Question Booklet (Parts A and B)

Transcription

1 Mathematics Secondar V June 01 Competenc Uses Mathematical Reasoning Science Option Question Booklet (Parts A and B)

2 Instructions 1. Write all the required information in the Student Booklet. Answers written in this Question Booklet will not be evaluated; onl the Student Booklet will be evaluated.. There are three parts to this evaluation situation. Part A consists of si multiple-choice questions. Part B consists of four short-answer questions. Part C consists of si application situations. Part A and Part B questions are found in this Question Booklet. Part C is found onl in the Student Booklet. 3. Permitted materials Geometr set (ruler, compass, set square, protractor) Calculator (with or without graphic displa) Handwritten memor aid prepared b the student prior to the evaluation situation. The memor aid consists of one letter-sized sheet of paper (8½ 11 ). Both sides of the sheet ma be used. An mechanical reproduction of this memor aid cannot be used. Note: Figures have not necessaril been drawn to scale. BIM Société GRICS Page 1

3 Part A Questions 1 to 6 In the Student Booklet, darken the letter that corresponds to our answer. Each question is worth 4 marks. 1. Given the following sstem of inequalities: A B D C Which region represents the solution set of this sstem? A) Region A C) Region C B) Region B D) Region D BIM Société GRICS Page

4 . Johnn graphed m n( p) q as illustrated below. Maria transformed Johnn s graph b keeping the values of p and q the same, changing the sign of n and doubling the value of m. Which of the graphs below represents the graph of Maria s function? A) C) B) D) BIM Société GRICS Page 3

5 3. A biologist epresses the growth of a bacterial culture with the formula: t where, = the number of bacteria t = time in seconds A mathematician wants to epress the same relation so as to calculate the time needed to produce a certain number of bacteria. Which epression will she use? A) log log 100 t C) 3log B) t log log 100 D) 3log t t 4. Given the following trigonometric function: f ( ) tan 1 What is the period of this function? A) 1 C) B) D) BIM Société GRICS Page 4

6 5. The logo used b a basketball team was drawn using an ellipse and a hperbola. The logo is represented below in a Cartesian plane. The shaded region is defined b the two curves. The length of the major ais of the ellipse is 0 units. The distance between the foci of the ellipse is 1 units. The vertices of the hperbola coincide with the foci of the ellipse. The foci of the hperbola coincide with the endpoints of the major ais of the ellipse. What relation defines the shaded region of the hperbola? A) 1 C) B) 1 D) BIM Société GRICS Page 5

7 6. A swimmer sets out to swim at an angle of 40 with the horizon at 5 km/h. However, she meets a current and as a result swims 6 km/h at an angle of 0 with the horizon What are the components of the current, rounded to the nearest hundredth? A) (1.81, -1.16) C) (9.47, 5.6) B) (-1.81, 1.16) D) (9.47, -5.6) BIM Société GRICS Page 6

8 Part B Questions 7 to 10 In the Student Booklet, write our answer in the space provided. Each question is worth 4 marks. 7. Given the following equation: 3 3 log 3 log log What is the solution set? 1 3 Q θ, is a point on the standard unit circle. 8. Point What is the eact value of the epression: (Rationalize our answer). 5 cosecθ cos3θ? 9. Given the function ( ) f and g() is the inverse of f (). What is f g? BIM Société GRICS Page 7

9 10. A beautiful fountain in the middle of a recreational park is situated at a distance of 10 m from the street as shown in the diagram below. A walking path must be added to this park so that no matter where ou are on the walking path, ou will alwas be the same distance awa from the drinking fountain as ou are from the street. The fountain is located at (-7,0). street (-7,0) fountain a) What is the rule that defines the street? b) What is the rule that defines the walking path? BIM Société GRICS Page 8