(a) In a class of 82 students, 10 students were found to perform well in all the three subjects…
(a) In a class of 82 students, 10 students were found to perform well in all the three subjects offered; Mathematics, English and Science. 32 students excelled in both Mathematics and English and 18 excelled in both Science and English. The number of students who excelled in Mathematics only exceeded those who excelled in Science only by 2. The number of students who excelled in English only was twice the number of students who excelled in Science.
(i) Represent the information in a well labeled venn diagram. (2 marks)
(ii) Determine the number of students who excelled in Mathematics only. (3 marks)
(ii) Determine the number of students who excelled in Science only. (3 marks)
(ii) Determine the number of students who excelled in English and at least one other subject. (4 marks)
(b) Factorize the polynomial x3– 17x2+ 54x– 8, given (x– 1) is a factor. (3 marks)(c) Solve for xin the following equations;
log6(x+ 4) + log6(x– 2) = log6(4x)
(3 marks)d) Simplify the following expression; . (2 marks)
