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 values of a , b and c .

[5]

Question A6 Use the substitution u = x − 3 x + 4 to evaluate 2

∫x

2

5

2

2x − 3 dx . − 3x + 4

[5]

Question A7 Use integration by parts to evaluate

∫

0

2

(6 x − 1)

4x + 1

dx .

[5]

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IFYMB001 Maths Part 2 (Business)

Question A8 A farmer is testing the effect of adding some fertilizer to a crop. He performs 10 experiments using different amounts ( x tonnes) of fertilizer and obtains corresponding yields ( y tonnes) of the crop. Given that

∑ xy = 25.58 , obtain the formula for the regression line in the form y = mx + c .

∑ x = 9 , ∑ y = 23.7 , ∑ x

2

= 11.4 ,

∑y

2

= 61.65 and

[5]

Question A9 Find the median and interquartile range of the following set of data: [6]

72, 63, 39, 52, 47, 63, 91, 48, 69, 58, 35, 60, 42, 78 .

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IFYMB001 Maths Part 2 (Business)

Section B Answer 4 questions. This section carries 60 marks. Question B1 A car rental company records the number of miles travelled by each customer during a holiday season. The results are shown in the grouped frequency table below. Number of Miles Frequency

0 ≤ m < 100 100 ≤ m < 150 150 ≤ m < 200 200 ≤ m < 250 250 ≤ m < 300 300 ≤ m < 400 400 ≤ m < 600

4

15 17 24 21 10 9

(i) (ii) (ii) (iv)

Calculate the mean number of miles travelled. Find the standard deviation. By copying and extending the table in an appropriate manner, draw the graph of the cumulative frequency polygon. Using your graph, estimate the median of the data.

[4] [5] [4] [2]

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IFYMB001 Maths Part 2 (Business)

Question B2 (a) During one week it is noted that 360 people visit a gym. The partially completed Venn diagram in Figure 1 shows three sets A , B and C where A represents the males using the gym, B the visitors who are under 30 years old and C represents those who wear shorts (the others all wear tracksuits).

A

66

B

54

54

36

C...