# 中六 數學試卷 (F6 Maths Past Paper)

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## 中六數學試卷 PDF 下載

2020-2021 S.6 Mock Examinations – Mathematics (Compulsory Part) Paper 2
Diocesan Girls' School
Secondary 6 Mock Examinations (2020-2021)
Mathematics (Compulsory Part)
Time Allowed: 1 hour 15 minutes
Instructions:
1. All questions carry equal marks.
2. ANSWER ALL QUESTIONS. You are advised to use an HB pencil to mark all the answers on
the Answer Sheet, so that wrong marks can be completely erased with a clean rubber. You must
mark the answers clearly; otherwise you will lose marks if the answers cannot be captured.
3. You should mark only ONE answer for each question. If you mark more than one answer, you
will receive NO MARKS for that question.
4. No marks will be deducted for wrong answers.
5. The diagrams in this paper are not necessarily drawn to scale.
1. Consider -ax= ab-bx. Express x in terms of a and b.
There are 30 questions in Section A and 15 questions in Section B. Choose the best answer for
each question.
- (2a + ²) (4a² - 7 + ²5³).
c. (2a-²) (4a² +5+ 25).
3. If A(x+2)² + B(x − 3) + C = x² - 4x+1, then C =
· (2a + ²) (4a²
Total marks: 45
D. ab-(a−b)
(2a-²) (4a² +10+ 25).
2020-2021 S.6 Mock Examinations – Mathematics (Compulsory Part) Paper 2
40. In the figure, O is the centre of the circle. AC and CD are tangents
to the circle at B and D respectively. If ZCAD = 30°, find
41. Let k be a constant. The straight line 3x-5y = k cuts the x-axis and the y-axis at A and B
respectively. It is given that C is a point lying on the x-axis. If the y-coordinate of the
orthocenter of AABC is a, find the x-coordinate of C in terms of a.
42. There are 4 fair coins and 1 biased coin in a bag. The probability of getting a head in tossing
the biased coin is 0.8. A coin is drawn randomly from the bag. The coin drawn is then tossed 5
times. Find the probability of getting exactly 3 heads correct to 3 significant figures.
43. There are 5 pairs of couples taking a picture together. They are arranged in two rows of 5
where the wives sit randomly in the first row and the husbands stand randomly in the second
row. Find the probability that exactly 3 husbands stand just behind their wives.
2020-2021 S.6 Mock Examinations – Mathematics (Compulsory Part) Paper 2
44. In a Chinese exam, the mean score is 72 marks. Jason gets 50 marks in the exam and his
standard score is -2.75. If Karen gets 60 marks in the exam, then her standard score is
45. The mode, the inter-quartile range and the variance of a group of numbers are 21, 40 and 12
respectively. If 6 is added to each number of the group and each resulting number is then
divided by 2 to form a new group of numbers, find the mode, the inter-quartile range and the
variance of the new group of numbers.
Inter-quartile range
END OF PAPER
2020-2021 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 2
Diocesan Girls' School
Secondary 6 Mock Examinations (2020-2021)
Mathematics (Compulsory Part)
2020-2021 S.6 Mock Examinations – Mathematics (Compulsory Part) Paper 2
[3(x-2)≥0
A. x ≥ 2.
5. If(y-1)-² (1-x) = — ; then y=
6. If a polynomial f(x) is divisible by x² -1, the polynomial f(x-2) must be divisible by
C. 2≤x≤5.
B. 12 cm².
7. A sum of \$50 000 is deposited at an interest rate of 8% per annum, compounded quarterly.
Find the interest after half a year, correct to the nearest dollar if necessary.
8. The scale of a map is 1:30 000. If the actual area of a park is 1.08 × 106 m², then the area of the
park on the map is
A. 3.6 cm².
C. 36 cm².
9. It is given that z varies directly as √√x and inversely as y². Which of the following must be a
D. -5≤x≤-2.
D. 120 cm².
10. The weight of an object is measured to be 0.45 kg by using an electronic balance with a scale
interval 0.01 kg. Which of the following must be true ?
A. The actual weight of the object may be 0.46 kg.
B. The absolute error of the measurement is 0.05 kg.
C. 0.449 kg ≤ actual weight of the object <0.451 kg
D. The relative error of the measurement is
2020-2021 S.6 Mock Examinations – Mathematics (Compulsory Part) Paper 2
25"+1 -52n+1
25"+2_52n+2
11. If n is an integer,
A. 48 cm².
12. In the figure, the 1st pattern consists of 2 dots. For any positive integer n, the (n + 1)th pattern
is formed by adding (2n + 1) dots to the nth pattern. Find the number of dots in the 10th pattern.
and EGF is a straight line, find the value of x.
B. 64 cm².
13. If the volume of a right circular cylinder of base radius 4s cm and height 5t cm is 160 cm³, then
the volume of a right circular cone of base radius 3s cm and height 8t cm is
C. 108 cm².
14. In the figure, E, F and G are the mid-points of AB, DC and DB respectively.
If BC = 12 cm, EF = x cm, AD = (x² −60)cm
15. Refer to the figure, which of the following must be correct?
A. x+z = 2y
B. x+z = y +180°
C. x+y+z=540° D. x+y=z+180°
D. 144 cm².
2020-2021 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 2
16. In the figure, DB and DC are the angle bisectors of
ZABC and ZACE respectively. If ZBDC = 25° and
BCE is a straight line, find ZBAC.
A. 208 cm².
A. 135 cm².
17. The base of a solid right pyramid is an equilateral triangle of side 12 cm. If the height of the
pyramid is 10 cm, then the total surface area of the pyramid, correct to the nearest cm², is
A. 80.1 cm²
B. 253 cm².
18. In the figure, ABCD is a parallelogram. E is a point on AD such that AE ED = 5 : 3. CD
produced meets BE produced at F. AC cuts BF and BD at points G and H respectively. If the
area of ADEF is 117 cm², then the area of quadrilateral HDEG is
B. 142 cm².
C. 324 cm².
B. 109.2 cm²
19. The figure shows a semicircle with centre O. ASOB is its
diameter and SUT is a straight line. If OA = 16 cm and
OU SU = 8 cm, find the area of the shaded region ATS
correct to the nearest 0.1 cm².
C. 152 cm².
C. 147.1 cm²
D. 417 cm².
D. 165 cm².
D. 172.8 cm²
2020-2021 S.6 Mock Examinations – Mathematics (Compulsory Part) Paper 2
20. In the figure, A, B, C and D are concyclic. AED is a straight line.
A. 1+ sin x.
B. 1-tan x.
C. 1-√√3 tan x.
1+√√3 tan x.
21. In the figure, PQRS is a semi-circle. PR and QS intersect at T.
If PQ = 12 cm, RS = 4 cm and RT = 3 cm, find cos ZQTR.
II. bm+ck=0
22. In the figure, L₁ and L2 intersect at a point on the y-axis. The equations of L₁ and L2 are
ax+by+c= 0 and hx-ky+m=0 respectively. Which of the following must be true?
B. I and II only
C. I and III only
D. I, II and III
2020-2021 S.6 Mock Examinations – Mathematics (Compulsory Part) Paper 2
23. The equation of the circle C is 4x² +4y² −11x+18y-30=0. Which of the following is/are
I. The radius of C is greater than 10.
II. (1, 2) lies outside C.
III. C passes through all the four quadrants.
is a 2-digit number, where and are non-repeated integers from 1 to 9 inclusive. Find
the probability that the difference between the tens digit and the units digit is at least 2.
B. I and III only
C. II and III only
25. A box contains ten balls numbered from 1 to 10. In a lucky draw, a ball is randomly drawn
from the box and a certain number of tokens will be awarded according to the following table:
Number on the ball drawn
Number of tokens awarded
Find the expected number of tokens awarded in the lucky draw.
Prime number
D. I, II and III
2020-2021 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 2
26. The box-and-whisker diagram below shows the distribution of the test scores of the students in
Which of the following frequency curve may represent the distribution of their scores?
27. Let a, b, c and d be the mean, the median, the mode and the range of the group of 8 numbers
{x-4, x, x, x, x + 1, x + 3, x + 5, x + 7} respectively. Which of the following must be true?
28. In the figure, f(x)=
A. cos x + 2.
B. I and II only
B. cos2x+1.
29. Convert the decimal number 2¹0 +24 -3 to a binary number.
A. 10 000 001 101₂
C. 10 000 000 101₂
C. I and III only
B. 10 000 001 001₂
D. 10 000 101 101₂
D. II and III only
2020-2021 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 2
30. For 0° ≤x≤360°, how many roots does the equation cos²x+2sinx=1 have ?
A. x³y² = 4096
31. It is given that log y is a linear function of log, x. The intercepts on the vertical axis and on
the horizontal axis of the graph of the linear function are 2 and 3 respectively. Which of the
following must be true?
32. If 52 and 7 = 29, then log₂ 0.7 =
B. x²y³ = 4096
35. If a + ß,
33. If a +i is a root of x² + mx +3=0, where a and m are real numbers, then a =
B. +√√2.
[2a² =ma + n
2p²-mß= n²
A. m = a + ß, n=
C. m=2a +2ß, n = -2aß.
C. xy = 4096
34. The straight line y = 4x intersects the circle x² + y² + 5x+3y+k=0 at two distinct points A
and B. The x-coordinate of the mid-point of A and B is
C. +√√3.
D. x³y² = 4096
B. m-a-B, n = -aß.
D. m-2a-2ß, n=2aß.
2020-2021 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 2
36. The figure shows the graph of y=-x² +mx+6. It cuts the x-axis
at A and B, and the y-axis at C. If the area of AABC is 21 square units,
find the value of m.
37. Consider the following system of inequalities:
Let S be the region which represents the solution of the above system of inequalities. Find the
constant c such that the greatest value of 5x+4y+c is 49, where (x, y) is a point lying in S.
38. The figure shows a cuboid. CBFG is a square and ZCHG= 30°,
find cos ZHCF.
39. In the figure, PQ is a tangent to the circle at C. BCD is a straight line
and ZQCD = 60°. If AB: BC= 2:3, find ZACQ.
y=-x² +mx+6