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MA1505 Mid-term Test Information General Information Date: Monday 4 March 2013. Time: 8:30pm to 9:30pm. Venue: MPSH1 Section A. (Multi-Purpose Sports Hall 1 at the NUS Sports Centre). Topics: Chapter 1 (Functions), Chapter 2 (Differentiation), Chapter 3 (Integration), Chapter 4 (Series), Chapter 5 (Three Dimensional Space). Format: 10 multiple-choice questions. The test will be ‘closed-book’: no textbook, no lecture notes, no helpsheet will be allowed. A short formula list will be provided (see attached list below). Bring matriculation card, calculator(s), 2B pencils, and erasers. Rough paper for calculations must not be brought to the test venue. There will be enough blank space in the test paper for calculations. Calculators may be used during the test. Only non-programmable, non-graphing calculators will be allowed. For guidelines on calculator usage, please check the General Information folder in the Workbin of the module IVLE website. The seating plan (seat numbers) will be announced later and the list of seat numbers will be placed under General Information folder in the Workbin. During the Test All examination rules must be strictly followed during the test. In particular, students must not start writing before they are told to do so. They must not communicate with each other during the test. When the chief invigilator announces that the test has ended, students must stop writing immediately. Students caught breaking any examination rules will be referred to the Registrar’s Office to face disciplinary action.

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Students will write their answers (choices A, B, C, D or E) by shading appropriate circles on an ‘optical’ form (pink form CC1) using 2B pencils. A sample is attached below. As the CC1 answer form will be graded by a computer, it is very important that students shade the correct circles for • matriculation number; and • choices for their answers to questions 1 to 10. The appropriate circles must be completely shaded and must be shaded dark enough for the computer to read them. If a student changes his answer later, he must ensure that the old answer is properly erased; otherwise, the computer will grade it wrong and no appeal on this matter will be entertained. NUS has two matriculation number structures. Students should only shade the appropriate circles for matriculation number in the correct section: Section B or Section C. Students should also write their name in the space below the date on the CC1 answer form (see sample CC1 answer form attached). If you miss the Test Students who miss the test without a valid MC or written permission from the lecturer will receive zero mark for CA. Students who miss the test with a valid MC should e-mail the lecturer (Dr Yap) at matyapwy@nus.edu.sg by Tuesday 5 March 2013 to inform him of their valid MC so that he will know the number of students who will take the make-up test. Students who miss the test with a valid MC or written permission from the lecturer will take a make-up test on Saturday 23 March 2013 from 3 pm to 4 pm. They will be informed via e-mail about the venue by Thursday 21 March 2013. These students should bring their valid original MC or written permission from the lecturer for admission to the make-up test on that day. As students taking the make-up test will have more days for their preparation, the make-up test will be proportionally more difficult than the mid-term test. The make-up test will cover Chapters 1, 2, 3, 4, 5, and will also include Chapter 6. The make-up test will also have the format of 10 multiple-choice questions. Students who miss the mid-term and the make-up tests, but have valid excuses for both dates, will have to take a second make-up test to be arranged at a later time. The second make-up test will not have multiple-choice questions but will have essay-type questions. The second make-up test will cover the same

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material as the first make-up test but will have more challenging questions and will also require short proofs. After the Test Students’ CC1 answer forms will be graded by a computer. Thus, it is crucial that students shade their matriculation number and answer choices correctly on the CC1 answer form. If a student fails to shade his matriculation number correctly on the CC1 answer form and the form cannot be found later, he will receive zero mark for his CA. Students’ test results will be posted on the IVLE website after the computer has finished grading and recording the marks. From past experience, the computer does not make mistakes. However, in past semesters there were a few students who made some of the following common mistakes: • shaded the matriculation number incorrectly; • shaded only part of the circle but not the whole circle; • shaded the circle too lightly (not dark enough); • shaded two circles for the same question; • forgotten to shade the circle for some of the questions; and • claimed to have calculated the correct answer but shaded the wrong circle on

the CC1 answer form. Students are urged to exercise extra care to avoid these and any other mistakes. Updates Students should check the module website frequently for any updates or important changes to the information contained here. ________________________________________________________________ Appendices 1. sample Test cover page, 2. list of formulas, and 3. sample CC1 answer form.

NATIONAL UNIVERSITY OF SINGAPORE

Department of Mathematics

MA 1505 Mathematics 1

2012/2013 Semester * Mid-term Test Time: 1 hour

Instructions

1. This test paper consists of ten (10) multiple choice questions and comprises twelve

(12) printed pages.

2. Answer all 10 questions. One mark for each correct answer. No penalty for wrong

answers. Maximum score is 10 marks.

3. All answers (Choices A, B, C, D, E) are to be submitted using the pink form (FORM

CC1).

4. Use only 2B pencils for FORM CC1.

5. On FORM CC1 (section B or section C), write your matriculation number and

shade the corresponding numbered circles completely. A computer will grade your

FORM CC1. The computer will record a ZERO for your score if your matriculation

number is not correct.

6. Write your full name in the space below the Date on FORM CC1.

7. Only circles for answers 1 to 10 are to be shaded.

8. For each answer, the circle corresponding to your choice should be properly and

completely shaded. If you change your answer later, you must make sure that the

original answer is properly erased.

9. For each answer, do not shade more than one circle. The answer for a question

with more than one circle shaded will be marked wrong.

10. Do not fold FORM CC1.

11. Submit FORM CC1 before you leave the test hall.

MA1505 Mid-term Test Formulas

List of Formulas

1. The Taylor series of f(x) at x = a is

∞∑k=0

f (k)(a)

k!(x− a)k = f(a) + f ′(a)(x− a) +

f ′′(a)

2!(x− a)2

+ · · · +f (n)(a)

n!(x− a)n + · · ·

2. Let Pn(x) be the nth order Taylor polynomial of f(x) at x = a. Then

f(x) = Pn(x) + Rn(x), where Rn(x) =f (n+1)(c)

(n + 1)!(x− a)n+1

for some c between a and x.

3. Some Taylor series

ex =∞∑n=0

1

n!xn ln (1 + x) =

∞∑n=1

(−1)n−1

nxn

sinx =∞∑n=0

(−1)n

(2n + 1)!x2n+1 cosx =

∞∑n=0

(−1)n

(2n)!x2n

tan−1 x =∞∑n=0

(−1)n

2n + 1x2n+1

4. Shortest distance from a point S(x0, y0, z0) to a plane Π : ax+by+cz = d

is given by|ax0 + by0 + cz0 − d|√

a2 + b2 + c2

5. The projection of vector b onto vector a is projab =a · b||a||2

a .

2

Sample Shaded

Sample

Shade circles for answers 1 to 10 only.

MA1505

Student's Name

Shade circles in SECTION B or SECTION C.

Shade only ONE setof circles, in eitherSECTION B orSECTION C.