# Sleeping Patterns Essay

(MAY 2012 SESSION)

MATHEMATICS I

FMT0013

LECTURER :……………………………………………………………………………

MATRIC NO

: ………………………………………….

VENUE

PROGRAMME : ..……………………………………

: ………………………………………….

OCTOBER 2012

DURATION : 3 HOURS

INSTRUCTIONS:

1. Candidates must read all questions carefully.

2. The examination script consists of the followings:

Part

A

Types of

Questions

5 Short Answers

B

3 Short Answers

Instruction

Answer ALL questions Answer TWO (2) questions ONLY

Answer Sheets to be

Used

Answer booklet

Answer booklet

THIS EXAMINATION SCRIPT CONTAINS 7 PAGES INCLUDING THE FRONT COVER

DO NOT OPEN THE EXAMINATION SCRIPT UNTIL FURTHER INSTRUCTION

PART A

CONFIDENTIAL

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*…show more content…*

(4 marks)

3.

(a)

Find the number of terms in each of the following arithmetic sequence:

3.2, 4.3, 5.4, ..., 31.8

(2 marks)

(b)

The second and fifth terms of a geometric sequence are -12 and 324 respectively. Find the seventh term.

(3 marks)

(c)

Expand 1

2x

10

in ascending powers of x , up to and including the 4th term.

10

Hence, evaluate 1 . 0002

, correct to four decimal places.

(5 marks)

1

4.

(a)

Given the matrix Q

2

1

3

1

0 . Find the value of Q .

1

1

1

(2 marks)

(b)

2

Given

R

1

3

x

0

i.

x

4

2

and R

25

.Find

5

1

3

the value of x .

(3 marks)

ii.

the adjacent of R .

(4 marks)

iii.

inverse of matrix R .

(2 marks)

(c)

By using matrix Q in question 4(a) and matrix R in question 4(b), find matrix

1

P so that QR

P

4

2

0

1

2 .

1

1

1

(4 marks)

5.

(a)

Given two points A (5,2) and B(-4,-5). Find

i.

gradient , m AB

FMT0013 MATHEMATICS I

2/6

CONFIDENTIAL

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(2 marks)

ii.

the equation of straight line that passing through points A and B in general form

(2 marks)

iii.

the equation of straight line that passing through points A that is parallel to the line 2 x

3y

5

.

2

(2 marks)

(b)

Functions f and g are defined by :

(x ) f 2 x g x) 4

(

x

2

Evaluate

i.

h

gf

(2 marks) ii. fg

1

3

(3 marks)