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HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY

HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION 2017

Compulsory Part

PAPER 1

MATHEMATICS

C~\ 2017-DSE MATH CP

PAPER 1

Question.Answer Book

8.30 am - 10.45 am (2% hours)

This paper must be answered in English

INSTRUCTIONS

After the announcement of the sta吋 of the examination, you should first write your Candidate Number in the space provided on Page 1 and stick barcode labels in the spaces provided on Pages 1, 3, 5, 7, 9 and 11.

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This paper consists of THREE sections, A(1), A(2) and B.

(2)

Attempt ALL questions in this paper. Write your answers in the spaces provided in this Question­Answer Book. 00 not write in the margins. Answers written in the margins will not be marked.

(3)

• Graph paper and supplementary answer sheets will be supplied on request. Write your Candidaté Number, mark the question number box and stick a barcode label on each sheet, and fasten them with string INSIDE this book.

(4)

Unless otherwise specified, all working must be clearly shown.

(5)

Unless otherwise specified, numerical answers should be either exact or correct to 3 significant figures.

(6)

The diagrams in this paper are not necessarily drawn to scale.

(7)

No extra time will be given to candidates for sticking on. the barcode labels or filling in the question number boxes after the ‘Time is up' announcement.

(8)

@香港考試及評核局 保留版權

Hong Kong Examinations and Assessment Authority AII Rights Reserved 2017

2017-DSE-MATH-CP 1-1

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SECTION A(l) (35 marks)

3x-y Make y the subject of the formula k =一一一.

y (3 marks)

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2017-DSE-MATH-CP 1-2 2

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3. Factorize

(a) x2 一 4xy+ 3y2 ，

(b) x2-4秒l+3y2+11x-33y .

(3 m缸ks)

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There are only two kinds of admission tickets for a thea甘e: regular tickets and concessionaηtickets. The prices of a regular ticket and a concessionary ticket are $126 and $ 78 respectively. On a certain

day, the number of regular tickets sold is 5 times the number of concessionary tickets sold and the sum of money for the admission tickets sold is $50976. Find the total number of admission tickets sold

that day. (4 marks)

Answers written in the margins will not be marked.

2017-DSE心1ATH-CP 1-3 3 |州州P甸

5. (a) llx+8

Find the range of values of x which satisfy both 7廿一 2) 至一了.:....:. and 6-x < 5 .

(b) How many integers satisfy both inequalities in (a)?

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~16. The coordinates of the points A and B are (一3 ， 4) and (9 ，一 9) respectively. A is rotated I 言:

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anticlockwise about the origin through 900 to A' . B' is the reflection image of B with respect to I'~I) the x-axis. I 站

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(a)

(b)

Write down the coordinates of A' and B' .

Prove that AB is perpendicular to A'B' .

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2017-DSE-MATH-CP 1-4 4

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The pie chart below shows the distribution ofthe seasons ofbirth ofthe students in a school. 7 .

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Distribution of the seasons of birth of the students in the school

If a student is randomly selected from the school, then the probability that the selected student was bom

9 m spnng IS

Find x.

In the school, there are 180 students bom in winter. Find the number of students in the school. (4 marks)

(a)

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2017-DSE-MATH-CP 1-5

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9. A bottle is termed standlαrd if its capacity is measured as 200 mL correct to the nearest 10 mL .

(a) Find the least possible capac社y of a standard bottle.

(b) Someone claims that the total capacity of 120 standard bottles can be measured as 23 .3 L

correct to the nearest 0.1 L . Do you agree? Expla姐 your answer.

(5 marks)

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2017-DSE-MATH-CP 1一7 7 |Goontothe…>

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intersect at the PR and OQ OP=OQ=OR.

SECTION A(2) (35 marks)

In Figure 1, OPQR is a quadrilateral such that

point S. S is the mid圖point of PR. 10.

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(2 marks)

It is given that 0 is the centre of the circle which passes through P , Q and R. If OQ = 6 cm

and LPRQ = 100 , find the area ofthe sector OPQR 凶 terms of Jr. (4 m的s)

Prove that ðOPS == ðORS . (a)

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2017-DSE-MATH-CP 1-8

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The stem-and-leaf diagram below shows the distribution ofthe hourly wages (in dollars) ofthe workers magroup.

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and $22 respectively. It is given that the mean and the range ofthe above dis甘ibution are $ 70

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(5 marks)

If a worker is randomly selected from the group，血ld the probability th前 the hourly wage of the selected worker exceeds $ 70 . (2 m訂ks)

Find the median and the standard deviation of the above distribution. (a)

(b)

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2017-DSE-MATH-CP 1-9

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is melted and recast into two similar

The ratio of the base area of the

A so1id metal right prism of base area 84 cm 2 and height 20 cm

solid right pyramids. The bases of the two pyramids are squares. smaller pyramid to the base area of the larger pyramid is 4: 9 .

12.

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(3 marks)

If the height of the larger pyramid is 12 cm , find the total surface area of the smalIer pyramid.

(4 marks)

Find the volume of the larger pyramid. (a)

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2017-DSE-MATH-CP 1-10

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2017-DSE-MATH-CP 1-11 11 |臼on仿制陶

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13. The coordinates of the points E , F and G are (一6 ， 5) ， (一3 ， 11) and (2 ，一1) respectively. The

circle C passes through E and the centre of C is G.

(a) Find the equation of C . (2m訂ks)

(2 marks) (b) Prove that F lies outside C.

(c) Let H be a moving point on C. When H is farthest 企om F ,

(i) describe the geometric relationship between F , G and H;

(ii) find the equation ofthe s甘aight line which passes through F and H. (3 m訂ks)

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2017-DSE品的TH-CP 1-12 12

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2017-DSE-MATH-CP 1-15 15 |叫叫阿〉

SECTION B (35 marks)

15. Let a and b be constants. Denote the graph of y = α + 10gb X by G. The x-intercept of G is 9 and

G passes t趾ough the point (243 , 3) . Express x 姐 terms of y . (4 m缸ks)

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2017-DSE-MATH-CP 1-16 16

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16. A city adopts a plan to import water 企om another city. It is given that the volume of water imported 扭

the 1 st year since the start of the plan is 1.5 x 107 m 3 and in subsequent years, the volume of water

imported each year is 10% less than the volume ofwater imported in the previous year.

(a) F恆d the total volume ofwater imported in the frrst 20 years since the start ofthe plan. (2 marks)

(b) Someone claims th前 the total volume of water imported since the start of the plan will not

exceed 1.6xl08 m3 • Do you agree? Explain your answer. (2 marks)

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2017-DSE-MATH-CP 1-17 17 |Goontothe叫v

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2017-DSE-MATH-CP 1-21 21 iGo…馴陶v

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19. ABC is a thin triangular metal sheet, where BC = 24 cm , LBAC = 300 and LACB = 420 •

(a) Find the length of AC . (2 marks)

(b) In Figure 2, the thin metal sheet ABC is held such that only the vertex B lies on the horizontal ground. D and E are points lying on the horizontal ground vertically below the vertices A and C respectively. AC produced meets the horizontal ground 的 the point F. A craftsman finds that AD = 10 cm and CE = 2 cm .

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(i) Find the distance between C and F.

(ii) Find the area of ð. ABF .

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Find the inclination of the thin metal sheet ABC to the horizontal ground.

(11 marks)

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2017-DSE-MATH-CP 1-22 22

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2017-DSE-MATH-CP 1-23 23 |Goon伽馴陶 •