Quod Erat Demonstrandum



F.5 General Mathematics Quiz

(A.S. and G.S., Linear Programming)

2009-10-30

Total score: 60 Time allowed: 80 minutes Attempt ALL questions.

Part one : Multiple Choice (24 marks) Write on the answer sheet

1. The first term of a geometric sequence is (1. If the sum of the sequence to

infinity is less than twice of the common ratio by 3, then the common ratio =

A. 2 B. [pic] or 2 C. [pic] D. ([pic]

2. Three consecutive numbers are in arithmetic sequence, if their sum is 9 and

their product is (21. Find the smallest number.

A. (5 B. (3 C. (1 D. 0

3. 1 + 52 + 54 + … + 52n =

A. 52n + 2 ( 1 B. [pic] C. [pic] D. [pic]

4. Find the sum of all multiples of 13 between 299 and 1240 inclusively.

A. 54550 B. 54881 C. 55224 D. 55991

5. If the ratio of the mth term to the nth term (m ≠ n) in an arithmetic sequence is

(n ( 1) : (m ( 1), then the (m + n ( 1)th =

A. 0 B. 1 C. m + n ( 2 D. [pic]

6. In the figure, at which point in the shaded region will the value of 2x + 3y – 5 be the greatest?

[pic]

A. A(1, 1) B. B(2, 3) C. C(5, 4) D. D(6, 2)

7. Among the points in the figure, at which point does p = 3x + y attain its

maximum value?

[pic]

A. (7, 1) B. (5, 4) C. (3, 4) D. (1, 3)

8. In the figure, which point in the shaded region does C = 2x + 2y attain its

minimum value?

[pic]

A. Point P B. Point Q C. Point R D. Point S

Part two : Short Questions (14 marks)

9. Refer to the figure.

(a) Determine the equations of CD and DE.

(b) Write down the system of inequalities

representing the shaded region ABCDE.

(c) Find the minimum value of x ( 2y within

the shaded region ABCDE.

(d) Find the minimum value of x2 + y2 within

the shaded region ABCDE.

(8 marks)

10. The figure shows the growth way of certain kind of plant. In the 1st month, three branches are generated and form new nodes at their ends; then three

branches will be generated from every new node in the 2nd month, and totally

12 braches formed. Continue with the same manner, which is, three branches

will be generated from newly formed nodes in the following month (assume: the

plant grows healthy with no branch missing). How many branches in the 10th

month?

(6 marks)

Part three : Long Questions (22 marks)

11. John started working in SFXC in 1994 and will be retired by the end of 2044.

He had deposited $10,000 to the Kowloon Bank at the end of 1994 and he will

deposit the same amount of money to the Bank at the end of every 4 years

during his working period. The interest rate is 4% per annum throughout the

whole working period which is compound annually.

(a) By the time of his retirement, find

(i) the sum of money that John has deposited to the Bank;

(ii) the total amount of money John will get from the Bank.

(The answer should be corrected to the nearest $10.)

(7 marks)

(b) John will withdraw $x from the Bank at the end of every year starting from

2045. Let $A be the answer in (a)(ii), show that the amount of money in the

Bank after n withdrawals is [pic].

(4 marks)

12. A company produces two brands, A and B, of mixed nuts by putting peanuts and

almonds together. A pocket of brand A mixed nuts contains 40 g of peanuts and

10 g of almonds. A pocket of brand B mixed nuts contains 30 g of peanuts and

25 g of almonds. The company has 2400 kg of peanuts, 1200 kg of almonds and

70 carton boxes. Each carton box can pack 1000 brand A packets or 800 brand

B packets.

The profits generated by a box of brand A mixed nuts and a box of brand B

mixed nuts are $800 and $1000 respectively. Suppose x boxes of brand A mixed

nuts and y boxes of brand B nuts are produced.

(a) Use the graph paper on the sheet, find values of x and y so that the profit is

the greatest.

(8 marks)

(b) If the number of boxes of brand B mixed nuts is to be smaller than the

number of boxes of brand A mixed nuts, find the greatest profit.

(3 marks)

END OF PAPER

Answer Sheet of F.5 General Mathematics Quiz (2009-10-30)

Name: ___________________________________ F.5 ____ ( )

Answers to Part one

|1. |2. |3. |4. |

|5. |6. |7. |8. |

Answers to Q.12 (a)

[pic]

-----------------------

0th month

1st month

3 branches

2nd month

12 branches

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