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Binary Arithmetic - Mathematics - Past Exam, Exams of Mathematics

Chitkara UniversityMathematics

main points of this exam paper are: Simultaneous Equations, Decimals, Solve, Graph, Roots, Value, Passes, Line, Distance, Hexadecimal

Typology: Exams

2012/2013

Uploaded on 03/24/2013

anagha
anagha 🇮🇳

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Cork Institute of Technology
Higher Certificate in Science in Computing in Information
Technology Support – Award
(KITSU_6_Y2 – ITS2)
Spring 2008
Mathematics
(Time: 2 Hours)
Instructions
Answer FOUR questions.
All questions carry equal marks
Examiners: Mr. D. O'Shea
Mr. J. Walsh
Mr. J. Greenslade
1. (a) Solve for x in each of the following equations:
(i) 5(2 3) 4 7 (4 5 )
x
x−+=−− (4 marks)
(ii) 2
412 3 0xx−+= (6 marks)
(Correct to two places of decimals)
(b) Solve for x, y and z in the following simultaneous equations:
754 26
343 2
22215
xyz
xyz
xyz
−+=
+−=
−+ + =
(15 marks)
2. (a) Draw a graph of the function, 32
() 2 5 2 5
f
xxxx
=
−−+ in the domain 23x−≤ ≤.
(10 marks)
Use this graph to find:
(i) The roots of
()
3.fx
=
(4 marks)
(ii) The value of
()
1.5f−. (2 marks)
(b) Given the points a (5, -4) and b (-3, 7).
(i) Find the equation of the line which passes through a and b. (5 marks)
(ii) Find the distance from a to b. (4 marks)
pf3
pf4
pf5

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Cork Institute of Technology

Higher Certificate in Science in Computing in Information

Technology Support – Award

( KITSU_6_Y2 – ITS2 )

Spring 2008

Mathematics

(Time: 2 Hours)

Instructions Answer FOUR questions. All questions carry equal marks

Examiners: Mr. D. O'Shea Mr. J. Walsh Mr. J. Greenslade

  1. (a) Solve for x in each of the following equations: (i) 5(2 x − 3) + 4 = 7 − (4 − 5 ) x (4 marks) (ii) 4 − 12 x + 3 x^2 = 0 (6 marks) (Correct to two places of decimals) (b) Solve for x, y and z in the following simultaneous equations: 7 5 4 26 3 4 3 2 2 2 2 15

x y z x y z x y z

(15 marks)

  1. (a) Draw a graph of the function, f ( ) x = 2 x^3^ − 5 x^2 − 2 x + 5 in the domain − 2 ≤ x ≤ 3. (10 marks) Use this graph to find:

(i) The roots of f ( x ) = 3. (4 marks)

(ii) The value of f ( −1.5 ). (2 marks)

(b) Given the points a (5, -4) and b (-3, 7). (i) Find the equation of the line which passes through a and b. (5 marks) (ii) Find the distance from a to b. (4 marks)

  1. (a) Perform the following conversions. Show all your workings clearly.

(i) 125.625 10 to binary. (4 marks) (ii) 1011101.1011 2 to decimal. (4 marks) (iii) 8419.225 10 to hexadecimal. (4 marks) (iv) A8F.9D 16 to binary. (4 marks) (v) 1110101.10101 2 to octal. (4 marks)

(b) Perform the following binary arithmetic: 1101101 2 + 10111 2. Verify your answer. (5 marks)

  1. (a) If

A B C

= ^ − ^ = ^ −  =  

Evaluate the following: (i) B ⋅ C (5 marks) (ii) 2 A B ⋅ − 5 B (6 marks) (iii) A (6 marks)

(b) Solve the following simultaneous equations, using matrix methods: 5 9 30 6 2 28

x y x y

− = (8 marks)

  1. The given table shows the heights of 100 students.

Height (cm)

Number of Students 150 - 156 5 157 - 163 18 164 - 170 20 171 - 177 27 178 - 184 22 185 - 191 8

(i) Calculate the mean height of the students, correct to one place of decimals. (4 marks) (ii) Calculate the standard deviation from the mean. (7 marks) (iii) Construct a cumulative frequency table. (3 marks) (iv) Draw a cumulative frequency curve (ogive). (3 marks) (v) Use the cumulative frequency curve to find the median and the interquartile range. (5 marks) (vi) Calculate the co-efficient of skewness. (3 marks)

Required Formulae

  • Quadratic equation:

x b^ b^ ac a

=^ −^ ±^ −

  • Slope of a line: 2 1 2 1

y y x x

  • Equation of a line: y − y 1 (^) = m x ( − x 1 ) or y = mx + c
    • Distance: (^) ( x 2 (^) − x 1 (^) ) 2 + (^) ( y 2 (^) − y 1 )^2
  • Mean = ΣΣ ffx
  • Standard deviation = Σ f^^ (^ X Σ^ f − X )
    • Z = x σ^ −^ μ
  • Binomial: p x ( ) = N^ cX p qx^ N^ − x
  • Poisson: ( ) (^)!

x (^) e p x (^) x

λ −^ λ

  • Co-efficient of skewness = standard deviation 3 (^ mean^^ − median )