中三 數學試卷 (F3 Maths Past Paper)

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內容節錄：
160 students
Instructions for Candidates:
Cumulative frequency
The table below shows the distribution of the numbers of
siblings of a group of $3 students.
1. This paper consists of TWO sections, A and B.
2. Answer ALL questions in the spaces provided in this Question-Answer Paper.
Section A (40%)
All rough work should be done on the rough work paper provided, but will not be marked.
St. Stephen's Girls' College
Mid-Year Examination 2015-2016
MATHEMATICS
Time Allowed: 1 hour 30 minutes
Find the mean, the median and the mode(s) of the numbers of
siblings of the group of S3 students.
The graph below shows the cumulative frequency polygon of 2.
the time taken for the runners to complete an 800 m race.
For Marker's Use Only
159.5 169.5 179.5 189.5 199.5
MWC, LHK, WYL, SCHL
Find the 30th percentile of the time taken for this group of
runners to complete the race.
F.3 Mathematics Mid Year Exam 2015-2016
28. (a) Factorize x³ - 64.
(b) Factorize x² -24x+80.
(c) Using (a) and (b), or otherwise, factorize 3x³ +2x² - 48x-32.
F.3 Mathematics Mid Year Exam 2015-2016
29. In the figure, square ABCD is inscribed in a circular carpet with
radius 2 m. A smaller circle is inscribed in the square ABCD.
(a) Find the length of the side of square ABCD.
(Leave your answer in surd form.)
(b) A bug lands on the carpet at random. Find the probability that
it lands on the shaded region. (Give the answer correct to 3
significant figures.)
* End of Paper *
F.3 Mathematics Mid Year Exam 2015-2016
3. Express the following numbers in scientific notation.
(a) 14 700 000
(b) 0.000 102 5
Fill in each of the following blanks with the inequality sign
(a) If s>t, then 2s-3
(b) If f>g, then
Factorize 12x²-27y².
Factorize - 32x² +16xy-2y².
Convert 10001012 into a hexadecimal number.
Convert the decimal number 2¹¹ +2° +25+7 into a binary 7.
12. The annual income of Tom is $580 000 and he is eligible for a
salaries tax allowance of $379 000. With reference to the table
below, how much salaries tax should he pay?
Net chargeable income
On the first $50 000
On the next $50 000
On the next $50 000
Peter deposits $40 000 in a bank at an interest rate 5% per 9.
annum compounded quarterly. Find the compound interest
received after 2 years. Give your answer correct to the nearest
10. The number of bacteria in a culture decreases by 20% per hour. 10.
If there are 38 000 bacteria in the culture, how many bacteria
were there 4 hours ago? Give your answer correct to 3
significant figures.
11. Mr. Chan has to pay $4680 of rates quarterly. If the rate 11.
percentage is 5%, what is the rateable value of the property?
F.3 Mathematics Mid Year Exam 2015-2016
13. Which of the following cannot be the probability of an event?
(You may choose more than one of the below.)
14. A shuttle bus arrives every 10 minutes and it waits for 3 minutes 14.
at the bus stop. Peggy arrives at the bus stop at a random time.
Find the probability that she has to wait for more than 3 minutes
before getting on the bus.
15. In a game, there are 5 targets marked with scores -1, 0, 1, 2 and 15.
3 respectively. Each player has to throw 2 balls to hit the targets
in order to get the scores as marked. John has played the game
and all of his balls hit the target. If the probabilities of hitting
any of the 5 targets are the same, find the probability that he
gets a total score less than 4.
17. Factorize 3x"+1 +5x" -12x"-1.
16. In the figure, POQ is a sector with radius 12 cm. If APOQ is an 16.
equilateral triangle, find the area of the shaded region.
(Give the answer correct to 3 significant figures.) P
18. Simplify
Section B (60%)
All working must be clearly shown in the spaces provided.
and express the answer with positive indices.
F.3 Mathematics Mid Year Exam 2015-2016
<0. Also, write down the greatest integer satisfying the inequality. (4 marks)
20. In a Science competition, 3 marks are given for each correct answer and 5 marks are deducted for
each wrong answer. If Mandy has answered 14 questions and has obtained a positive score, at least
how many questions has she answered correctly?
F.3 Mathematics Mid Year Exam 2015-2016
21. The length and width of a rectangle are x cm and y cm respectively. When the length and width of
the rectangle are increased by 25% and p% respectively, the area of the rectangle is increased by
(a) Express the new area of the rectangle in terms of x and y.
(b) Find the value of p.
22. It is known that there are 8.25×10¹¹ bacteria on a lawn with dimensions of 25 mx150 m.
(a) Find the number of bacteria on the lawn per m².
(b) If the weight of each bacterium is about 1.1×10-¹3 g, estimate the weight of the bacteria on
the lawn per m².
(Express your answers in scientific notation.)
F.3 Mathematics Mid Year Exam 2015-2016
23. An organization issues 100 000 lucky draw tickets. The prizes are as follows:
Consolation prize
24. Simplify
Number of prizes
(a) Find the expected value of the prize of each of the lucky draw tickets.
(b) If Jacky buys a lucky draw ticket of $10, does he gain or suffer a loss on average? Explain your
F.3 Mathematics Mid Year Exam 2015-2016
25. The table below shows the results of David and John in the subjects Chinese, English, Mathematics
and P.E. and the weight of each subject.
Mathematics
(a) It is given that the weighted mean mark of David is higher than that of John by 5. Find the value
(b) Suppose the weight of P.E. is tripled. Using the result of (a), who has a higher weighted mean
mark? Explain your answer.
F.3 Mathematics Mid Year Exam 2015-2016
26. Carmen borrowed a loan $200 000 from a bank for two years. Interest was calculated at the end of
every year at an interest rate of 8% per annum. She planned to repay $x at the end of every year. It
was assumed that the interest was calculated before Carmen made the repayment.
(a) Find, in terms of x, the amount she still owed the bank after the first: repayment.
(Express the answer as an expanded and simplified algebraic expression.)
(b) Find, in terms of x, the amount she still owed the bank after the second repayment.
(Express the answer as an expanded and simplified algebraic expression.)
(c) The loan was fully paid after two repayments. Find the amount of each repayment.
Give the answer correct the nearest dollar.
F.3 Mathematics Mid Year Exam 2015-2016
27. A circular tank of base radius 2 m is filled with water to a depth of 8 m. A
rectangular prism of height 12 m is then lowered until it stands upright on the tank's
as shown in the figure. If the base of the prism is a rectangle whose length and width
are 1 m and 2 m respectively, find
the rise in water level,
the total area of the region that the prism is in contact with water.
(Give the answers correct to 3 significant figures.)