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Cork Institute of Technology
Higher Certificate in Science in Computing in Information
Technology Support โ Award
(NFQ Level 6)
Summer 2006
Mathematics
(Time: 2 Hours)
Instructions Answer FOUR questions. All questions carry equal marks. Log tables are available
Examiners: Mr. L. OโHanlon Mr. J. Greenslade Mr. J. Walsh
Q1. (a) Find the mean, median, mode, range and standard deviation for the following data: 2, 7, 3, 5, 4, 6, 4, 7, 9. (10 marks) (b) The given table shows the weight in lbs for a class of 40 male students picked at random.
Weight (lbs) Number of students 111 โ 119 3 121 โ 129 5 131 โ 139 8 141 โ 149 12 151 โ 159 6 161 โ 169 4 171 โ 179 2
Calculate (i) The mean weight. (5 marks) (ii) The standard deviation from this mean. (10 marks)
Q2. Solve the following equations.
(a) (^3) x โ 4 = x โ 5 (5 marks)
(b) 3 x^2 + 2 x โ 5 = 0 (10 marks)
(c) 2x + 3y + z = 5 x โ y โ 3z = 9 3x + 2y + 2z = 8 (10 marks)
Q3. (a) For the following matrices
C
B
A
Calculate the matrix given by 2 A ร B + 4 C (10 marks)
(b) Solve, by matrix methods
5 4
x y
x y (15 marks)
Q4. (a) Find the probability of getting exactly 3 heads in six tosses of a fair coin. (B I N O M I A L) (12 marks)
(b) If 2% of bricks manufactured by a process are defective, find the probability that out of 100 bricks made, exactly 4 would be defective (poisson) (13 marks)
Q5. Graph the function
Required Formulae:
1. mean = โ nx
1
1 1 F
FX
- Standard deviation for a small sample
2 โ
= โ^ โ
N
S D Xi X
3. For N โช 30 , (^ )
= โ^ โ
Fi S. D Fi Xi X^2
- For matrix equations A.X = B solution is X = A -1^ .B
- Binomial = NC (^) X pXqN โ X
6. For poisson: ฮป = mean = NP
p ( ) x xe!
ฮป x โ^ ฮป
7. Slope of a line joining ( x 1 , y 2 ) and ( x 2, y 2 ) is m =( y 2 โ y 1 ) (/ x 2 โ x 1 )
- If two lines are perpendicular then m 1. m 2 =โ 1
- Mid point of points ( x 1 , y 1 ) and ( x 2 , y 2 ) is ๏ฃท ๏ฃธ
= ๏ฃซ^ + +
z
y y z
x (^) 1 x (^2) , 1 2
- Equation of a line of slope m through the points ( x 1 , y 1 ) and ( x2, x 1 ) is
y โ y 1 = m ( x โ x 1 )where m =
2 1
2 1 x x
y y โ
