中六 數學試卷 (F6 Maths Past Paper)

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Instructions:
Read carefully the instructions on the Answer Sheet. Put down the information required in the
spaces provided.
La Salle College
Mock Examination 2019-2020
Mathematics
Compulsory Part
Time allowed: 1 hour 15 minutes
When told to open this question paper, you should check that all the questions are there. Look for
the words 'END OF PAPER' after the last question.
All questions carry equal marks.
ANSWER ALL QUESTIONS. You should use an HB pencil to mark all your answers on the
Multiple Choice Answer Sheet. Wrong marks must be completely erased with a clean rubber.
Examination Number
You should mark only ONE answer for each question. If you mark more than one answer, you
will receive NO MARKS for that question.
No marks will be deducted for wrong answers.
The diagrams in this paper are not necessarily drawn to scale.
Use of HKEAA approved calculator is allowed.
2019-20 F.6 MOCK EXAM MATH CP 2 - Page 1
Let a be the nth term of an arithmetic sequence. If a = 225 and an
which of the following must be true?
- 480 is a term of the sequence.
II. There are 20 non-negative terms in the sequence.
III. a₁ + a₂ + a3 + ··· + A41 = 0.
A. I and II only
B. I and III only
C. II and III only
D. I, II and III
Which of the following may represent the graph of y=f(x) and the graph of y = -f(x - 1) on
the same rectangular coordinate system?
y = -f(x - 1)
- an+2 = 30, then
2019-20 F.6 MOCK EXAM MATH CP 2 - Page 10
y = -f(x - 1)
y = -f(x - 1)
y = -f(x - 1)
In the figure, circles C₁ and C₂ touch externally at E.
AB is a common tangent touching C₁ and C₂ at A
and B respectively. The radii of C₁ and C₂ are 4 cm
and 1 cm respectively. Find the area of AABE.
A. 1.6 cm²
B. 3.2 cm²
C. 4.8 cm²
D. 6.4 cm²
40. In the figure, O is the centre of the circle. BC and AC
are tangents to the circle at D and E respectively. AB
intersects the circle at F and G, FC intersects the
circle at H and BC LAC. M is the mid-point of FG.
Which of the following must be true?
C, O and M are collinear.
B, D, O and M are concyclic.
OC² = 2CFxCH.
41. The figure shows a cuboid ABCDEFGH with AB = 16,
BC = 12 and CH = 30. If the angle between the triangle
BFH and the plane EFGH is 0, then tan =
I and II only
I and III only
II and III only
MiN 11007/00
2019-20 F.6 MOCK EXAM MATH CP 2 - Page 11
42. Consider the graph of y= Asin(2x+B)° +C, where A> 0 and 0graph cuts the y-axis at (0, -1), touches the line y = -4 and also touches the x-axis at (3, 0),
where 043. In a company, there are 8 male workers including Mr. Chan, and 15 female workers including
Mrs. Chan. A committee is formed by selecting 3 male workers and 4 female workers such that it
cannot include both Mr. and Mrs. Chan. How many different committees can be formed?
An urn contains 3 blue balls, 4 red balls and 5 yellow balls. John repeats drawing one ball at a
time randomly from the urn with replacement until a blue ball is drawn. Find the probability that
John needs at least four draws.
The mean, variance and the median of a group of 10 numbers are 24, 5.2 and 24.5 respectively.
Now, two numbers 22 and 26 are inserted. Which of the following statements must be true?
I. The new mean will remain unchanged.
II. The new variance will decrease.
III. The new median will increase.
A. I and II only
B. II and III only
C. I and III only
D. I, II and III
- End of paper -
2019-20 F.6 MOCK EXAM MATH CP 2 - Page 12
There are 30 questions in Section A and 15 questions in Section B.
The diagrams in this paper are not necessarily drawn to scale.
Choose the best answer for each question.
4x² - 4y² + 4y-1=
A. (2x+2y-1)(2x-2y+1).
B. (2x+2y+1)(2x-2y-1).
C. (2x-2y-1)(2x-2y+1).
D. (2x+2y+1)(2x+2y-1).
If (a-3)(b +1) = a, then a =
0.0949495 =
(correct to 3 decimal places).
C. 0.094950 (correct to 5 decimal places).
(correct to 3 significant figures).
D. 0.094950 (correct to 5 significant figures).
2019-20 F.6 MOCK EXAM MATH CP 2 - Page 2
If f(x+1)=2x² + 4x+2, then f(x-1)=
The solution of x--
2x² - 4x+2.
2x² - 8x+8.
Let m and n be constants. If m(x−1)² +n(x+2)² = x² −20x−8, then m =
Let k be a constant. If the quadratic equation x² - 6x=k(x-8) has equal roots, then k =
A sum of $10 000 is deposited at 2% p.a., compounded half-yearly. Find the interest earned in
the second year, correct to the nearest dollar.
<3 and 6-x>-2 is
-= 3, then 5p : 4q =
2019-20 F.6 MOCK EXAM MATH CP 2 - Page 3
In AABC as shown, AC = BC. E is a point on AB such that
CE LAB. BC is produced to D such that ZADC = 90°.
Which of the following must be true?
D is the orthocentre of AABC.
II. The incentre of AABC lies on the line segment CE.
III. The circumcentre of AABC lies on the line segment CE.
C. III only
D. I and III only
When a watch is sold at a 20% discount, the loss percentage is 10%. What is the profit
percentage when the watch is sold at a 10% discount?
13. In the figure, the 1st pattern consists of 6 dots. For any positive integer n, the (n + 1)th pattern is
formed by adding (2n + 5) dots to the nth pattern. Find the number of dots in the 7th pattern.
Given that the volumes of a hemisphere, a right circular cylinder and a right circular cone are
the same. The radius of the hemisphere is a, the cylinder has base radius a and height b, the cone
has height a and base radius c. Which of the following must be true?
D. c < b 2019-20 F.6 MOCK EXAM MATH CP 2 - Page 4
Given that y partly varies directly as x and partly varies directly as x². Which of the following
graphs may show this relation?
In the figure, PQRS is a rectangle. RS is produced to I such
that RS = ST. V is a point on QR such that QV: VR = 2:3. TV
intersects PS at U. Find PU: QV.
A. 604 cm²
B. 612 cm²
C. 618 cm²
D. 624 cm²
2019-20 F.6 MOCK EXAM MATH CP 2 - Page 5
The compass bearing of R from P and Q are S15°E and S35°W respectively.
Given that PQPR, find the compass bearing of Q from P.
In the figure, E is a point on AB such that AECD is a parallelogram and EB : DC = 3:5. BD and
EC intersect at P. If the area of AEPD is 330cm², find the area of the quadrilateral ABCD.
In the figure, CD =
A. a cos-bsiny.
B. asin-bsiny.
C. a cos+bcos y.
D. asin+b cosy.
In the figure, P, Q, R and S are points lying on a circle.
If PQ: QR 3: 1, which of the following is/are true?
In the figure, ABCD is a parallelogram. E is a point on BC such that AAED ≈ ABCD.
If ZDCE = x, then ZBDE =
A. 3x - 180°.
B. 5x - 360°.
C. 180° - 3x.
D. 360° - 5x.
I. PQ: OR=3:1
II. ZPSR: ZQSR = 4:1
III. ZPSQ: ZPRQ=1:1
21. Given that the remainders when f(x) is divided by (x-3) and (x-9) are the same.
The polynomial f(2x-1)-f(x-2) must be divisible by
A. x² - 6x +5.
2x² -5x+2.
x² - 4x-5.
2x² - 5x+3.
A. III only
B. I and II only
C. II and III only
D. I, II and III
In the figure, O is the centre of the circle ABCD. Let
ZADB = x and ZOCB = y, then ZAOC =
B. 90° +x-y.
C. 180° + 2x - 2y.
D. 360° - 2x - 2y.
2019-20 F.6 MOCK EXAM MATH CP 2 - Page 6
In the figure, the equation of L₁ is x + ay+b= 0 and the
equation of L2 is x + cy + d = 0. L₁ and L2 intersect at the
same point on the y-axis. Which of the following are true?
III. ad = bc
A. I and II only
B. I and III only
C. II and III only
D. I, II and III
25. ABCD is a rectangle with AB = 1 and BC = 2. P is a moving point inside the rectangle ABCD,
such that it maintains an equal distance from B and D. Find the length of the locus of P.
III. The diameter of C is √19.
A. I and II only
B. I and III only
C. II and III only
D. I, II and III
26. The equation of the circle C is 2x² +2y² +4x-6y-3=0. Which of the following is/are true?
I. The origin lies inside the circle.
II. The line x+2y-2=0 divides the circle C into two equal parts.
2019-20 F.6 MOCK EXAM MATH CP 2 - Page 7
In AABC, the mid-points of AB, BC and CA are P(3, 0), Q(6, 5) and R(12, 7). Find the length
There are 10 white, 10 yellow and 2 green socks in a drawer. Tom randomly takes out 3 socks
from the drawer. Find the probability that at least two socks taken out are of the same colour.
Two numbers are obtained from throwing two fair dice. Find the probability that the ratio of the
two numbers can give an integer.
The standard deviation of 1 and x is 4, where x is positive. Find the mean of 1 and .x.
31. The H.C.F. and L.C.M. of three expressions (x-2)(x³ -8), (x-2)³ and P(x) are (x-2) and
(x+2)(x−2)³(x²+2x+4) respectively. The expression of P(x) can be
II. (x²-4)(x³ -8)
III. (x+2)(x³-8)
B. I and II only
C. I and III only
D. II and III only
2019-20 F.6 MOCK EXAM MATH CP 2 - Page 8
In the figure, the graph shows the linear relation between
log₂x and logat. Which of the following must be true?
A. x² = 3t³
D. x² = 64t³
8x26 +2³+5x2² - 2² =
A. 10 0000 11002
B. 10 0001 10002
C. 100 0000 11002
D. 100 0001 10002
Let a be a real number and i=√√1. If x=- then
36. Consider the following system of inequalities:
3x+2y-30 ≤0
2019-20 F.6 MOCK EXAM MATH CP 2 - Page 9
35. If the straight line y = x + k and the circle x² + y² - 6x + 4y - 12 = 0 intersect at A and
B, then the y-coordinate of the mid-point of AB is
Let R be the region on a rectangular coordinate plane which satisfies the above system of
inequalities. If (x, y) is a point lying in R, then the greatest value of 2x -y +18 is