Mathematics Exam Questions and Answers for August 2009, Exams of Mathematics

Download Mathematics Exam Questions and Answers for August 2009 and more Exams Mathematics in PDF only on Docsity! Page 1 of 16 Mathematics 3205 August 2009 PART I Total Value: 50% Answer all items. Shade the letter of the correct answer on the computer scorable answer sheet. 1. What is the common difference between successive terms generated by the sequence 2 3 4nt n= + ? (A) 4− (B) 2 3 (C) 3 2 (D) 4 2. Which represents a quadratic relationship? (A) x 0 1 2 3 4 y –3 1 5 9 13 (B) x 0 1 2 3 4 y 0 4 16 64 256 (C) x 0 1 2 3 4 y 3 4 7 12 19 (D) x 0 1 2 3 4 y –2 –1 6 25 62 3. What is the value of 3D for the sequence generated by 3 24 3 2 1nt n n n= − + − + ? (A) 24− (B) 12− (C) 8− (D) 4− 4. A quadratic sequence is given by 2a b 5nt n n= + + . What is the value of b if 2 6D = and 3 14t = ? (A) 15− (B) 9− (C) 6− (D) 3− 5. What is the value of the discriminant for ( ) 0f x = in the graph provided? (A) 9− (B) 3− (C) 0 (D) 3 y x Mathematics 3205 August 2009 Page 2 of 16 6. Which represents the area of a rectangle with a perimeter of 80 m? (A) 22 80A x x= − + (B) 2 40A x x= − + (C) 2 40A x x= − (D) 22 80A x x= − 7. Which has the smallest vertical stretch factor when compared to 2y x= ? (A) 22( 1) ( 3)y x− + = − (B) 23 4 ( 1) ( 3)y x− + = − (C) 227 ( 1) ( 3)y x+ = − (D) 23( 1) ( 3)y x+ = − 8. Which describes the graph of 22( 3) ( 1)y x− + = − when compared to 2y x= ? (A) reflected across the x-axis, vertical stretch factor of 2− , translated 3 units down and 1 unit right (B) reflected across the x-axis, vertical stretch factor of 1 2 − , translated 3 units up and 1 unit left (C) reflected across the x-axis, vertical stretch factor of 1 2 , translated 3 units down and 1 unit right (D) reflected across the x-axis, vertical stretch factor of 2 , translated 3 units up and 1 unit left 9. What is the value of ( )3f − for the quadratic function ( ) 22 3 1f x x x= − + − ? (A) 28− (B) 10− (C) 8 (D) 26 10. What is the y-intercept of the function 21 2 1) ( 3)(y x− − = + ? (A) 20− (B) 17− (C) 11− (D) 5− 11. What is the range of 21a ( q) ( p) where a 0y x+ = − < ? (A) { }q,y y y R≥ − ∈ (B) { }q,y y y R≤ − ∈ (C) { }q,y y y R≥ ∈ (D) { }q,y y y R≤ ∈ 12. What is the value of k if 2k 5 6 0x x+ − = has a root of 2− ? (A) 4− (B) 1− (C) 1 (D) 4 Page 5 of 16 Mathematics 3205 August 2009 25. What is the range of the function 20(1.8) 3.4xy = + ? (A) { }3.4,y y y R> ∈ (B) { }3.4,y y y R≥ ∈ (C) { }23.4,y y y R> ∈ (D) { }23.4,y y y R≥ ∈ 26. The graph of 3 kxy = + is translated vertically upward by 5 units. What is the equation of the horizontal asymptote for the translated graph? (A) 5y = (B) ky = (C) k 5y = − (D) k 5y = + 27. Which describes the function 2(3) 5xy −= + ? (A) a decay function with y-intercept 5 (B) a decay function with y-intercept 7 (C) a growth function with y-intercept 5 (D) a growth function with y-intercept 7 28. What is the focal point for the graph of 12 5xy += − ? (A) ( )1, 4− − (B) ( )0, 5− (C) ( )1,6 (D) ( )2,5 29. What transformations have been applied to 2xy = to result in the graph for the function 2 31 2 xy −− = ? (A) horizontal stretch of 1 2 , 3 2 units to the right, 1 unit up (B) horizontal stretch of 1 2 , 3 units to the right, 1 unit up (C) horizontal stretch of 2 , 3 2 units to the right, 1 unit up (D) horizontal stretch of 2 , 3units to the right, 1 unit up 30. The population of a city is increasing at a rate of 0.5 % every 6 months. If the population of the city is currently 200 000, what will it be after 60 months? (A) 200 832 (B) 208 299 (C) 210 228 (D) 325 778 Mathematics 3205 August 2009 Page 6 of 16 31. Which is the graph of 5logy x= ? (A) (B) (C) (D) 32. What is the logarithmic form of 3 481 27= ? (A) ( )3 4 log 27 81= (B) ( )27 34log 81= (C) ( )27 34log 81 = (D) ( )81 34log 27 = 33. What is the new equation if the graph of 2logy x= is reflected in the x-axis? (A) ( )2logy x= − (B) ( )2logy x= − (C) 2x y= (D) 2 y x= y x y x y x y x Page 7 of 16 Mathematics 3205 August 2009 34. What is the simplified form of 1 3 2log 5 log 6 log 8a a a+ − ? (A) log 29a (B) log 30a (C) log 75a (D) 2 log 15a 35. What is the exact value of x for (1.3) 28x = ? (A) log1.3 log 28 (B) 1.3 28 log       (C) log 28 log1.3 (D) 28 1.3 log       36. What is the value of x for 32log 2 0x + = ? (A) 3− (B) 1 256 − (C) 1 256 (D) 3 37. What transformation of 2 2( 4) ( 3) 1x y− + − = produces 2 2 1 1 52 ( 4) ( 3) 1x y   − + − =    ? (A) horizontal stretch of 1 2 , vertical stretch of 15 (B) horizontal stretch of 2 , vertical stretch of 5 (C) horizontal stretch of 2, vertical stretch of 5 (D) horizontal stretch of 4, vertical stretch of 25 38. What is the length of the major axis of the ellipse given by the equation 2 2 1 1 53 ( 1) ( 3) 1x y   − + − =   ? (A) 3 (B) 5 (C) 6 (D) 10 Mathematics 3205 August 2009 Page 10 of 16 46. In the circle with centre O shown, diameter PS 16= . What is the approximate total area, in square units, of the shaded regions? (A) 42 (B) 84 (C) 168 (D) 336 47. Which mapping rule transforms 2 2( 4) ( 2) 9x y− + + = to 2 2( 10) ( 2) 36x y− + + = ? (A) ( ) ( ), 2 6, 2x y x y→ − (B) ( ) ( ), 4 6, 4x y x y→ − (C) ( ) ( ), 2 6,2x y x y→ + (D) ( ) ( ), 4 6,4x y x y→ + 48. What is a possible value for D such that 2 2 D 6 4 0x y x y+ + − − = represents a circle with a radius of 7? (A) 6 (B) 12 (C) 18 (D) 36 49. If a point P ( )6,0− is rotated 120° on a circle with its centre at the origin, what are the new coordinates of P? (A) ( )3,3 3− (B) ( )312 2,− (C) ( )3, 3 3− (D) ( )3 12 2,− 50. In the circle with centre O shown, OB 12 cm= and the total perimeter of the shaded sector is 3 24π+ . What is the measure, in degrees, of AOB∠ ? (A) 7.5 (B) 21 (C) 22.5 (D) 45 R P S Q O 30° A B O 12 cmx Page 11 of 16 Mathematics 3205 August 2009 PART II Total Value: 50% Answer ALL items in the space provided. Show ALL workings. Value 4 51. Algebraically determine the exact roots in simplest form for 2 1 6 2 3 2 x x x x + = + + + . 4 52. A flower bed is in the shape of a rectangle and its length is twice its width. The bed is surrounded by a 4 m wide walkway. If the total area of the bed and walkway is 504 m2, algebraically determine the width of the flower bed. 4 4 w Mathematics 3205 August 2009 Page 12 of 16 Value 4 53. The sum of the roots for 22 (k 3) 1 0x x+ − + = is equal to the product of the roots for 25 3 (k 1) 0x x− + + = . Algebraically determine the value(s) of k. 4 54. A soccer player takes a shot on goal 20 m away from the goal line. The ball reaches a maximum height of 8 m and lands 4 m behind the goal line. If the top of the net is 3 m high, algebraically determine whether or not the player scored a goal. Soccer Net 20 m Goal Line Page 15 of 16 Mathematics 3205 August 2009 Value 3 60. Write the equation 2 24 9 8 72 112 0x y x y+ − + + = in transformational form. 3 61. In the circle shown, algebraically determine the measure of AED∠ in degrees. C D B A E 10x + 8 4x + 8 x 2 Mathematics 3205 August 2009 Page 16 of 16 Value 4 62. Using coordinate geometry, prove that the line segment joining A to the midpoint of BC and the line segment joining C to the midpoint of AB are congruent. 4 63. In the circle with centre O shown, XY is tangent to the circle at Z. Calculate the total area of the shaded regions if YZP 60∠ = ° and the radius is 7.5. Y Z O P7.5 X 60° W A (0,0) C (4a,0) B (2a,2b) x y