中六 數學試卷 (F6 Maths Past Paper)

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2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 2
Diocesan Girls' School
Secondary 6 Mock Examinations (2019-2020)
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. a²-b²-2a + 2b =
There are 30 questions in Section A and 15 questions in Section B. Choose the best answer for
each question.
A. (a+b)(a−b+2).
C. (a-b)(a+b+2).
B. (a+b)(a-b-2).
D. (a−b)(a+b-2).
Total marks: 45
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 2
37. Consider the following system of inequalities:
Let R be the region which represents the solution of the above system of inequalities. If (x, y)
is a point lying in R, the greatest value of y-3x+10 is
38. In the figure, AABC is an equilateral triangle with P and Q
lying on BC. If BP = PQ = QC, find ZPAQ correct to the
nearest degree.
39. In the figure, ABCDEFGH is a rectangular block. M is
the midpoint of GH. AD 24 cm, EH = 12 cm and
DE 10 cm. Find the angle between the planes AME
40. In the figure, BFC is the tangent to the circle at C. AB
and AF cut the circle at D and E respectively.
ZADE = 112°, ZABC = 46° and DE = EC. Which of
the following is/are true?
AC is the diameter of the circle.
B, D, E and F are concyclic.
B. I and II only
C. II and III only
D. I, II and III only
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 2
41. A circle is inscribed in AABC. The coordinates of A, B and C are (0, 10), (0, -14) and
(18,-14) respectively. Find the coordinates of the centre of the circle.
42. There are 12 cats and 18 dogs in a pet shop. 6 pets are selected from the pet shop. In how many
different ways can the pets be selected if the number of dogs is not less than that of cats?
43. When Alice throws a dart, the probability that she hits the target is 0.8. If Alice throws the dart
5 times, find the probability that she hits the target at most 4 times.
44. The box-and-whisker diagram below shows the distribution of the scores of some students in an
English test. The standard deviation is 62 marks and the mean is higher than 119 marks but
lower than 136 marks. Given that Alice's score is above the third quartile, which of the
following may be her standard score?
END OF PAPER
45. The variance of the 4 numbers {x₁, x₂, X3, X₁} is 7.5 and the variance of the 5 numbers
{Y₁9 Y29 Y39 Y49 Ys} is 4.2. It is given that the mean of the two sets of numbers are the same.
Find the standard deviation of the 9 numbers {x₁, x₂, X3, X49 V₁9 V 29 V 39 V 49 V₁} correct to 3
significant figures.
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 2
4. √√2=
A. 2.50 (correct to 3 significant figures).
B. 2.5066 (correct to 4 significant figures).
C. 2.50662 (correct to 5 decimal places).
D. 2.507 (correct to 3 decimal places).
5. The solution of 2-2x ≥-
C. m 1 and n =
6. Let k be a constant. If f(x+k) = x² −k², f(x) =
A. x² -2kx.
B. (x-k)².
Let n be a positive integer. Find the value of k if x² +kx-2k is divisible by x+1.
8. If m and n are constants such that 2mx(x+1)+
C. x²-2kx-2k².
9. In the figure, the graph of a quadratic function cuts the x-axis at
two points A(-1,0) and B(3,0). The y-intercept of the graph is 6.
C(p, q) lies on the graph and -1possible area of AABC.
= nx(x-4)+7x, find the values of m and n.
D. m 1 and n =.
D. (x-k)(x+k).
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 2
10. A sum of $7000 is deposited at an interest rate of 9% per annum for 1 year, compounded
quarterly. Find the interest correct to the nearest dollar.
11. Let u and y be non-zero constants. If (2u+4v): (5u-2v) = 2:3, u: v=
12. If z varies directly as x and inversely as the square root of y, which of the following must be
z decreases by 50% when y increases to 4 times of its original and x remains
is a constant.
B. I and II only
13. In the figure, the first pattern consists of 2 dots. For any positive integer n, the (n + 1)th pattern
is formed by adding 2"+2 dots to the nth pattern. Find the number of dots in the 8th pattern.
C. II and III only
14. The radii of a sphere and the base of a right circular cone are both equal to r. If the surface area
of the sphere equals the curved surface area of the cone, find the volume of the cone in terms of
D. I, II and III only
2019-2020 S.6 Mock Examinations – Mathematics (Compulsory Part) Paper 2
15. In the figure, AB // DC, AD = BD = CD and ZADB = 28°.
16. In the figure, PQRS is a quadrilateral. PR intersects SQ at T.
TP = TS and TQ = TR. ZQSR=32° and ZQTR = 44° .
Which of the following is/are true?
17. In the figure, BC =
B. I and III only
A. AB sina + AD cosb.
B. AD sinb+ AB cosa.
C. AB sinb+ AD cosa.
D. ADsina + AB cosb.
C. II and III only
D. I, II and III
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 2
18. In the figure, AB = EF = 1 cm, BC = CD =
FG= x cm. If AG=
C. 168 cm²
B. 22.5 cm²
D. 25.5 cm²
19. In the figure, ABCDE is a pentagon with
ZA= LB=LC = 90°, AB = BC = 12 cm, DE = 4√√2 cm
and AE = CD. Find the area of the pentagon ABCDE.
A. 136 cm²
B. 144 cm²
DE 2 cm and
D. 180 cm²
20. In the figure, ABCD is a trapezium with AD//BC and
BC: AD= 2:1. E is a point lying on CD such that
CE: ED=3:1. If the area of AABE is 10 cm², find the
area of the trapezium ABCD.
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 2
21. Simplify
C. I and III only
22. In the figure, ABCD is a square with side 10 cm. EF,
FBG, GH and HDE are four arcs centred at A, D, C
and B respectively such that FAD, EAB, HCB and GCD
are straight lines. Find the area of the shaded region
bounded by GC, CH and GH correct to the nearest cm².
23. In the figure, the equations of the parallel
straight lines L₁ and L2 are ax+2y+b=0
and px+y+q=0 respectively. Which of the
following is/are true?
B. I and II only
D. II and III only
24. The straight line L is perpendicular to the straight line 2x+y-4 = 0. If the y-intercept of L is 4,
the equation of L is
A. 3x-6y+4=0. B. x-2y-4=0.
C. 3x-6y-4=0. D. x-2y+8=0.
25. The polar coordinates of the points P, Q and R are (4, 75°), (q, 165°) and (8,255°)
respectively. If the area of APQR is 18, q =
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 2
26. The equations of the circles C₁ and C₂ are x² + y² + 4x-12y-40=0 and x² + y² - 4x-8y=0
respectively. Let G₁ and G₂ be the centres of C₁ and C₂ respectively. Denote the origin by O.
Which of the following are true?
OG₂ LG₁G₂
C₁ and C₂ touch each other internally.
The area of C₁ is 4 times that of C₂.
A. I and II only B. I and III only
D. y=x²-2x+4.
27. It is given that A and B are two distinct points lying on the circle x² + y² - 4x-2y+1=0. The
mid-point of AB is (2, 0). Let P be a moving point in the rectangular coordinate plane such that
AP² + BP² = AB2. The equation of the locus of Pis
A. x² + y²-4x+1=0.
B. (x-2)² + y² = 4.
28. The table below recorded the admission scores of candidates applying for a programme in a
university.
C. II and III only
If the expected admission score of the programme is 24.6, n =
D. I, II and III
29. Daniel has 8 pens and only 1 of them is a black ball pen. He selects the pens one by one at
random without replacement. Find the probability that he selects the black ball pen in more
than 2 trials.
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 2
30. Consider the following numbers:
The mean and the mode of the above data are 51 and 58 respectively. Find the median.
31. The real part of
32. 85 +8¹¹=
A. 2000080016.
25 32 32 50 58 63
6i6 +7i7 +81 +9iº +10i¹0
B. 20000200016.
A. g(x)=-2f(x) +2
33. The graphs of y = f(x) and y = g(x) are shown below. Express g(x) in terms of f(x).
C. g(x)=-—ƒ(x)+3
C. 20000800016.
B. g(x)=-2 f(x)+3
)=-=-2 /(x) +2
D. 10000010000016.
2019-2020 S.6 Mock Examinations - Mathematics (Compulsory Part) Paper 2
34. In the figure, ABCD is a semicircle. It is given
that AC= 24 cm and CD=10 cm. Find the area
of the segment ABC correct to the nearest cm².
B. 139 cm²
C. 145 cm²
D. 199 cm²
35. The graph in the figure shows the linear relation between
log9 x and log3 y. Which of the following must be true?
be the nth term of a geometric sequence. It is given that a
sum to infinity of the sequence is smaller than
The first term of the sequence is
a₁ + a₂ + a₂ + a₁ +...+ a₂ + a₁0 <
a₂ + a₁ + a +Ag + ···=·
C. I and III only
which of the following is/are true?
D. II and III only