中三 數學試卷 (F3 Maths Past Paper)

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內容節錄：
155 students
ST. STEPHEN'S GIRLS' COLLEGE
Mid-Year Examination 2020-2021
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
5. Unless otherwise specified, numerical answers should
either be exact or correct to 3 significant figures.
For Markers' Use Only
WYL, SCHL, CYN, YLN
F3 Mathematics Mid-Year Examination 2020-2021
26. In Figure 1, a piece of wire is bent into a sector of radius 12 cm and the angle of sector is 60°.
Find the area enclosed by the wire in Figure 1.
In Figure 2, the sector is reshaped into a circle. Someone claims that the area of the circle is
smaller than the area of the sector. Do you agree? Explain your answer.
F3 Mathematics Mid-Year Examination 2020-2021
27. John deposits a fixed amount $x into an account at the beginning of each month in Bank A at an
interest rate of 12% p.a. compounded monthly.
(a) Find the total amount in the account at the end of the first month in terms of x.
It is given that the total amount in the account at the end of the third month is $306
Someone claims that the total amount in the account at the end of the second month can
be exactly twice that of the amount in the account at the end of the fourth month if John
deposits $2x at the beginning of each month. Is the claim correct? Explain your answer.
F3 Mathematics Mid-Year Examination 2020-2021
End of Paper
F3 Mathematics Mid-Year Examination 2020-2021
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) x²-7x-30
(b) -2p² +50g²
(c) 2³-24y²+72y
Determine which of the following statements is/are true. 2.
Circle the correct answer.
(a) 144y²-120xy+25x² = (5x-12y)²
(b) a² +6a-9=(3-a)²
(c) 64x³-125= (4x-5)(16x²+20x+25)
Make b the subject of y=a--
=a", where a is an integer, find a.
Express the following numbers in scientific notation.
(a) -2 530 000
(b) 0.000 000 39
Arrange the following numbers in ascending order.
-2.34 x 10-70
III. -2.34 x 107⁰
II. 2.34 × 107⁰
2.34 x 10-⁹⁰
Consider the binary number 101100(2).
(a) Write down the place value of the underlined digit.
(b) Express 101100(2) in the expanded form.
Answer for (b):
Convert the decimal number 8+8 into a hexadecimal 8.
If $32 000 is deposited in a bank at a simple interest rate of 3% 9.
p.a., how many years will it take to receive an amount of $34 880?
F3 Mathematics Mid-Year Examination 2020-2021
If the length and the width of a rectangle are increased by 10% 10.
and decreased by 30% respectively, find the percentage change
in the area of the rectangle.
The table below shows the salaries tax rates:
Net chargeable income
On the first $40 000
On the next $40 000
On the next $40 000
(a) (i) If the net chargeable income is $40 000, find the
salaries tax payable.
(ii) If the net chargeable income is $80 000, find the
salaries tax payable.
It is given that x<- and y=-x. Find the range of the
values of y.
(b) If David's salaries tax payable is $4 200, find his net
chargeable income.
(a) Solve the inequality
(b) Represent the solution of (a) on the following number line.
16. Consider the positive integers: 4,4,5,6,x,y.
If the mean of the above data is 4, which of the following is/are
Determine whether each of the following statements must be 14.
true. Circle the correct answer.
(a) Ifa>b>c, then ab>bc.
(b) Ifx>y>z, then x-y>y-z.
(c) If p>q>r>0, then P>9.
II. Median = 4
III. Mode = 4
It is given a set of data: 15, 3, 10, 15, 22, 11, m, n.
If the mode of the above set of data is 10, find the values of m=
(a) True/False
(b) True/False
(c) True/False
F3 Mathematics Mid-Year Examination 2020-2021
Section B (60%)
All working must be clearly shown in the spaces provided.
17. Simplify
and express the answer with positive indices.
(b) Write down all negative integers satisfying the inequality in (a).
18. (a) Solve the inequality
F3 Mathematics Mid-Year Examination 2020-2021
19. A shop produces cheese cakes and chocolate cakes only. The costs of producing one cheese cake
and one chocolate cake are $65 and $35 respectively. If 140 cakes are produced on one day and the
total cost should not exceed $8000, at least how many chocolate cakes should be produced?
20. In a cylinder, its base radius is 5 cm and volume is 150 cm³. Find the total surface area of the
cylinder. Give your answer in terms of .
F.3 Mathematics Mid-Year Examination 2020-2021
The value of a pair of earphones was $800 in 2015 and its value has decreased at a fixed rate each
year. In 2017, the value of the earphones decreased to $648.
(a) Find the decay factor of the value of the earphones.
(b) Suppose the decay factor of the value of the earphones remains unchanged, find the value of
the earphones in 2011. Give your answer correct to the nearest dollar.
A carbon dioxide molecule consists of one carbon atom and two oxygen atoms. The weights of a
carbon atom and an oxygen atom are 1.99 x 10-26 kg and 2.67 x 10-26 kg respectively.
(Express the answers of (a) and (b)(i) in scientific notation.)
(a) Find the weight of a carbon dioxide molecule.
(b) A carbon dioxide extinguisher contains 1.9791 kg of carbon dioxide.
(i) Find the number of carbon dioxide molecules in the extinguisher.
(ii) Find the total weight of the oxygen atoms in the extinguisher.
F.3 Mathematics Mid-Year Examination 2020-2021
23. The table below shows the marks that Mak and Millie got in various subjects in an examination and
the weight of each subject.
It is given that the weighted mean mark of Millie is 80.
Mathematics
Given that the weighted mean mark of Mak is higher than that of Millie by 5 marks, find y.
F3 Mathematics Mid-Year Examination 2020-2021
24. In the figure, PRT and QRS are straight lines.
PQ=QT and PQ // ST.
(a) Prove that APQR - ATSR.
(b) Prove that PT is the angle bisector of ZOTS.
If PQ=ST, is QR a perpendicular bisector
of APOT? Explain your answer.
F3 Mathematics Mid-Year Examination 2020-2021
25. Factorize
(a) 5a²-8ab-4b².
(b) 25a²-4b².
(c) 100a²x-5a² +4b²-16b²x+8ab.