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內容節錄：

178 students

3. ALL working must be clearly shown.

Please read the following instructions very carefully.

1. Write your class, class number, name and division in the spaces provided on this cover.

2. This paper carries 100 marks. Attempt ALL questions in this paper. Write your answers in the spaces

provided in this Question/Answer Paper.

St. Stephen's Girls' College

Final Examination 2018-2019

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

MATHEMATICS

Time Allowed: 1 hour 30 minutes

For Markers' Use Only

Page 1 of 15

VC, LHK, LL, JSCL, CYN

For Markers' Use Only

F.1 Mathematics Paper I Final Examination 2018-2019

Peter buys a toy from a shop. The packing of the toy is a prism as shown.

It is given that the volume of the toy is 14112 cm³.

(a) Find the value of h.

(b) Find the total surface area of the prism.

Page 10 of 15

F.1 Mathematics Paper I Final Examination 2018-2019

10. Carol had six chocolate cubes each of side 2 cm. To celebrate Valentine's Day, she melted all the

chocolate cubes to form a number of 'heart-shaped' prisms as shown in Figure (a). Figure (b) shows

the dimensions of the base of the prism.

(a) Find the total volume of chocolate cubes.

(b) Find the volume of a 'heart-shaped' prism.

Page 11 of 15

Find the maximum number of 'heart-shaped' prisms she can make and the volume of the

chocolate remained.

F.1 Mathematics Paper I Final Examination 2018-2019

11. Find the unknowns in the figure.

Page 12 of 15

F.1 Mathematics Paper I Final Examination 2018-2019

12. It is given that AABC~AAED. Find x and y.

Page 13 of 15

F.1 Mathematics Paper I Final Examination 2018-2019

13. In the figure, APQRB and CSTD are straight lines where AB // CD.

(a) Find x.

(b) Determine if QS // RT. Explain your answer.

Page 14 of 15

F.1 Mathematics Paper I Final Examination 2018-2019

14. In the figure, PR and QS intersect at T. It is given that ZSPR=RQS and PS = QR.

(a) Prove that APST = AQRT.

If TR = 4 cm and PT = 3 cm, find ST and QT.

(c) Using the results of (b), prove that ARST ~ AQPT.

* End of Paper *

Page 15 of 15

F.1 Mathematics Paper I Final Examination 2018-2019

1. The pie chart below shows the favourite subjects of 180 S1 students. There are 54 students who like

Mathematics.

Favourite subjects of

180 S1 students

Mathematics

(a) Find the value of x.

(b) (i) Find the total number of students who like Science or History.

(ii) If the number of students who like Science is 6 more than that of History, find the number of

students who like Science.

Page 2 of 15

F.1 Mathematics Paper I Final Examination 2018-2019

2. The back-to-back stem-and-leaf diagram below shows the lifetimes (in hours) of dry cells brand A and

Lifetimes of dry cells of 2 different brands

Leaf (1 hour) Stem (10 hours) Leaf (1 hour)

(a) Find the values of a and b.

(b) Dry cells with lifetimes less than 20 hours fail a quality control test.

(i) Find the percentage of dry cells of brand A that fail the test.

(ii) Find the percentage of dry cells of brand B that fail the test.

(iii) Someone claims that the percentage of all the dry cells that fail the test is 65%.

Do you agree? Explain your answer.

0 4 5 5 6 8 9

Page 3 of 15

F.1 Mathematics Paper I Final Examination 2018-2019

3. Some sweets were evenly shared among x children. Each of them got 39 sweets.

(a) Express the total number of sweets in terms of x.

(b) If the number of children is reduced by 2, each of the remaining children will have 13 more

sweets. How many sweets are there in total?

Page 4 of 15

F.1 Mathematics Paper I Final Examination 2018-2019

4. Daisy has 3 books on her shelf, a Chinese book, an English book and a Mathematics book. The

Chinese book has 30 pages more than twice the number of pages in the English book. The total

number of pages in 6 copies of the Chinese book and 2 copies of the English book is equal to that in a

copy of the Mathematics book.

(a) If the number of pages in the English book is x, express in terms of x, the number of pages in

each of the Chinese and Mathematics books.

If the number of pages in 44 copies of the Chinese book is equal to that in 7 copies of the

Mathematics book, find the number of pages in each of the three books.

Page 5 of 15

F.1 Mathematics Paper I Final Examination 2018-2019

5. The figure shows a polar coordinate plane. Denote the pole by O. The coordinates of points P and Q

are (4, 210°) and (3, 120°) respectively.

(a) Is OP perpendicular to OQ? Explain your answer.

(b) (i) Plot R(5, 30°) in the polar coordinate plane.

Find the area of APQR.

110° 100° 90° 80°

260 270 280°

Page 6 of 15

1 2 3 4 5 6

F.1 Mathematics Paper I Final Examination 2018-2019

In the figure, A₁D1 is the image of AD after reduction.

(a) Draw the image A₁B₁C₁D₁ after reducing ABCD.

(b) Write down the reduction factor.

(c) Draw the image A2B2C2D2 after translating A1B₁C₁D₁ 6 units to the right, and then 2 units

Page 7 of 15

F.1 Mathematics Paper I Final Examination 2018-2019

7. The figure shows the points A and B in a rectangular coordinate plane. A and B are rotated clockwise

about O through 90° to points R and S respectively.

(a) Mark R and S in the rectangular coordinate plane.

(b) (i) Plot T(-1,-5) in the rectangular coordinate plane.

If A undergoes a transformation to T, describe the transformation.

Draw the quadrilateral BSRT. Draw all the axes of symmetry of BSRT.

Page 8 of 15

F.1 Mathematics Paper I Final Examination 2018-2019

The figure shows a rectangular coordinate plane. The coordinates of points A and C are (2, 5) and

(-7, -1) respectively. A is reflected along the y-axis to a point B. C is translated 9 units to the right

and then 2 units downwards to a point D.

-7 -6 -5 -4 -3 -2

Page 9 of 15

(a) Write down the coordinates of B and D.

(b) Draw the quadrilateral ABCD in the rectangular coordinate plane.

(c) Let P be the point of intersection of the diagonals of ABCD. Mark P in the rectangular

coordinate plane. Which quadrant does P lie in?

(d) Find the area of ABCD.