ANMCHARA SENIOR HIGH SCHOOLEND OF SECOND TERM EXAMINATION, APRIL, 2014 ELECTIVE MATHEMATICS FORM 2 TIME: 2HRS OBJECTIVE 1. In the diagram below n(A)=2n(B).Find the value of x A. 1 B. 2 C. 3 D. 4 2. Use the information below to answer question 2 and 3. The binary operation is defined on the set of rational numbers by Find the identity element. A. B. C. 2 D. 4 3. Find the rational number that has no inverse under the operation * A. 3 B. 2 C. 1 D. 0 Use the information to answer question 4 and 5. Two functions are defined on the set of real numbers by 4. Find A. B. C. D. 5. For what values of x is not defined. A. B. C. D. 6. Find the inverse of the function A. B. C. D. 7. Find the equation of a straight line which intersects the x-axis at 5 and y-axis at -2 A. B. C. D. 8. Use the table below to compute ( ) * a b c D a b D a c b d C b a c a B c d d c a d b A. d B. c C. b D. a The binary operation Δ is defined on the set of real numbers by . Use the information to answer question 9 and 10 9. Find the identity element A. B. 0 C. 2 D. 4 10. Find the real number that has no inverse under the operation. A. B. C. 2 D. 3 11. Which of the following statement is equivalent to ? A. B. C. D. 12. Find the solution of A. ( ) B. ( ) C. ( ) D. ( ) 13. Express in the form A. B. C. D. 14. Express in the form , where a and b are real numbers. A. B. C. D. 15. Evaluate A. 8 B. 16 C. 32 D. 12 16. The table below shows the scores obtained by candidates in an examination Score 0-9 10-19 20-29 30-39 40-49 No. of candidates 8 14 48 18 12 What is the median class? A. 10-19 B. 20-29 C. 48 D. 30-39 17. Which of the following binary operations is not commutative? A. B. C. D. 18. Which of the number lines illustrate ? A. B. C. D. 19. State the domain of the function A. -1 B. 1 C. 0 D. Undefined 20. If , find . a b a b a b a b A. 8 B. 10 C. 17 D. 20 21. Simplify A. B. C. D. 22. Simplify ( ) A. B. C. D. An operation is defined over the set R of real numbers by . Use the information to answer questions 23 and 24. 23. Find the identity element under the operation. A. 3 B. 2 C. 1 D. 0 24. Find the inverse of 1 under the operation A. 3 B. 2 C. 1 D. 0 25. Convert 12 in to the form A. B. C. D. 26. Simplify ( )( ) A. 4 B. 3 C. 2 D. 1 27. Simplify ( ) A. B. C. D. 28. Express in the form , and find the value of a. A. B. C. D. 29. For what values of x are the expression undefined. A. 3 and 4 B. 3 and 6 C. -3 and -4 D. -3 and -6 30. Which of the following does not satisfy ? A. B. C. D. SECTION B PART 1 Answer all the questions from this part 1. A binary operation Δ is defined on the set of real numbers R by where , and R is closed under the operation Δ. Find under the operation Δ, the a. Identity element b. Inverse element of ( ) c. 2. An operation is defined on the set Z of integers by i. Construct a table for this operation on the set S={-1 , 0 , 1, 2} ii. Find, from your table, a number such that for all 3. The table below defines the operation * on the set S={a , b , c , d} * a b c d a b d a c b d c b a c a b c d d c a d b a. Show that the operation * is commutative b. Find the inverse under the operation. PART 2 Answer any four (4) questions 4. If the polynomial where p, q, and r are constants; is divided by , the remainder is 2 and if it is divided by , the remainder is 8. If is a factor of . Find the values of p, q, and r and hence find the zeros of . 5. a. Divide by b Two functions f and g are defined by and Find a. b. 6. a. Solve b.. Simplify ( ) ( ) c. Simplify , leaving your answer in the form . 7. a. Simplify c. Solve 8. There are 65 pupils in a class, 29 of them do Arts, 37 do Business and 38 do Science. All the pupils do at least one of the three subject or programs. 10 do all the three program while 18 do Arts and Business, 7 do Business and Science but not Art and 14 do Arts and Science. Represent this information on a Venn diagram. i. How many pupils do only two subject j. If a pupil is selected at random , what is the probability that he studies either Arts or Science.