SECTION A1
QUEEN’S COLLEGE
Half-Yearly Examination, 2011 – 2012
MATHEMATICS PAPER 1
Question-Answer Book
Secondary 1 Date: 12 – 01 – 2012
Time: 8:30 am – 9:45 am
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1. Write your class, class number in the spaces provided on this cover.
2. This paper consists of TWO sections, A and B. Section A and Section B carry 80 marks and 40 marks respectively.
3. Attempt ALL questions in this paper. Write your answer in the spaces provided in this Question-Answer Book.
4. Unless otherwise specified, all working must be clearly shown.
5. The diagrams in this paper are not necessarily drawn to scale.
6. Use of calculator is NOT ALLOWED for this paper.
|Class | | |
|Class Number | | |
| |Teacher’s Use Only |
|Question No. |Max. Marks |Marks |
|Section A | | |
|1 |10 | |
|2 |7 | |
|3 |6 | |
|4 |9 | |
|5 |10 | |
|6 |10 | |
|7 |5 | |
|8 |5 | |
|9 |9 | |
|10 |9 | |
|Section B | | |
|11 |20 | |
|12 |20 | |
|Total |120 | |
SECTION A Short questions. (80 marks)
|1 |Evaluate the following expressions | |
| |(a) |[pic] |( 4 marks) |
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| |(b) |[pic] | |( 6 marks) |
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|2 |Given an algebraic expression [pic] | |
| |(a) |Write down the number of terms. |( 1 mark ) |
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| |(b) |Write down all constant term(s). | |( 2 marks ) |
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| |(c) |List 2 pairs of like terms. | |( 2 marks ) |
| | |(i) |(ii) | |
| |(d) |List any 2 pairs of unlike terms. | |( 2 marks ) |
| | |(i) |(ii) | |
|3 |Among the following numbers [pic], [pic], 1, 0 ,[pic] | |
| |(a) |Arrange all positive numbers in ascending order |( 2 marks ) |
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| |(b) |Arrange all negative numbers in descending order |( 2 marks ) |
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| |(c) |Arrange the above numbers in descending order |( 2 marks ) |
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|4 |Given the formula [pic]. | |
| |(a) |If b ( 8, c ( 4 and d ( -1, find the value of R. |( 4 marks ) |
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| |(b) |If R ( 6, b ([pic] and c ( 8, find the value of d. |( 5 marks ) |
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|5 |Consider the sequence [pic], [pic], [pic], [pic],[pic], [pic]…… | |
| |(a) |Write down the next two terms of the sequence. |(2 marks ) |
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| |(b) |Use an algebraic expression to express the nth term (i.e. an ) of the sequence in terms of n. |(2 marks ) |
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| |(c) |Using the result in (b), | |
| |(i) |find the 30th term of the sequence. |(2 marks ) |
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| |(ii) |if the mth term of the sequence is [pic], find the value of m. |(4 marks ) |
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|6 |A box of Japan milk powder is sold for $1560 and the profit is 30% . Since the tsunami devastated northern Japan, the new selling price |
| |of a box of Japan milk powder is increased 80% of the original selling price. |
| |(a) |Find the cost of a box of Japan milk powder. |( 4 marks ) |
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| |(b) |Find the new selling price. |( 3 marks ) |
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| |(c) |Find the total profit per cent after Tsunami devastated Japan. |( (3 marks ) |
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|7 |In the figure, | |(5 marks ) |
| |Join EB with dotted line, draw line L1 passing through A and |[pic] | |
| |perpendicular to EB, | | |
| |Join AB with dotted line, draw line L2 passing through E and parallel| | |
| |to AB. | | |
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|8 |Refer to the figure |[pic] |(5 marks ) |
| |(a) |Count and write down the numbers of vertices, edges and faces of the | | |
| | |polyhedron. | | |
| | |Number of faces= | | |
| | |Number of vertices= | | |
| | |Number of edges= | | |
| |(b) |Identify and draw the cross-section when it is cut | |[pic] | |
| | |along the line CD. | | | |
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| | | | |The cross-section is a: | |
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|9 |Find the unknowns in the following triangle. |( 9 marks ) |
| | |[pic] |
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|10 |The table below shows the prices and quantities of the items which Mr. Prince buys at the supermarket. | |
| |Product | |
| |chips | |
| |juice | |
| |candies | |
| |steak | |
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| |Price | |
| |$8.4 | |
| |$24.8 | |
| |$6.3 | |
| |$38.9 | |
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| |Quantities bought | |
| |3 | |
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| |(a) |Estimate the total price of all goods, |(4 marks) |
| | |(i) by rounding up the price to the nearest dollars. | |
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| | |(ii) by rounding off the price to the nearest dollars. |(3 marks) |
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| |(b) |It is known that Mr. Prince has $120, which estimation method of total price is suitable? Why? |(2 marks) |
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SECTION B Long questions (40 marks)
|11 |QC Government suggested that a sum of HK$6000 will be given to each holder of QC Permanent Identity Card aged 18 or above. $200 bonus |
| |will be given to eligible person who opt to receive the amount a year later. |
| |(a) |Mrs. Queen decides to collect it in a year later and she treats that bonus as the interest provided by the |(5 marks) |
| | |government. Find the corresponding interest rate. | |
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| |(b) |Mr. King decides to collect it immediately through bank A to earn interest. Bank A provides 0.08%p.a. as the | |
| | |interest rate. | |
| | |(i) Find the simple interest that Mr. King will receive a year later. |(3 marks) |
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| | |(ii) Find the time required for Mr. King to obtain the same amount of simple interest as Mrs. Queen. |(4 marks) |
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| |(c) |Mr. King wants to earn more money in the stock market, | |
| | |(i) he deposits all $6000 in the stock market. In the first half year, the stock price increased 35% and he |(3 marks) |
| | |also received $100 interest. Find the amount at the end of first half year. | |
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| | |(ii) Unfortunately, the stock market drops in the second half of the year. He losses 35% of his amount at the |(5 marks) |
| | |end of first half year. Find the total percentage change at the end of the year. | |
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|12 |QCPost provides postal service and the postage rate is as follow: | |
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| |Local | |
| |Overseas | |
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| |Weight not over 30g | |
| |$1.4 | |
| |$4.5 | |
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| |Weight not over 50g | |
| |$2.2 | |
| |$6.9 | |
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| |Miss Princess has a certain number of X’mas cards for her friends. The number of cards weighted not over 50g to local| |
| |is 10 more than the number weighted not over 30g to local. The number of cards weighted not over 30g to overseas is | |
| |three times of that to local. While the cards weighted not over 50g to overseas is fifteen less than the twice of | |
| |that to local. | |
| |(a) |If Miss Princess has k cards weighted less than 30g to local, find | |
| | |(i) the number of cards weighted less than 50g to local |(2 marks) |
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| | |(ii) the number of cards weighted less than 30g to overseas |(2 marks) |
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| | |(iii) the number of cards weighted less than 50g to overseas |(2 marks) |
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| |(b) |If the total postal fee is $365.5 , find the total number of X’mas cards. |(7 marks) |
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| |(c) |Miss Princess thinks that the calculation of postal fee is too complicated, she decides to use the same | |
| | |stamps (the highest postal fee) for each area. Find the increased postal fee. |(5 marks) |
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| |(d) |Mr. King said that the postal fee of X’mas cards must not exceed $300 and Miss Princess agreed. What should | |
| | |Miss Princess do in order to maximize the number of X’mas cards to her friends? | |
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| | | |(2 marks) |
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END OF PAPER
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