Page 07 MARKS 14. (a) Evaluate log5 25. (b) Hence solve ( ) 4 4 5 log log 6 log 25 x x + − = , where 6 > x . 15. The diagram below shows the graph with equation ( ) = y f x , where ( ) ( )( ) 2 = − − f x k x a x b . y (1, 9) −5 O 4 x (a) Find the values of a, b and k. (b) For the function ( ) ( ) = − g x f x d , where d is positive, determine the range of values of d for which ( ) g x has exactly one real root. [END OF QUESTION PAPER] 1 5 3 1 Page 08 [BLANK PAGE] do not write on this page Write your answers clearly in the spaces provided in this booklet. The size of the space provided for an answer should not be taken as an indication of how much to write. It is not necessary to use all the space. Additional space for answers is provided at the end of this booklet. If you use this space you must clearly identify the question number you are attempting. Use blue or black ink. Before leaving the examination room you must give this booklet to the Invigilator; if you do not you may lose all the marks for this paper. FOR OFFICIAL USE X747/76/01 Mathematics Paper 1 (Non-Calculator) Answer Booklet Fill in these boxes and read what is printed below. Full name of centre Town Forename(s) Surname Number of seat Day Month Year Scottish candidate number © Mark Date of birth H National Qualications 2016 THURSDAY, 12 MAY 9:00 AM – 10:10 AM A/PB Page 02 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 2. 1. Page 03 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 3.(a) 3.(b) 3.(c) Page 04 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 4. Page 05 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 5. 6.(a) 6.(b) Page 06 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 7.(b) 7.(a) Page 07 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 8. Page 08 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 9.(b) 9.(a) Page 09 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 10. y (1, 0) O (4, 1) x f(x) = log4 x Page 10 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 11.(a) Page 11 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 11.(b) Page 12 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 12.(a) Page 13 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 12.(b) Page 14 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 13. Page 15 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 14.(a) 14.(b) Page 16 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER 15.(a) 15.(b) Page 17 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER ADDITIONAL SPACE FOR ANSWERS Page 18 DO NOT WRITE IN THIS MARGIN QUESTION NUMBER ADDITIONAL SPACE FOR ANSWERS Page 19 ADDITIONAL SPACE FOR ANSWERS DO NOT WRITE IN THIS MARGIN QUESTION NUMBER Page 20 For Marker’s Use Question No Marks/Grades © National Qualications 2016 H Total marks — 70 Attempt ALL questions. You may use a calculator. Full credit will be given only to solutions which contain appropriate working. State the units for your answer where appropriate. Answers obtained by readings from scale drawings will not receive any credit. Write your answers clearly in the spaces provided in the answer booklet. The size of the space provided for an answer should not be taken as an indication of how much to write. It is not necessary to use all the space. Additional space for answers is provided at the end of the answer booklet. If you use this space you must clearly identify the question number you are attempting. Use blue or black ink. Before leaving the examination room you must give your answer booklet to the Invigilator; if you do not, you may lose all the marks for this paper. X747/76/12 Mathematics Paper 2 THURSDAY, 12 MAY 10:30 AM – 12:00 NOON A/PB Page 02 FORMULAE LIST Circle: The equation x2 + y2 + 2gx + 2fy + c = 0 represents a circle centre (−g, −f ) and radius The equation (x − a)2 + (y − b)2 = r2 represents a circle centre (a, b) and radius r. Scalar Product: a.b = |a||b| cos θ, where θ is the angle between a and b or a.b = a1b1 + a2b2 + a3b3 where a = 1 1 2 2 3 3 = and a b a b a b b ⎛ ⎞ ⎛ ⎞ ⎟ ⎟ ⎜ ⎜ ⎟ ⎟ ⎜ ⎜ ⎟ ⎟ ⎜ ⎜ ⎟ ⎟ ⎜ ⎜ ⎟ ⎟ ⎜ ⎜ ⎟ ⎟ ⎜ ⎜ ⎟ ⎟ ⎟ ⎟ ⎜ ⎜ ⎝ ⎠ ⎝ ⎠ . Trigonometric formulae: sin (A ± B) = sin A cos B ± cos A sin B cos (A ± B) = cos A cos B ± sin A sin B sin 2A = 2 sin A cos A cos 2A = cos2 A − sin2 A = 2 cos2 A − 1 = 1 − 2 sin2 A Table of standard derivatives: Table of standard integrals: f (x) f ′(x) sin ax cos ax a cos ax – a sin ax f (x) ∫ f (x)dx sin ax cos ax cos ax + c sin ax + c 1 – a 1 a 2 2 + – g f c .