中二 數學試卷 (F2 Maths Past Paper)

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內容節錄：
170 students
Instructions:
St. Stephen's Girls' College
Final Examination 2017-2018
MATHEMATICS
Time Allowed: 1 hour 30 minutes
Attempt ALL questions.
Write your answers in the spaces provided in this
Question-Answer Paper.
ALL working must be clearly shown.
The diagrams in this paper are not necessarily
drawn to scale.
This paper carries 100 marks.
Unless otherwise specified, numerical answers
should be either exact or correct to 3 significant
Question Marks
Page 1 of 14
LC, WMC, LL, WYL, CYN
Question Marks
F.2 Mathematics Paper I
14. It is given that 0°< < 90°.
Final Examination 2017-2018
(a) Prove the identity tan(90°- 0) + tan 0 = -
Is it possible to have a value of such that tan(90° - 0) + tan == ? Explain your answer.
Page 10 of 14
F.2 Mathematics Paper I
15. In the figure, a vertical pole PQ with length h m is
fixed on the horizontal ground AB. It is known
that AB = 6 m, ZPAB = 45° and ZPBA = 30°.
(a) Express AQ and QB in terms of h. (2 marks)
(b) Find the total length of PA and PB. (4 marks)
Final Examination 2017-2018
Page 11 of 14
F.2 Mathematics Paper I
Final Examination 2017-2018
16. Carrot juice and apple juice are mixed to prepare Drink A and Drink B. The ratio of the volume of
carrot juice to that of apple juice in Drink A is 3:2. The ratio of the volume of carrot juice to
that of apple juice in Drink B is 3: 7. Now, Drink A and Drink B are mixed in the ratio 1 : 2 by
volume to prepare Drink C. Suppose the volume of Drink A in Drink C is x mL and the volume of
Drink B in Drink C is 2x mL.
(a) Express the volume of carrot juice in Drink C in terms of x.
(b) Express the volume of apple juice in Drink C in terms of x.
(c) Hence, find the ratio of the volume of carrot juice to that of apple juice in Drink C.
Page 12 of 14
F.2 Mathematics Paper I
Final Examination 2017-2018
17. ABCD is a parallelogram. Let E be the mid-point of AD. If ZCBD = ZDBE = x, determine
whether AABD is a right-angled triangle. Explain your answer.
Page 13 of 14
F.2 Mathematics Paper I
Final Examination 2017-2018
18. It is given that 3+3² +3³ +...+3″ =- (3"-1), where n is a positive integer greater than 1.
(a) Find the value of 3+3² +3³ +...+3⁹.
It is given that 3+3² +3³ +...+3″ = A(3+3³ +3³ +....+3"-¹), where n can be any positive
even number and A is a constant. Find the value of A.
[Hint: 3+3² +3³ +...+3" =(3+3³ +3³ +...+3″¯¹)+(3² +3¹ +3° +...+3″)]
(c) Hence, show that 3+3³ +35 +...+3"-1
(3"-1) if n is a positive even number.
End of Paper
Page 14 of 14
F.2 Mathematics Paper I
Final Examination 2017-2018
1. If (x+y): 3 = (2y - x): 4, find x : y.
2. (a) Make a the subject of the formula
(b) Find the value of a when b = 2.
-= a + b(a + 1).
Page 2 of 14
F.2 Mathematics Paper I
Final Examination 2017-2018
3. If A and B are constants such that Ax(x - 5) - x² = Bx(x + 6) 93x, find the values of A and B.
4. In AABC, BA = BC and ZA=2ZB = x. Find x.
It is given that the sum of interior angles of an n-sided polygon is 9 times that of its exterior
angles. Find the value of n.
Page 3 of 14
F.2 Mathematics Paper I
Final Examination 2017-2018
The following tables show the recorded time, correct to the nearest second, for 100 athletes to
cover a lap of a running track.
Cumulative frequency table:
Recorded time
less than (s)
Frequency distribution table:
Class Mark (s)
75-79 80-84 85-89
Page 4 of 14
(a) Complete the cumulative frequency table and the frequency distribution table above. (2 marks)
(b) According to the information in (a), draw the corresponding frequency polygon. (5 marks)
(c) To qualify for an international athletic competition, an athlete needs to have a lap time of less
than 79.5 seconds. Find the percentage of athletes who are not qualified for the competition.
F.2 Mathematics Paper I
Final Examination 2017-2018
7. It is given that the graph of the equation ax + y - 7 = 0
passes through P(2, 1).
(a) Find the value of a.
(b) If the graph cuts the y-axis at B(0, b), find the value
is a line parallel to the x-axis. I cuts the y-axis at A and
passes through P. Find the area of AABP. (2 marks)
Page 5 of 14
8. (a) Factorize -27a - 3.
Factorize 9ab + 18a + b + 2.
(c) Using the results of (a) and (b), factorize 9ab +18a+b+2-27a - 3.
F.2 Mathematics Paper I
Final Examination 2017-2018
9. In the figure, ZB = 90°, AD = 53 cm and CD = 28 cm. It is given that AB BC = 3 : 4 and the
perimeter of ABCD is 144 cm.
(a) Find the length of AB.
(b) Is AACD a right-angled triangle? Explain your answer.
(c) Find the area of ABCD.
Page 6 of 14
F.2 Mathematics Paper I
10. (a) Expand and simplify √a (√a+√12b).
(b) Write down a pair of values for a and b such that √(√a+√126) is a rational number.
11. Simplify
Final Examination 2017-2018
and rationalize the denominator of the result if necessary.
Page 7 of 14
F.2 Mathematics Paper I
Final Examination 2017-2018
12. In the figure, AABC and AADC are two right-angled triangles. It is
given that ZDAC = 22°, BC= 5 and CD = 2. Find
(a) the length of AC,
the length of AB.
Page 8 of 14
F.2 Mathematics Paper I
13. It is given that cos : sin = 5:12.
(a) Find the values of cos, sin and tan 0.
Final Examination 2017-2018
(b) By using the result in (a), find the value of
2 tan (90°- 0)
Page 9 of 14
cos (90°-0)