中六 數學試卷 (F6 Maths Past Paper)

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2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
Time Allowed: 2 hours 15 minutes
Instructions:
1. This paper consists of THREE sections, A(1), A(2) and B.
2. Attempt ALL questions. Write your answers in the spaces provided in this Question-Answer Book.
3. Graph paper and supplementary answer sheets will be supplied on request. Write your name, class and
class number on each sheet, and staple them 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.
Diocesan Girls' School
Secondary 6 Mock Examinations (2019-2020)
Mathematics (Compulsory Part)
Total marks: 105
Total Marks:
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
12. Let h(x) = 4x² +7x+3 and g(x) = 8x² +26x+15. If 12g(x)-11xh(x) is divisible by x-3.
(a) Find the H.C.F. and L.C.M. of h(x) and g(x).
(b) Simplify
(c) If 4g(x)-h(x)-3a is divisible by x-3, find the value of a.
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
Figure la shows a metal bucket A in the shape of a right cylinder. The curved surface of the
bucket is formed by the iron sheet PQRS shown in figure 1b, where PQ = 10 cm and
area = 807 cm².
(a) Find the base radius of bucket A.
(b) Find the capacity of bucket A in terms of 7.
(c) Another metal bucket B in the shape of a right cylinder is shown in the figure below. Its
curved surface is formed by the iron sheet TWYZ, where TW =12 cm and TZ = 87 cm.
Are buckets A and B similar? Explain your answer.
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
14. In the figure, O is the centre of the circle and AEODC is a straight line. AB and BC are tangents
to the circle at X and Y respectively and AB I BC. AB = 12 and BC = 16.
(a) Find the radius of the circle,
(b) (i) Without finding the angles, prove that YOD=2ZCYD.
(ii) Hence, find ZCYD.
(c) Vis a point between X and B such that YD//VO. Find VX.
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
Section B (35 marks)
15. In a box there are 3 green balls, 6 red balls and 7 blue balls. 4 balls are drawn randomly from the
box at the same time.
(a) Find the probability that exactly 2 green balls, 1 blue ball and 1 red ball are drawn.
(b) Find the probability that at least one ball of each colour is drawn.
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
The 3rd term and the 5th term of a geometric sequence are 900 and 400 respectively.
(a) Find the first term of the sequence.
(b) If the common ratio is positive, find the least value of n such that the difference between the
(n + 1)th term and the (2n + 1) th term is less than 2x10-5.
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
17. It is given that AB is a line segment of length 5 and P is a moving point in the rectangular
coordinate plane such that the area of AABP is 20. Denote the locus of P by I. Suppose that A
and B are the points (0, 3) and (4, 6).
(a) Find the equation of I.
(b) Find the coordinates of P when AABP is an isosceles triangle.
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
Section A(1) (35 marks)
1. Simplify
and express your answer with positive indices.
(a) 8a² +24ab+ 18b²,
(b) 8a² +24ab+18b² -32a-48b.
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
18. The figure shows a triangular prism in which the bases are equilateral triangles PQR and TWS.
PRST, POWT and ROWS are squares. It is given that PR = 2 cm and M is the mid-point of TW.
(a) Find ZMPS.
(b) Find the angle between the plane MPS and the plane PTSR.
(c) If D is a moving point on APQR, is the area of ADSW minimum when D is at P? Explain
your answer.
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
19. It is given that A(2, 6) is the centre of a circle C with radius r.
(a) Write down the equation of the circle C in terms of r.
A circle C'is obtained by reflecting the circle C with respect to the y-axis and then translated
vertically by c units. P(a, b) and Q(d, e) are the points of intersection of C and C. The slope of
Find the value of c and determine whether the reflected circle should be translated
upward or downward.
(ii) Find the equation of PQ.
(iii) Hence find, in terms of r, the value of (a-d)².
(c) A student claims that when PQ = 4√5, B(-1, 1) lies inside C. Do you agree? Explain your
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
End of Paper
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
3. If a ==(p+2) and b=3(2p+5), express b in terms of a.
(a) Round up 643.742 to 2 significant figures.
(b) Round down 648.752 to 1 decimal place.
(c) Round off 648.742 to the nearest integer.
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
5. The marked price of a bag is 25% above its cost. A profit of $75 is made by selling the bag at a
discount of 10% on its marked price. Find the marked price of the bag.
6. (a) Find the range of values of x which satisfy both
(b) Write down the smallest integer satisfying the inequalities in (a).
23-x and 37 >5+4x.
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
7. The frequency distribution table and the cumulative frequency distribution table below show the
distribution of the weights of newborn babies in a hospital.
Weight (kg)
Weight less than (kg)
Cumulative frequency
(a) Find a, b and c.
(b) If a baby is randomly selected from the hospital, find the probability that the weight of the
selected baby is less than 4.05 kg but not less than 3.25 kg.
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
In a polar coordinate system, O is the pole. The polar coordinates of the points A and B are
(20, 70°) and (20, 160°) respectively. P is point on AB such that OP is the axis of reflectional
symmetry of AOAB.
(a) Describe the geometric relationship between OP and AB.
(b) Find the polar coordinates of P. (Give the answer in surd form if necessary.)
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
9. Town A and town B are 15 km apart. The figure shows the graphs for Ken and Billy running on
the same straight road between town A and town B during the period 9:00 to 11:00 in the
morning. They start at 9 a.m. and Billy runs at a constant speed. Ken comes to rest at 9:22.
Distance travelled
(a) How far are Ken and Billy from town B when they meet?
(b) Billy claims that he runs faster than Ken on average. Do you agree? Explain your answer.
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
Section A(2) (35 marks)
10. The stem-and-leaf diagram below shows the time spent on reading (in hours) in a week of the
students in a reading club.
Stem (tens) Leaf (units)
It is given that the inter-quartile range of the distribution is 11 hours.
(a) Find the value of c.
(b) It is given that the mean of the distribution is 23 hours and the range of the distribution is not
less than 25 hours. Find a and b.
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 1
11. It is given that h partly varies directly as a and partly varies directly as a². h=100 when a = 1
and h = 280 when a = 2.
(a) Express h in terms of a.
(b) If a: h=1:300, find the values of a and h.
(c) Using the method of completing the square, find the minimum value of h and the
corresponding value of a.