Math Pass Year Paper

IFYMB001 Maths Part 2 (Business)

THE NCUK INTERNATIONAL FOUNDATION YEAR (IFY)
Mathematics Part 2 (Business) Second Semester Examination
Examination Session Summer 2009 Time Allowed 2 hours 10 minutes (Including 10 minutes reading time)

INSTRUCTIONS TO STUDENTS
SECTION A Answer ALL questions. This section carries 40% of the exam marks. SECTION B Answer FOUR questions. This section carries 60% of the exam marks. The marks for each part of the question are indicated in square brackets [ ] • • • • • • • • • • • No answers must be written during the first 10 minutes. Write your Candidate Number clearly on the Answer Book in the space provided. Write your answers in the Answer Book provided. Additional sheets will be provided on request. Clearly write the number and parts of questions attempted at the start of each answer. No written material is allowed in the examination room. No mobile phones are allowed in the examination room. An approved calculator may be used in the examination. State the units where necessary. Where appropriate, working should be carried out to 4 significant figures and answers given to 3 significant figures. Full marks will only be given for full and detailed answers. Students will receive a formula book.

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IFYMB001 Maths Part 2 (Business)

Section A Answer ALL questions. This section carries 40 marks.
Question A1 In a class of 40 students the mean weight of the 15 males is 64 kg and the mean weight of the 25 females is 56 kg. Calculate the mean weight of the students in the class. [3]

Question A2 Differentiate

cos(3 x + 1) . (It is not necessary to simplify your answer.) x +1

[3]

Question A3 The random variable Y has mean 6 and variance 7 . Find the mean and variance of 5Y − 2 . [4]

Question A4 If f ( x ) = 4e x + 5 find f
−1

(x ) .

[4]

Question A5

3 2 ⎞ ⎛2 ⎛ 1 3 4⎞ ⎜ ⎟ ⎜ ⎟ −1 Given the matrix A = ⎜ 1 − 5 − 2 ⎟ has inverse A = ⎜ 1 4 b ⎟ find ⎜−1 3 ⎜− 2 a c⎟ 1 ⎟ ⎝ ⎠ ⎝ ⎠ the