編號:

6954

年級:

中三 (F3)

科目:

數學 (Maths)

學校

檔案格式:

pdf

頁數:

12

檔名:

st_stephen_girl_college_F3-Maths-18-19-my

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內容節錄：

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 x

(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.)