Write your IDENTIFICATION NUMBER clearly on each page of your answer booklet DO

Write your identification number clearly on each page

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Write your IDENTIFICATION NUMBER clearly on each page of your answer booklet . DO NOT WRITE YOUR NAME . NB. Your script will not be marked if it has your name. DO NOT TURN OVER UNTIL YOU ARE TOLD TO DO SO
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SAMPLE Page 2 of 4 Question 1 a) Find the domain of each function below i. ? ? = 9( 𝑎 2 1) (3 marks) ii. ? ? = 1 ? 2 13 ?− 30 (3 marks) b) Given that ? ? = 5 ? − 3 and ? ? = 1 3 ?− 1 , determine i. The value of ? for which ? ? is undefined (2 marks) ii. The value of ? for which ? ( ? ) = 4 (3 marks) iii. An expression for ?? ( ? ) (3 marks) iv. ?? (0) (1 mark) Question 2 Given that ? ? = 3 ?− 1 3 ? +2 and ? ( ? ) = 4 3 ? a) Evaluate ? ( 1) and ?? ( 1) (4 marks) b) Determine ? 1 (2 marks) c) Evaluate ? 1 (2) (1 mark) d) Given that ? ? = ? − 2 2 , find and simplify i. ? ( 𝑎 ) (2 marks) ii. ? ( 𝑎 + ? ) (2 marks) iii. ? 𝑎 + ? − ? ( 𝑎 ) ? (4 marks)
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SAMPLE Page 3 of 4 Question 3 a) Express log 1 2 ? = 8 in exponential form (1 mark) b) Express 2 3 1 = 3 2 in logarithmic form (1 mark) c) Express each of the following as a single logarithm i. ?𝑜? 4 192 − ?𝑜? 4 3 ?𝑜? 4 1 (3 marks) ii. 1 2 ?𝑜? 3 ? − 1 3 ?𝑜? 3 ? − 5 ?𝑜? 3 ? (3 marks) d) Solve each of the following equations i. ?𝑜? 2 ? − 3 + ?𝑜? 2 ? − 2 = ?𝑜? 2 2 ? + 24 (4 marks) ii. 27 ? × 3 2 = 9 ? (3 marks) Question 4 a) Copy and complete the table below for the function ? ( ? ) = 3 ? 2 5 ? 6 over the domain 3 ? 3 . ? 3 2 1 0 1 2 3 ? 36 2 6 4 (3 marks) b) Using a scale of 2cm to represent 1 unit on the x -axis and 1cm to represent 5 unit son the y - axis draw the graph of ? ( ? ) (5 marks) c) Using your graph, determine the roots of the equation ? = 3 ? 2 5 ? 6 (2 marks) d) On the same axes and using the same scale, draw the line ? ? = 3 ? − 1 over the domain 3 ? 3 (3 marks) Use your graph to determine the solution to the equation ? ( ? ) = ? ( ? ) . END OF QUESTION PAPER
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  • Fall '17
  • BURSON-POLSTON,MARYJANE
  • Department of Mathematics, University College, Ocho Rios, OAS Consortia of Universities, School of Technology & Mathematics

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