中三 數學試卷 (F3 Maths Past Paper)

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Secondary 3
INSTRUCTIONS
Belilios Public School
Yearly Examination, 2019-2020
Mathematics
1920-YE-S3-MATHEMATICS-1
Time allowed: 1-hours
1. After the announcement of the start of the examination, you should write your Name, Class and
Class Number in the spaces provided.
2. This paper consists of THREE sections, A(1), A(2) and B.
Attempt ALL questions in this paper. Write your answers in the spaces provided in this
Question-Answer Book. Do not write in the margins. Answer written in the margins will not be
Maximum marks: 105
4. Graph paper and supplementary answer sheets will be supplied on request. Write your Name,
Class, Class Number and question number on each sheet, and fasten them with a paper clip
INSIDE this book.
5. Unless otherwise specified, all working must be clearly shown.
6. Unless otherwise specified, numerical answers should be either exact or correct to 3 significant
7. The diagrams in the paper are not necessarily drawn to scale.
Answers written in the margins will not be marked.
14. A paper cup is in the shape of an inverted right circular cone of base diameter 6 cm and height
12 cm. Suppose the cup is held vertically and it is originally filled up with water. If some water
flows out of the cup until the depth of water drops 6 cm as shown in Figure 9, find the volume
of the water flowed out in terms of .
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Answers written in the margins will not be marked.
Answers written in the margins will not be marked.
Section B (35 marks)
15. Figure 10 shows a quadrilateral ABCD, where AD = CD. AP is an
altitude of AABC. E is a point on AC such that DE is the angle
bisector of ZADC in AACD. DE is produced to B. BD, AP and CQ
intersect at point F.
(a) Prove that AABD = ACBD.
Given that AQ: QB = 2:1.
Find ZBEC and ZCQB
Prove that ACFP ~ ACBQ.
Express BC in terms of BQ
Find CF FP.
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Answers written in the margins will not be marked.
Answers written in the margins will not be marked.
Answers written in the margins will not be marked.
In Figure 11, L1, L2 and L3 are straight lines,
where L₁ // L2 and L2 L3. L3 cuts L₁ and L2 at A(0, a)
and B(b, 0) respectively, and OA : OB = 2 : 3. C(a, 5)
and D(7, 6) are points on L₁ and L2 respectively.
(a) (i) Find
Find the slope of L3.
Hence, find the values of a and b. (6 marks)
(b) If C and D are fixed points while P is a point that
can move along line segment AB, find the possible
greatest area of ACPD.
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Answers written in the margins will not be marked.
Answers written in the margins will not be marked.
Answers written in the margins will not be marked.
17. Figure 12a shows 8 squares each of side 1 cm and two circles. The squares are joined at one of
their vertices and one side of each square touches the smaller circle. Two vertices of each square
lie on the larger circle. Figure 12b shows the central part of Figure 12a with AB as the edge of a
square, and K is the mid-point of AB.
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(b) By considering Figure 12c, find the radius of the larger circle.
(a) (i) Find the interior angle of the regular octagon ABCDEFGH.
(ii) By dividing the octagon into triangles or otherwise, find the radius r of the inner circle.
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END OF PAPER
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Answers written in the margins will not be marked.
Answers written in the margins will not be marked.
Section A(1) (35 marks)
(a) x² − 3xy + 2y²,
(b) x² − 3xy + 2y² – 12x + 24y.
2. In Figure 1, ACE and ABD are straight lines. AB = BD and AC = CE. Find the unknowns.
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Answers written in the margins will not be marked.
3. Figure 2 shows a right triangular prism.
(a) Name the angle between lines QR and UR. (1 mark)
(b) Find the distance between point T and line PS.
(c) Name the angle between the line TR and the
plane PQRS.
If L2 cuts the y-axis at P, find the coordinates of P.
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4. Figure 3 shows two parallel lines L₁ and L₂. L₁ passes through A(−2, 5) and B(4, −3) while
L2 passes through C(3, 5).
(a) Find the slope of L₁.
★B(4, -3)
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Answers written in the margins will not be marked.
Figure 4 shows a dartboard formed by two concentric semi-circles of radii 10 cm and 30 cm.
Kevin throws a dart randomly and it hits the dartboard. Find the probability that the dart hits the
shaded region of the dartboard.
Find the height of the tree.
(b) Another birdwatcher Q is 60 m away from the tree.
Find the angle of elevation of T from Q.
6. In Figure 5, a bird stands on the top T of a tree TR. The angle of elevation of T from a
birdwatcher P is 28°. The distance between T and P is 140 m.
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Answers written in the margins will not be marked.
Figure 6 shows a rectangular tank containing some water.
Let S cm² be the total area of the surface in contact with
(a) Express S in terms of d.
If the depth of water is less than 40 cm, find the range
of values of S.
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8. In Figure 7, trees A and B are due west of the house at O, while tree C is due south of the house.
The compass bearings of trees A and B from tree C are N73°W and N39°W respectively.
Trees A and B are 50 m apart.
(a) Let OC be x m. Express OB in terms of x.
(b) Find the distance between tree C and the house.
Answers written in the margins will not be marked.
Answers written in the margins will not be marked.
Section A(2) (35 marks)
The frustum shown in Figure 8 is formed by cutting the small right pyramid VEFGH from the
large right pyramid VABCD. The bases of the two pyramids are
squares. Find the volume of the frustum.
5 1 3 4 5 699
Find the mean, the median and the mode of the given data.
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10. The following stem-and-leaf diagram shows the weekly pocket money of a group of students.
Stem ($10) Leaf ($1)
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Answers written in the margins will not be marked.
11. Kenneth borrows a sum of money from a bank at an interest rate of 9% p.a. compounded yearly.
If he repays the loan after 6 years, he needs to pay an amount of $154 000.
(Give the answers correct to the nearest $100.)
(a) How much does Kenneth borrow?
If the loan is repaid after 3 years, find the interest he should pay.
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Answers written in the margins will not be marked.
Winnie's purse contains two $2 coins, one $5 coin and one $10 coin. On a flag day, Winnie
takes out two coins randomly from her purse at the same time for donation.
(a) Draw a tree diagram in the space provided to show all the possible outcomes.
(b) Find the probability that the donation amount is between $5 and $13.
(c) Find the expected donation amount.
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Answers written in the margins will not be marked.
13. A magazine recruits a reporter. Each interviewee will be assessed on three items: creativity,
writing skills and oral skills. The table below shows the scores obtained by three interviewees
and the weight of each item.
It is known that May's weighted mean score is 83. Whose performance is the best?
Explain your answer.
Writing skills Oral skills
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