中三 數學試卷 (F3 Maths Past Paper)

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157 students
ST. STEPHEN'S GIRLS' COLLEGE
Mid-Year Examination 2017 - 2018
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 2017-2018
23. A cylindrical metal pillar, with base radius 4 cm, stands upright on the base of the
cylindrical vessel, with base diameter 20 cm, and the pillar is taller than the vessel,
as shown in the figure. The original depth of water is h cm. If the cylindrical metal
pillar is removed from the vessel, the depth of water is 12.6 cm.
(a) Find the value of h.
Find the total area of the wet surfaces of the pillar (including the base) before
removing it from the vessel. Give your answer in terms of . (3 marks)
24. The volumes of carrot juice, apple juice and water in bottle A are in the ratio 3 : 2:4, while those in
bottle B are in the ratio 1:4:1. 800 cm³ of the liquid in bottle A is mixed with the liquid in bottle
B. If the volume of carrot juice in the mixture is less than the volume of apple juice in the mixture
by at least 30% of the total volume of the mixture, find the minimum possible volume of the liquid
from bottle B, correct to the nearest cm³.
F.3 Mathematics Mid-Year Examination 2017-2018
25. Daniel borrowed a loan of $150 000 from a bank. Interest was calculated at the end of every year
at an interest rate of 12% per annum. He planned to repay $x at the end of every year. It was
assumed that the interest was calculated before Daniel made the repayment.
Find, in terms of x, the amount he still owed the bank after the first repayment.
(Express the answer as an expanded and simplified algebraic expression.)
It is given that the amount Daniel still owed the bank after the second repayment is
(i) Find x.
(ii) Daniel claimed that he should increase the repayment by $8 000 in order to fully
repay his loan in two years. Do you agree? Explain your answer.
F.3 Mathematics Mid-Year Examination 2017-2018
26. Simplify
where n is an integer.
27. (a) Factorize x³ - 64.
Factorize x² +25x-116.
Using (a) and (b), or otherwise, factorize 2x³ - x² -25x-12.
End of Paper
F.3 Mathematics Mid-Year Examination 2017-2018
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) 4m²-25n²
(b) x² + 5x - 14
(c) 2x² - xy - 10y²
Express the following numbers in scientific notation.
(a) 0.000 0034
(b) -270 000 000
Convert the decimal number 11x167 +495 into a hexadecimal
(4) * (2 500) ².
A sum of $20 000 is deposited at an interest rate of 12% p.a. for 5.
3 years compounded quarterly. Find the amount received
correct to the nearest dollar.
(a) If x 3y - 2.
The value of a mobile phone decreases by 8% every 3 months. 6.
Mary bought the mobile phone one year ago at $5 400. Find
its present value, correct to 1 decimal place.
This month, Mr. Chan's family consumes 14% less electricity 7.
than that last month, but the charge per unit of electricity is
increased by 5% as compared to last month. Find the
percentage change in the charge of electricity over these two
Determine whether each of the following statements must be 8.
If a b > 0, then
If p < q, then p² < (a) True False
(b) True False
(c) True / False
F.3 Mathematics Mid-Year Examination 2017-2018
In a bakery, the prices of a cream cake and a cheese tart are $15 9.
and $18.5 respectively. Miss Lee has to buy a total of 15
pieces of cakes and tarts from the bakery. If she has $250 and
she wants to buy as many cheese tarts as possible, how many
cream cakes should be bought?
The following table shows the number of times that S3 students 10.
of a school watched movies last month.
times watching 0 1
28 41 31 32 24 21 23
Find the mean, median and mode of the number of times that
S3 students of a school watched movies last month.
The median of the five numbers 20, x + 1, x + 5, x - 4 and 11.
x + 19 is 15. Find the mean of these five numbers.
Cumulative frequency
The following cumulative frequency polygon shows the 12.
number of books S2 students in a school read last year.
Number of books S2 students in a school read last year
Number of books
Find the 80th percentile.
Students who read 12 books or more were given (b)
certificates last year. Find the percentage of students
who got the certificate.
F.3 Mathematics Mid-Year Examination 2017-2018
13. In the figure, O is the orthocentre of AABC, where 13.
ZOAC = 30° and ZOCA = 20°. Find ZABC.
The perimeter of sector AOB is 10 cm and ZAOB = 30°, 14.
where O is the centre. Find the radius of sector AOB, correct to
3 significant figures.
15. In the figure, OQRP is a sector with radius 6 cm. If ZPOQ = 15.
120° and OR is the angle bisector of ZPOQ, find the area of the
shaded region, correct to 3 significant figures.
Section B (60%)
All working must be clearly shown in the spaces provided.
16. Simplify (-4p¯³q³)-²
and express the answer with positive indices.
F.3 Mathematics Mid-Year Examination 2017-2018
17. (a) Solve the inequality x--
3x+421-12-20
(b) If x is an integer, find the least possible value of x.
18. Given that 2x <
312-414 and y=
(2-x), find the range of values of y.
F.3 Mathematics Mid-Year Examination 2017-2018
19. The government of city A imports water from cities X and Y. City X agrees to supply a total amount
of 1.52 x 10¹2 L of water, while the water supply from city Y is 9.5 × 10¹¹ L more than that from
city X. It is known that the population of city A is 7.5 × 106 and the average yearly water
consumption of city A is 4.56 × 10¹ L per person.
(a) Find the total amount of water supply from city X and city Y.
Find the water consumption of city A in a year.
The government of city A claims that if the yearly water consumption of city A remains
unchanged, the total water supply from cities X and Y is enough for 11 years of consumption for
the people in city A. Do you agree? Explain your answer.
F.3 Mathematics Mid-Year Examination 2017-2018
20. The following table shows the test marks of Peter and Tom in 4 subjects.
Mathematics
(a) Find the weighted mean mark of Peter.
(b) If Peter and Tom have the same weighted mean mark, find the value of x.
(c) Suppose the weights of Mathematics and Science are doubled. Find the minimum value of x (if x
is an integer) so that Tom has a better performance than Peter.
F.3 Mathematics Mid-Year Examination 2017-2018
21. In the figure, PQ is the perpendicular bisector of BC and ZBAC = 90°.
(a) Prove that AABC - AQBP.
(b) If PQ = 3 and BQ = 4, hence or otherwise, find the perimeter of AABC.
F.3 Mathematics Mid-Year Examination 2017-2018
22. In the figure, PQR, UTWR, STVP, UVQ and SWQ are straight lines. UQ and SQ are the angle
bisectors of ZPQS and ZUQR respectively. Given that PQ = QR, ZQUR = 20° and (a) Find UQS.
(b) Prove that AUQR = ASQP.