Reading Time: 15 minutes Writing Time: 1 hour Student Name: Structure of Booklet Number of questions Number of questions to be answered Number of marks 10 10 40 Students are permitted to bring into the examination room: pens, pencils, highlighters, erasers, sharpeners, rulers. Students are NOT permitted to bring into the examination room: notes of any kind, blank sheets of paper, white out liquid/tape or a calculator of any type. Materials Supplied Question and answer book of 13 pages. A separate sheet of miscellaneous formulas. Working space is provided throughout the book. Instructions Write your name in the space provided above on this page. All written responses must be in English. Students are NOT permitted to bring mobile phones and/or any other unauthorised electronic devices into the examination room.
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Instructions Answer all questions in the spaces provided. In all questions where a numerical answer is required, an exact value must be given unless otherwise specified. In questions where more than one mark is available, appropriate working must be shown. Unless otherwise indicated, the diagrams in this book are not drawn to scale. QUESTION 1 (4 marks) Consider the function with equation 2 f ( x) 2x 16x 25. (a) State the equation describing y 2 f (1 x). (b) Write 2x 2 16x 25 in the form a( x h) 2 k. 1 mark 2 marks The School For Excellence 2016 Unit 1 Mathematical Methods Examination 1 Page 1
(c) State the inequality that describes the graph below given that the rule for y is written in the form y ( x a)( x b). 1 1 mark The School For Excellence 2016 Unit 1 Mathematical Methods Examination 1 Page 2
QUESTION 2 (3 marks) 3 2 Given that x 2 is a factor of 2x x 13x 6, find the other two linear factors. 3 marks The School For Excellence 2016 Unit 1 Mathematical Methods Examination 1 Page 3
QUESTION 3 (4 marks) The graph of the relation y x 3 5x 2 x 10 is shown below. 2 (a) Write the relation in the form y x ax bx c 2 marks. The School For Excellence 2016 Unit 1 Mathematical Methods Examination 1 Page 4
(b) Hence find the values of x where the graph cuts the horizontal axis. 2 marks The School For Excellence 2016 Unit 1 Mathematical Methods Examination 1 Page 5
QUESTION 4 (6 marks) 4 (a) Sketch the graph of the function f ( x) 1 on the axes below. Indicate the 2 x 3 coordinates of any intercepts and equations of any asymptotes on the graph. 3 marks The School For Excellence 2016 Unit 1 Mathematical Methods Examination 1 Page 6
(b) Find the equation for f 1 ( x ). 3 marks The School For Excellence 2016 Unit 1 Mathematical Methods Examination 1 Page 7
QUESTION 5 (5 marks) A quadrilateral OABC is formed by joining the points O (0, 0 ), A (5, 3), B (8, 8) and C (3, 5). (a) Prove that the quadrilateral OABC is a rhombus. 2 marks (b) Find the equations of the diagonals OB and AC and show that they intersect at the point (4, 4). 3 marks The School For Excellence 2016 Unit 1 Mathematical Methods Examination 1 Page 8
QUESTION 6 (4 marks) 2 If x 3x 5 A( x 3)( x 2) B( x 2) C( x 3) find the values of AB, and C. 4 marks The School For Excellence 2016 Unit 1 Mathematical Methods Examination 1 Page 9
QUESTION 7 (3 marks) State the equation describing the family of cubic functions with x intercepts at 2 and 3 5. Hence find the equation for the member of the family whose graph has a Y intercept of 1 2. 3 marks The School For Excellence 2016 Unit 1 Mathematical Methods Examination 1 Page 10
QUESTION 8 (4 marks) The rule for the graph shown is of the form y k a x b. Find the values of ab, and k. 4 marks The School For Excellence 2016 Unit 1 Mathematical Methods Examination 1 Page 11
QUESTION 9 (4 marks) (a) Find the points of intersection of the graphs with equations f ( x) 6 x and g( x) x. 2 marks (b) Find f( x) 0 given that f ( x) 3x 2x 8x 12x 4 2 3. 2 marks The School For Excellence 2016 Unit 1 Mathematical Methods Examination 1 Page 12
QUESTION 10 (3 marks) A function f has roots at 1, 3 and 5. Given that f ( 2) and f (2) are negative, while f (4) and f (6) are positive, sketch the graph of f. END OF QUESTION AND ANSWER BOOKLET The School For Excellence 2016 Unit 1 Mathematical Methods Examination 1 Page 13