中三 數學試卷 (F3 Maths Past Paper)

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146 students
ST. STEPHEN'S GIRLS' COLLEGE
Mid-Year Examination 2019-2020
Mathematics
Time allowed: 1 hour 30 minutes
Question/Answer Paper
Please read the following instructions very carefully.
1. This paper consists of TWO sections, A and B.
2. Write your class, class number and name in the spaces provided
on this cover.
3. This paper carries 100 marks. Attempt ALL questions in this
paper. Write your answers in the spaces provided in this
Question/Answer Paper.
4. The diagrams in this paper are not necessarily drawn to scale.
5. Unless otherwise specified, numerical answers should
either be exact or correct to 3 significant figures.
For Markers' Use Only
MWC, WYL, SCHL
F.3 Mathematics Mid-Year Examination 2019-2020
26. (a) Factorize
(1) 2y² + 5yz-3z²,
(ii) 4x² + 5x-6.
(b) Hence or otherwise, factorize 4x² + 3z² + 2xy +13xz-2y² - 5yz.
F.3 Mathematics Mid-Year Examination 2019-2020
F.3 Mathematics Mid-Year Examination 2019-2020
27. Sam borrowed $36 000 from Bank A at 18% p.a. compounded monthly. He agreed to repay $12 400
each month. The last repayment may be less than or equal to $12 400.
(a) How much did Sam owe Bank A for the 1st month after paying the 1st repayment? (1 mark)
(i) Can he repay the loan after 3 repayments? Explain your answer.
Find the interest he paid to Bank A. Give your answer correct to the nearest dollar.
(c) Bank B offers the same loan to Sam at 9 % p.a. compounded monthly. He has to
repay $24 800 to Bank B every two months. If he wants to pay less interest, which bank
should he choose? Explain your answer.
End of Paper
F.3 Mathematics Mid-Year Examination 2019-2020
Section A (40%)
All rough work should be done on the rough work paper provided, but will not be marked.
Factorize the following polynomials.
(a) 98m² 162n²
(b) 8x +4x²+3
(c) 3a³ + 108a - 36a²
Make b the subject of x=- -C.
(-) (3²) 498.
Express the following numbers in scientific notation.
(a) 14 200 000
(b) -0.000 000 043
Consider the binary number 1101012.
(a) Write down the place value of the underlined digit.
(b) Hence, express 1101012 in the expanded form.
Convert the decimal number 9×164 +12×2¹2 +27
hexadecimal number.
The temperature of the water in a pot is 60°C now. If the
temperature decreases by 5% every 5 minutes, find the
temperature of the water in the pot 30 minutes ago, correct to
3 significant figures.
The length of each side of a cube is decreased by 10%. Find the 7.
percentage change in its volume.
John pays $3200 per quarter for the rates of his flat. If the rates 9.
are charged at 5% p.a., what is the rateable value of his flat?
F.3 Mathematics Mid-Year Examination 2019-2020
10. The table below shows the salaries tax rate:
Net chargeable income
On the first $40 000
On the next $40 000
On the next $40 000
If the net chargeable income of David is more than $120 000
and his salaries tax payable is 11% of his net chargeable
income, how much salaries tax should he pay?
Write down the smallest integer that satisfies the following 11.
inequality.
number line.
(a) Ifa > b>0, then 5-a<5_b.
If a>0>b, then a² (c) If p²>q² and p, q ‡ 0, then
Determine whether each of the following statements must be 13.
true. Circle the correct answer.
15. Find the mean and median of the following set of data.
Drink A contains 20% tea and 80% milk by volume. Drink B
contains 80% tea and 20% milk by volume. Some drink A and
drink B are mixed to produce drink C of volume 1000 mL. If
drink C contains at most 380 mL of tea, find the minimum
volume of drink A used.
(b) True/False
(c) True/False
F.3 Mathematics Mid-Year Examination 2019-2020
16. In the figure, C is the circumcentre of APQR. AP=BQ and
ZPQR = 52°. If A and B are the mid-points of PR and PQ
respectively, find x.
18. Simplify
In the figure, AABC is a right-angled triangle where AB = BC.
If P is a point lying on AC such that BPL AC, which of the
following is/are true?
Point B is the orthocentre of A ABC.
A ABP is an equilateral triangle.
Point P is the circumcentre of AABC.
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 Examination 2019-2020
19. A Chinese examination consists of 4 papers I, II, III and IV. The following table shows the marks
Michelle and Nancy got in each paper. It is given that the weighted mean mark of Michelle is 53.
Michelle's marks
Nancy's marks
(a) Find the value of x.
Given that the weighted mean mark of Nancy is lower than that of Michelle, find the greatest
value of y if y is an integer.
F.3 Mathematics Mid-Year Examination 2019-2020
20. The value of a watch was $9 000 in 2012 and its value has increased at a fixed rate each year. In
2015, the value of the watch increased to $15 552.
(a) Find the growth factor of the value of the watch.
Suppose the growth factor of the value of the watch remains unchanged, find the value of the
watch in 2019. Give your answer correct to the nearest dollar.
21. Tim bought a flat at $7.37 x 10° in 2016.
(a) If Tim spent $780 000 in the renovation work, find the total amount he spent on the flat.
(Give your answer in scientific notation)
(b) If the value of the flat increases by 5% every year, will it be greater than 12 million dollars
in 2026? Explain your answer.
F.3 Mathematics Mid-Year Examination 2019-2020
22. A snack shop sells two kinds of candy, Candy A and Candy B. A bag of Candy A contains
44 candies while a bag of Candy B contains 32 candies. Tom wants to buy 8 bags of candy with not
less than 310 candies. It is given that Tom has bought n bags of Candy B.
(a) Find the maximum value of n.
(b) The prices of a bag of Candy A and a bag of Candy B are $80 and $70 respectively.
(i) Express the amount Tom should pay in terms of n.
(ii) Using the result of (a), if Tom has $600, does he have enough money to buy the candies?
Explain your answer.
23. A piece of wire of 48 cm long is bent into a sector OPQ as shown in the
figure, where the angle of the sector is 56°. Find the radius of the sector,
correct to 3 significant figures.
F.3 Mathematics Mid-Year Examination 2019-2020
24. In the figure, a solid is composed of two cylinders. The two cylinders have the
same curved surface area. The diameter and the height of the top cylinder are
1 mm and h mm respectively and those of the bottom cylinder are d mm and
1 mm respectively.
(a) Express h in terms of d.
(b) It is given that the volume of the top cylinder is 37 mm³.
(i) Find h.
(ii) Find the total surface area of the solid in terms of 7.
F.3 Mathematics Mid-Year Examination 2019-2020
25. In the figure, ABCD is a trapezium. It is given that CE and AF are altitudes of AABC and AB = AC.
(a) Prove that AABF=AACF.
(3 marks) By
Prove that AAFB
Hence, prove that CB x CF = BE× AC. (5 marks)