✅f5 syss 2015 exam2 paper2
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The Hong Kong Polytechnic University**We aren't endorsed by this school
Course
ABCT 1301
Subject
Mathematics
Date
Dec 29, 2024
Pages
9
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2016-FINAL EXAM-MATH-CP-2 (F.5 A & B) 1 SING YIN SECONDARY SCHOOL FINAL EXAMINATION 2015 – 2016 F.5MATHEMATICSCompulsory PartPAPER2 Time allowed: 1 hour 15 minutes 1. Read carefully the instructions on the Answer Sheet. Insert the information required in the spaces provided. 2. When told to open this book, you should check that all the questions are there. Look for the words ‘END OF PAPER’ after the last question. 3. All questions carry equal marks. 4. 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. 5. You should mark only ONEanswer for each question. If you mark more than one answer, you will receive NO MARKSfor that question. 6. No marks will be deducted for wrong answers. 2016 FINAL EXAM MATH CP PAPER 2 F.5A & B
2016-FINAL EXAM-MATH-CP-2 (F.5 A & B) 2 The diagrams in this paper are not necessarily drawn to scale. Choose the best answer for each question. 1. 201620151aa−=A. a. B. 1a. C. a−. D. 1a−. 2. If 1xax=−, then x= A. 1aa+. B. 1aa+. C. 1aa−. D. 1aa−. 3. 2212xxyy−+−=A. (1)(1)xyxy++−−. B. (1)(1)xyxy+−−−. C. (1)(1)xyxy++−+. D. (1)(1)xyxy+−−+. 4. If aand bare constants such that 2(2)()8xaxxb+≡+++, then a= A. 4−. B. 4. C. 8. D. 12. 5. The solution of 639x−<<or 127x−≤is A. 23x−<<. B. 23x−<<or 3x≤ −. C. 33x−≤<. D. 3x≥ −. 6. 0.0644505 = A. 0.064 (correct to 2 decimal places). B. 0.0645 (correct to 3 significant figures). C. 0.06445 (correct to 4 decimal places). D. 0.064450 (correct to 5 significant figures). 7. If 4759mnmn−=+=, then n=A. 2−. B. 1−. C. 1. D. 2. 8. Let 32( )32f xxxkx=++−, where kis a constant. If ( )f xis divisible by 31x+, find the remainder when( )f xis divided by 1x−. A. −10 B. −6 C. −4 D. 8
2016-FINAL EXAM-MATH-CP-2 (F.5 A & B) 3 A B C D 8 9 11 θ9. In the figure, find θcorrect to the nearest degree. A. 31o B. 36oC. 49oD. 54o10. In the figure, ABCDis a trapezium with DCAB//, 8==BCAD, 10=ABand 6=CD. Area of trapezium ABCD= A. 1516. B. 1716. C. 1532. D. 1732. 11. If a watch is sold at a 30% discount on its marked price, then the profit percentage is 40%. If the watch is sold at a 20% discount on its marked price, then the profit is $150. Find the marked price of the watch. A. $250 B. $300 C. $400 D. $500 12. xvaries directly as yand inversely as z. If yis increased by 20% and zis decreased by 36%, then xis A. decreased by1333%. B. decreased by 10%. C. increased by 50%. D. increased by 87.5%. 13. In the figure, the 1st pattern consists of 4 rods. For any positive integer n, the (n+1)th pattern is formed by adding (2n+4) rods to the nth pattern. Find the number of rods in the 6th pattern. A. 16 B. 40 C. 54 D. 70 14. A box contains 4 red pens and 6 blue pens. If 2 pens are randomly drawn at the same time from the box, find the probability that the pens are of different colours. A. 415B. 715C. 815D. 1225
2016-FINAL EXAM-MATH-CP-2 (F.5 A & B) 4 y x y = 3 y = f(x)−1 3 0 15. In the figure, ABCDEFGHis a cube. BHand GCintersect at M. Pis the mid-point of CH. The angle between DMand the plane BCHGis A. ∠DMG. B. ∠DMP. C. ∠DMC. D. ∠DMB. 16. In the figure, solve3)(≤xf. A. 13x− ≤≤B. 03x≤≤C. 10x− ≤≤or 3x≥D. 1−≤xor 03x≤≤17. 1sinsin(180)cosθθθ°−−= A. θtan1−. B. θtan1. C. θθtancos2−. D. θθtancos2. 18. If the five interior angles of a convex pentagon form an arithmetic sequence with a common difference of 10°, then the smallest interior angle of the pentagon is A. 72°.B. 88°.C. 98°.D. 108°. 19. If αand βare the roots of the equation x2+ 3x−1 = 0, find the value of 22αβ+. A. 5 B. 7 C. 9 D. 11 20. Which of the following about the graph of 222yxx=−+−is/are true? I. The equation of the axis of symmetry of the graph is 1x=.II. The graph intersects the x-axis. A. None of the above B. I only C. II only D. I and II C D B A M E H G F P
2016-FINAL EXAM-MATH-CP-2 (F.5 A & B) 5 21. The mean of five numbers p, q, r, s, tis 14. The mean of p, q, ris 16, find the mean of sand t. A. 11 B. 14 C. 15 D. 16 22. The mean mark of a Mathematics test was 58. The following table shows the marks and standard score of Billy and Charlie in the test. Find x. A. 2.25 B. 2.5 C. 2.75 D. 3.0 23. L1and L2are two parallel straight lines with different yintercepts. If the equation of L1is y= 3x−5, which of the following may be the equation of L2 ? A. 350xy−+=B. 350xy−−=C. 3150xy++=D. 3150xy+−=24. If the graph of y=( )f xis first translated 3 units to the right and then reflected along the x-axis, the equation of the image is A. (3)yf x=−−. B. (3)yf x=−+. C. (3)yfx=−+. D. (3)yfx=−−. 25. In the figure, AB//CD, AF= FEand CDis the tangent to the circle at E. If BED= 80°, find BAF. A. 60°B. 80°C. 100°D. 120°26. In the figure, Ois the centre of the circle ABCD. If 23ABBCCD==⌢⌢⌢and ∠AOD= 96°, then ∠ABC= A. 66°. B. 70°. C. 72°. D. 88°. 27. Two circles 221:(12)Cxyk+−=and 222: (9)100Cxy−+=touch each other externally at a point P. Find the radius of C1. A. 5 B. 6 C. 10 D. 25 Marks Standard Score Billy 72 1.75 Charlie 80 xB A 80°D F C E B C D O A
2016-FINAL EXAM-MATH-CP-2 (F.5 A & B) 6 28. A circle with centre (2, –3) cuts the y-axis at A and B. If AB= 10, then the equation of the circle is A. 2246100xyxy+−+−=. B. 2246160xyxy+−+−=. C. 2246160xyxy++−−=. D. 2246100xyxy++−−=. 29. Two fair dice are thrown. It is given that the sum of the two numbers thrown is less than five, find the probability that both numbers are odd. A. 21B. 61C. 121D. 12730. There are 9 boys and 3 girls in a class. 2 boys and 1 girl are chosen to join a competition. How many ways are there to choose the players? A. 36 B. 108 C. 144 D. 216 31. OABis a sector. OA = 3 cm and AB⌢=2 cm. Find the area of the sector. A. 3 cm2B. 6 cm2C. 3πcm2D. 6πcm232. If ( )log2f xx=, then (1)( )f xf x+−= A. log2. B. 21log()2xx+. C. 1log()xx+. D. log(22)log 2xx+. 33. If the variance of a, band cis 7, then the variance of 2a+ 1, 2b+ 1 and 2c+ 1 is A. 14. B. 15. C. 28. D. 29. 34. If Pis a moving point on the rectangular coordinate plane such that the distance between Pand the straight line6y=is equal to the distance between Pand the origin, then the locus of Pis A. a circle. B. a straight line. C. a parabola. D. a pair of parallel lines. 35. The diagram shows an equilateral triangle divided into six identical smaller triangles. Two of these triangles are randomly selected and shaded. What is the probability that the resulting figure has an axis of reflectional symmetry? A. 16B. 13C. 12D. 35
2016-FINAL EXAM-MATH-CP-2 (F.5 A & B) 7 36. A(0 , 6) and B(8 , 0) are two points in a rectangular coordinate plane. P(x, y) is a moving point such that PA⊥PB. Find the equation of the locus of P. A. x2+ y2– 8x– 6y= 0 B. x2+ y2– 6x– 8y= 0 C. 4x+ 3y– 25 = 0 D. 4x−3y– 7 = 0 37. If x > 1, then 24621......nxxxx++++=A. 2211nxx+−−. B. 2211nxx−−. C. 21211nxx+−−. D. 22211nxx+−−. 38. The figure shows the graph of A. 2cos2yx=+. B. 12cos 2yx=+. C. 12cos2xy=+. D. 2cos2xy=+. 39. The graph in the figure shows the linear relation between xand3logy. If xyab=, then a= A. −1. B. 13. C. 1. D. 3. 40. The figure shows a pyramid with a rectangular base ABCD. The plane VADis perpendicular to the base and VA= VD. VBand VCare each inclined at 50º to the base. Find the height of the pyramid. A. 2.38 m B. 3.58 m C. 4.77 m D.5.96 m 41. Let a, b, cand dbe the mean, median, inter-quartile range and standard deviation of the group of numbers {}4, 2, , , , , , 1, 2, 3xxxxxxxxxx−−+++respectively. Which of the following must be true? I. ab=II. cd=A. None of the above B. I only C. II only D. I and II Olog3y x−13A B C D V 4 m6 m y x 3 0 180°−1
2016-FINAL EXAM-MATH-CP-2 (F.5 A & B) 8 42. If 0k≠, which of the following groups of numbers has the greatest value of standard deviation? A. 4k, 6k, 6k, 7k, 7kB. 5k, 6k, 6k, 6k, 7kC. 4k, 5k, 6k, 7k, 8kD. 5k, 5k, 6k, 6k, 8k43. A(0, −3), B(0, 8) and C(2, 2) are the vertices of a triangle. Which of the following are true? I. The orthocentre of ∆ABClies on the line2y=. II. The circumcentre of ∆ABClies inside the triangle. III. The incentre of ∆ABClies inside the triangle. A. I and II only B. I and III only C. II and III only D. I, II and III 44. In the figure, ABCDis a square. Eand Fare the midpoints of BCand CDrespectively. AEand AFcut BDatMand Nrespectively. Area of Area of MNFCEABCD=A. 13. B. 25. C. 512. D. 37. 45. In the figure, AQBis a semicircle with centre Owhich is inscribed in the rectangle ABCD. APQCis a straight line and AP= PQ. Find APB. A. 135°B. 140°C. 142°D. 144°END OF PAPER A B C D F E M N C D Q P B A O
2016-FINAL EXAM-MATH-CP-2 (F.5 A & B) 9 Key:BADBD BBCDA DCCCC DABDB ACAAD CABAB ACCCD ADBBD BCBAA