中三 數學試卷 (F3 Maths Past Paper)

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166 students
ST. STEPHEN'S GIRLS' COLLEGE
Mid-Year Examination 2018 - 2019
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.
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 2018-2019
The base radius and the height of a cylinder are r cm and 19 cm respectively. Suppose its height is
increased by 12.5% and its volume is then decreased by 28%.
(a) Let y cm be the radius of the cylinder after the change. Express y in terms of r.
(b) Hence, find the percentage change in the radius of the cylinder.
F.3 Mathematics Mid-Year Examination 2018-2019
David borrowed $100 000 from a bank at 9% p.a. compounded monthly. He agreed to repay Sx
each month.
(a) How much did David owe the bank for the 1st month before paying the 1st instalment?
(c) David just repaid half of the original loan from the bank after paying the 2nd instalment. Find
the amount of each repayment. (Give the answer correct to the nearest dollar.)
Express, in terms of x, the amount that David still owes the bank after paying the
2nd instalment.
F.3 Mathematics Mid-Year Examination 2018-2019
28. The development of public housing in a city is under study. It is given that
the total floor area of public housing flats at the end of a particular year
= the total floor area of public housing flats at the end of the previous year x (1+ 10%) - 3.2 million m²
It is found that the total floor area of public housing flats at the end of the 1st year is 9 × 107 m².
(a) Express 3.2 million in scientific notation.
Find the total floor area of public housing flats at the end of the 2nd year and express the answer
in scientific notation.
(c) It is known that the total floor area of public housing flats needed at the end of the 4th year is
1.1 × 108 m². A researcher claims that, at the end of the 4th year, the total floor area of public
housing flats will be greater than the total floor area of the public housing flats needed. Is the
claim correct? Explain your answer.
End of Paper
F.3 Mathematics Mid-Year Examination 2018-2019
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) 64a²-256²
(b) m²-8m + 12
(c) -56xy+16y² + 49x²
Express the following numbers in scientific notation.
(a) 0.000 000 84
(b) 315 000 000
It is given that 9m-2
, express n in terms of m.
Convert the decimal number 6×29 +239 into a hexadecimal
(a) Find the growth factor.
(b) Find the population of the city 4 years ago.
answer correct to the nearest integer.)
The table below shows the salaries tax rate:
Net chargeable income
On the first $30 000
On the next $30 000
On the next $30 000
The annual income of David is $350 000. If he is eligible for a
salaries tax allowance of $192 000, how much salaries tax
should he pay?
The population of a city increases at a rate of 5% per year. It is 5.
known that the population in that city is 550 000 this year.
The price of a flat is $P in 2010. The price of the flat increases 7.
at a constant rate of 5% per year from 2010 to 2014 and
decreases at a constant rate of 9% per year from 2014 to 2017.
Find the percentage change in the price of the flat from 2010 to
2017. (Give your answer correct to 3 significant figures.)
F.3 Mathematics Mid-Year Examination 2018-2019
Make n the subject of 4n = 2x - (n − 2)y.
Solve 5(x-2)+8(7-x) <25 and represent its solutions
graphically on a number line.
Determine whether each of the following statements must be 10.
true. Circle the correct answer.
(a) If xy-3.
(b) If a>0> b, then
(c) If p² II. Median of the data = 5.5
III. Mode of the data = 4
12. Consider the following positive integers:
4, 4, 5, 6, m, n
If the mean of the above data is 4, which of the following is/are
Mary's mark
John's mark
13. A job interview is divided into three parts I, II and III. The
table below shows the marks obtained by Mary and John in
There are x candies and they are evenly distributed to 6
children. If there are 6 more candies and 3 more children, each
child will get at least 3 less candies. Find the least value of x.
It is given that the weighted mean mark of John is 63.5. Find
the weighted mean mark of Mary.
(c) True/False
F.3 Mathematics Mid-Year Examination 2018-2019
14. In the figure, ABC and AED are straight lines.
It is given that AB = 4, BC= 5, AE = 6 and ZACE = ZADC.
Which of the following is/are true?
ΔACE ~ ΔΑDC
ΔΑΒΕ ~ ΔΑCD
17. Simplify
In AABC, AB = 3x cm, BC = 16 cm and AC = x cm, where x is
an integer. Find the number of solutions for x.
In the figure, G is the centroid of AABC. AD and BE intersect
at G. The area of ABDG is 4 cm². Find the area of DCEG.
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 2018-2019
18. (a) Solve the inequality
If x is an integer, write down the least possible value of x that satisfies the inequality
Alan and Ken are given $40 and $25 as pocket money respectively every day. After their parents
increase their pocket money, Alan's pocket money does not exceed 1.5 times that of Ken. If the
total increase in their pocket money is $12, find Alan's maximum possible daily pocket money.
F.3 Mathematics Mid-Year Examination 2018-2019
20. The table shows the distribution of the hourly wages of the workers in a factory.
Hourly wage
Number of workers
The factory owner claims that the average hourly wage of the workers exceeds $35.
(a) What kind of average does the owner suggest? Justify your answer.
Do you think the average used by the owner is appropriate to reflect the hourly wage of the
workers in the factory? Explain your answer.
F.3 Mathematics Mid-Year Examination 2018-2019
21. (a) Factorize
(i) 3x². -x-4.
(ii) 18x4 -32.
(b) Hence or otherwise, factorize 18x4-32-6x³ - 8x.
22. If n is an integer and a > 1, simplify
and express the answer with positive indices.
F.3 Mathematics Mid-Year Examination 2018-2019
23. In the figure, PRT and QRS are straight lines. PQ=ST and PQ // ST.
(a) Prove that APQR = ATSR.
Prove that QR = RS.
(c) It is given that QS is the angle bisector of ZPOT.
(i) Prove that APQR = ATOR.
(ii) Hence, prove that QR is perpendicular bisector of APQT.
F.3 Mathematics Mid-Year Examination 2018-2019
24. The perimeter of sector AOB is 50 cm and ZAOB = 60°, where O is the centre. Find the area of the
sector AOB, correct to 3 significant figures.
25. A cylindrical metal pillar, with base radius 6 cm, stands upright on the base of the
cylindrical vessel, with base diameter 24 cm, and the pillar is taller than the vessel,
as shown in the figure. The original depth of water is 15 cm. If 1087 cm³ of water
is added into the vessel, find
(a) the rise in the water level;
(b) the percentage increase in the area of the wet curved surface of the
(Give the answer correct to 3 significant figures if necessary.)