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%)

8.if f(x)=dt,find f'(x). (5%)

9. Evaluate dx (5%)

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%)

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

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