ACJC 2010 H1 Promo Question Paper

ANGLO-CHINESE JUNIOR COLLEGEMATHEMATICS DEPARTMENT

MATHEMATICSHigher 1

11 October 2010

JC 1 PROMOTIONAL EXAMINATION

Time allowed: 1.5 hours

Additional Materials: List of Formulae (MF15)

READ THESE INSTRUCTIONS FIRST

Write your Index number, Form Class, graphic and/or scientific calculator model/s on the cover page. Write your Index number and full name on all the work you hand in. Write in dark blue or black pen on your answer scripts.You may use a soft pencil for any diagrams or graphs.Do not use paper clips, highlighters, glue or correction fluid.

Answer all the questions.Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question.You are expected to use a graphic calculator.Unsupported answers from a graphic calculator are allowed unless a question specifically states otherwise.Where unsupported answers from a graphic calculator are not allowed in the question, you are required to present the mathematical steps using mathematical notations and not calculator commands.You are reminded of the need for clear presentation in your answers.

The number of marks is given in brackets [ ] at the end of each question or part question.At the end of the examination, fasten all your work securely together.

This document consists of 4 printed pages.

[Turn Over

Anglo-Chinese Junior CollegeH1 Mathematics 8864: 2010 JC 1 Promotional Examination

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8864

ANGLO-CHINESE JUNIOR COLLEGEMATHEMATICS DEPARTMENT

MATHEMATICS 8864Higher 1JC 1 PROMOTIONAL EXAMINATION

Calculator model: _____________________

Arrange your answers in the same numerical order. Place this cover sheet on top of them and tie them together with the string provided.


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Question no. Marks

1

2

3

4

5

6

7

8

9

/ 50

Index No: Form Class: ___________

Name: _________________________

1 Express as , where a and b are constants to be determined.

By letting be y or otherwise, solve the equation

,

leaving your answer in exact form. [4]

2 Find the range of values of k such that the line does not intersect the curve

. [4]

3 Differentiate the following with respect to x:(a) [2]

(b) [2]

(c) [3]

4 Solve the simultaneous equations:

[5]

5 (a) Find the exact value of . [3]

(b) Find . [3]

6 On each Friday, Saturday and Sunday evening, Peter either watches a movie or plays soccer, but not both on the same evening. If he watches a movie on any particular day, the probability that he will watch a movie again the next day is 0.4. If he plays soccer on any particular day, the probability that he will play soccer again the next day is 0.7.Given that for a particular week he played soccer on Friday evening, draw a tree diagram to illustrate the above information. [1]Find the probability that(i) he plays soccer on both Saturday and Sunday. [1](ii) he plays soccer on Sunday. [2]Given that he played soccer on Sunday, find the probability that he also played soccer on Saturday. [2]


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7 The diagram shows a square, OABC, of side 1m. The point X, on AB, and the point Y, on BC, are such that AX = x m and BY = kx m, where BY is longer than AX.

By considering the area of the shaded triangles, show that the area of triangle OXY is

. [2]

Hence find the minimum area of triangle OXY in terms of k. [3]

8 The diagram shows the curve and the line .

Find(a) the coordinates of A and B. [2](b) the area of the shaded region. [4]

9 Write down the equations of asymptotes of the curve .

Sketch the graph of , indicating clearly its asymptotes and turning points, if

any. [3](i) Hence find the range of values of p if the equation has only one real

root. [1](ii) By sketching another graph on the same diagram, or otherwise, solve the inequality

. [3]

~End of Paper ~


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O

C

A

B

X

Y kx

x

x

y

4y x x

2y x

O B

A

ACJC 2010 H1 Promo Question Paper

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