? Support your arguments with concrete examples.