Questions Paper > 2020 VCE Mathematical Methods Trial Examination 2

2020 VCE Mathematical Methods Trial Examination 2 Question 1 The maximal domain of the function f x ( ) loge(x a) x b + = - where b a   0 is given by A. R b \{ } B. R a b \{ , } - C. (b , ) D. (-  a, ) E. ...

2020 VCE Mathematical Methods Trial Examination 2 Question 1 The maximal domain of the function f x ( ) loge(x a) x b + = - where b a   0 is given by A. R b \{ } B. R a b \{ , } - C. (b , ) D. (-  a, ) E. (-  a b b , , ) ( ) Question 2 Consider the polynomial p x x a x a ( )= - + 3 2 3 7 6 , where a R  \{0}, then which of the following is false? A. when p x ( ) is divided by x a + the remainder is 12 . a3 B. when p x ( ) is divided by x a -3 the remainder is 12 . a3 C. p x ( ) has x a - as a factor. D. p x ( ) has x a + 2 as a factor. E. p x ( ) has x a +3 as a factor. Instructions for Section A Answer all questions in pencil on the answer sheet provided for multiple-choice questions. Choose the response that is correct for the question. A correct answer scores 1; an incorrect answer scores 0. Mark will not be deducted for incorrect answers. No marks will be given if more than one answer is completed for any question. Unless otherwise indicated, the diagrams in this book are not drawn to scale. 2020 Kilbaha VCE Mathematical Methods Trial Examination 2 Section A Page 5 © Kilbaha Education Publishing https://kilbaha.com.au This page must be counted in surveys by Copyright Agency Limited (CAL) http://copyright.com.au Question 3 The graph of the function f is obtained from the graph of the function with rule g x b a x ( ) = + , where a b R ,  by a reflection in the y-axis, followed by a translation of one unit to the right parallel to the x-axis, followed by a dilation of a units away from the y-axis. Which of the following is a possible rule for the function f ? A. f x b a x ( )= + - B. f x b a ax ( ) = - + - C. f x b a a x ( )= + - 2 D. f x a b a x ( )= - + E. f x a b a x ( ) = - + - ( 1) Question 4 The graphs of y a k x = - 2 and y 1 x = where a  0 intersect at two distinct points when A. 2 2 a a -   k B. a 2 k  C. 2 2 a a   - k D. a 2 k  - and a 2 k  E. a 2 k =  Question 5 The function f has the property f x f y f x y f x f y ( )+ = + - ( ) ( ) 2 ( ) ( ) for x  0 and y  0. Which of the following is a possible rule for the function f ? A. f x x ( )= B. f x ( ) 1 x = C. f x x ( )= 2 D. f x e ( )= x E. f x x ( )= loge( ) 2020 Kilbaha VCE Mathematical Methods Trial Examination 2 Section A Page 6 © Kilbaha Education Publishing https://kilbaha.com.au This page must be counted in surveys by Copyright Agency Limited (CAL) http://copyright.com.au Question 6 Several students were considering the function f D R f x : , ( ) b a x x a - → = + where a R  \{0}. Allan stated that the maximal domain D R a = - \{ } and that the function has no turning points, as it is a one-to-one function. Ben stated that the graph crosses the x-axis at x b a = and the graph crosses the y-axis at y b a . Colin stated that the graph has a vertical asymptote at x a = - and a horizontal asymptote at y a = - . Then A. Only Allan is correct. B. Only Ben is correct. C. Only Colin is correct. D. Only Ben and Colin are correct. E. All of Allan, Ben and Colin are all correct. Question 7 The graph of g x x k x ( )= + 2log 2 e( ) has a stationary point at x = -2, then A. k = -1. B. k =1. C. k = 0. D. k = 2. E. k = -2. Question 8 Given that then | is equal to-12(2 1 3 f x dx ( )- = ) 1-2 f x dx ( ) A. -5 B. -3 C. -2 D. 2 E. 3 2020 Kilbaha VCE Mathematical Methods Trial Examination 2 Section A Page 7 © Kilbaha Education Publishing https://kilbaha.com.au This page must be counted in surveys by Copyright Agency Limited (CAL) http://copyright.com.au Question 9 Part of the graph of f x x ( ) = - 16 2 is shown below. The area of the region bounded by the graph of f and the co-ordinate axis is A. This area A can be approximated by four left rectangles equal to L, or four rectangles equal to R. Which of the following is false? A. R A L   B. L overestimates A by 11.27%. C. R underestimates A by 11.27%. D. L R - = 4 E. 1( ) 2 L R A +  Question 10 The tangent to the graph of log tan e 3 x y     =         is parallel to the line with the equation 3 4 5 y x + = ,