中三 數學試卷 (F3 Maths Past Paper)

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內容節錄：
152 students
Instructions for Candidates:
paper consists of TWO sections, A and B.
2. Answer ALL questions in the spaces provided in this Question-Answer Paper.
Cumulative frequency
Section A (40%)
All rough work should be done on the rough work paper provided, but will not be marked.
The following shows the marks of Billy in 10 subjects in the
mid-term examination.
42, 44, 62, 64, 65, 70, 72, 80, 80, 82
Find the mean, the median and the mode.
St. Stephen's Girls' College
Mid-Year Examination 2016-2017
MATHEMATICS
Time Allowed: 1 hour 30 minutes
The following cumulative frequency polygon shows the heights 2.
(in cm) of a group of S2 students.
Heights of a group of S2 students
110 130 150 170 190
Height (cm)
percentile.
Using the above figure, find the
(a) median,
(b) 3rd quartile,
For Markers only
MWC, SCHL, WYL
F.3 Mathematics Mid-Year Examination 2016-2017
28. A cylindrical tank of base diameter 6 m is filled with water to a depth of 5 m. A cylindrical metal
pillar of length 10 m is then lowered until it stands upright on the base of the tank as shown in the
figure. The base radius of the pillar is 1.2 m.
(a) Find the rise in water level.
(b) Find the total area of the wet surfaces of the pillar (including the base).
(Give your answers correct to 3 significant figures.)
F.3 Mathematics Mid-Year Examination 2016-2017
29. (a) Factorize m³ +27.
(b) Factorize m² +38m+105.
(c) Using (a) and (b), or otherwise, factorize 3m³ -m²-38m-24.
End of Paper
F.3 Mathematics Mid-Year Examination 2016-2017
3. Express the following numbers in scientific notation.
(a) 340 000 000
- 0.000 026
Factorize 16x²-24xy +9y².
(a) Factorize a²-b².
(b) Factorize 2x - 32y4.
Convert 111010101, into a hexadecimal number.
Convert the decimal number 12×16 +296 into a hexadecimal
Simplify 2 2017 x(0.5)2014
and represent its solutions graphically on a number line.
Given that x≤-3 and y=-
A sum of $30 000 is deposited at an interest rate of 12% p.a. for 9.
4 years compounded monthly. Find the amount received
correct to the nearest dollar.
10. Amy is 30% younger than Ben, and Ben is 15% younger than 10.
Candy. By what percentage is Candy older than Amy?
Correct your answer to 1 decimal place.
find the range of values of y
12. If John has to pay $56 000 of rates quarterly and the rates
percentage charge is 5%. Find the rateable value of the
below, how much salaries tax should he pay?
Net chargeable income
On the first $30 000
On the next $30 000
On the next $30 000
13. The annual income of Mr. Ng is $520 000 and he is eligible for 13.
a salaries tax allowance of $370 000. With reference to the table
F.3 Mathematics Mid-Year Examination 2016-2017
14. A coin is tossed 1000 times. The results are recorded as follows: 14.
Find the experimental probability of getting a head.
15. Phoenix has bought some roses, tulips and carnations. She put
them into three vases A, B and C. The number of flowers in
each vase is as follows:
If a flower is randomly picked, find the probabilities that
(a) it is in vase A,
(b) it is a rose,
(c) it is not a tulip and it is not in vase C.
16. The perimeter of sector AOB is 40 cm and ZAOB = 140°,
where O is the centre. Find the radius of sector AOB.
18. Simplify
Section B (60%)
All working must be clearly shown in the spaces provided.
ab 2² (2a-²6³)-¹
17. The base area of a cylinder is 167 cm² and its total surface area 17.
is 1047 cm². Find the volume of the cylinder in terms of 7.
and express the answer with positive indices.
F.3 Mathematics Mid-Year Examination 2016-2017
19. It is given that a factory produces 205 000 bottles of drink of 500 mL every day on average.
(a) How much drink in mL does the factory produce every day on average?
(Express your answer in scientific notation.)
(b) Can the factory produce drink of one million litres within 10 days? Explain your answer.
20. Find the greatest integer satisfying the inequality
F.3 Mathematics Mid-Year Examination 2016-2017
21. David has some $2 coins and $5 coins in his pocket where 80% of the coins are $2 coins. After
spending 10 $2 coins, at least 25% of the coins are $5 coins in his pocket. Find the maximum
number of coins in his pocket originally.
22. The length, width and height of a cuboid are 15 cm, 12 cm and h cm respectively. Suppose its
length is increased by 20%, its width is decreased by 25% and its volume is then increased by 8%.
(a) Let y cm be the height of the cuboid after the change. Express y in terms of h.
(b) Hence, find the percentage change in the height of the cuboid.
F.3 Mathematics Mid-Year Examination 2016-2017
23. The marks of Cherie in 6 mathematics tests are recorded as follows:
62, 70, 80, 57, 85, 48
(a) Find the mean mark and the median mark of Cherie in these 6 tests.
It is found that the mark 84 is wrongly recorded as 48.
Find the mean mark and the median mark after correction.
The teacher decides to ignore the worst result of each student among these 6 tests. Find the
new mean mark and new median mark of Cherie in these tests.
F.3 Mathematics Mid-Year Examination 2016-2017
24. A cylindrical metal of base radius 30 cm and height 20 cm is melted and recast to form a new
cylindrical metal. It is known that the height of the new metal is increased by 20%.
(a) Find the base radius of the new metal.
(b) Find the percentage change in the curved surface area.
(Give your answers correct to 3 significant figures.)
F.3 Mathematics Mid-Year Examination 2016-2017
25. The interest rate offered by bank A is 6% p.a. and the interest is compounded quarterly. The
interest rate offered by bank B is r% p.a. and the interest is compounded yearly. Mr. Wong wants
to deposit $ 100 000 into a bank for 3 years.
(a) Find the interest, correct to the nearest dollar, Mr. Wong will receive after 3 years if he
chooses bank A.
(b) In order to attract Mr. Wong to deposit his money in bank B, find the least possible interest
rate that bank B should offer. Correct your answer to 1 decimal place.
26. Simplify
25n+2 -2.32"+1
F.3 Mathematics Mid-Year Examination 2016-2017
27. In a lucky draw, a participant needs to draw a ball from each of bags A and B. Bag A contains 2
white balls, 1 blue ball and 1 red ball. Bag B contains 1 white ball, 1 blue ball and 1 red ball. The
prizes given to the participants are shown below.
Balls drawn
a pack of candies
a comic book
a pair of socks
Value of the prize
(a) Find the probabilities of drawing
(i) 2 white balls,
(ii) 2 blue balls,
(iii) 2 red balls.
(b) If David has to pay $5 to enter the lucky draw once, is the lucky draw favourable to him?
Explain your answer.