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Mathematics for Software Development Essay Example
 Category:Logic & Programming
 Document type:Coursework
 Level:Undergraduate
 Page:2
 Words:1229
LO1: understand core mathematical skills form software engineers
A1. Solve the following linear and quadratic equations:

2(35x)=15

i). 2(3 – 5x) = 15
610x =15
10x=156
X=0.9 or
+ x 20 = 0 ^{2}ii). x
Using
=
.algebraic methodA2. Solve the following sets of simultaneous equations by (a) algebraic method and (b)
(a) Algebraic method
i). y=2x; y=2x+1
=2x+1Thus 2x
4x =1, x=1/4, y=1/2
ii). y = 5x + 1; y =−5x + 1
5x + 1 =−5x + 1Thus
iii). −6y = 3x − 4; 2y = x + 5
x=2y5Thus
−6y = 3(2y5) – 4
−6y = 6y15 − 4
12y = 19; y=19/12 or 1
x=1.833
(b) Graphical method.
y=2x; y=2x+1
y = 5x + 1; y =−5x + 1
6y = 3x − 4; 2y = x + 5 −
Y=1.58, x=1.833
A3. Find the volume of the following shapes to three significant figures by showing your work step by: [P1.2]

A cube with a length of one side 27 metres
Volume = L x W x H
^{3}Volume = 27 x 27 x 27 = 19,683m

A sphere with radius 20 inches
,^{3}Volume = (4/3)*pi*R
^{3} inches = 33,510.32^{3}Volume = (4/3)*pi*20
(9:12:15) is a rightangled triangle.
A4. Using Pythagoras theorem, proof that
^{2}= 15^{2}+12^{2}9
81+144 =225
(i). calculate sine, cosine and tangent for each angles of
Sine Function: 
) = Opposite / Hypotenuseθsin( 
Sin(B)= 15/15 =1.00 
Sin(B)= 9/15=0.6 
Sin(B)= 12/15 =0.8 
Cosine Function: 
) = Adjacent / Hypotenuseθcos( 
Cosine(B)= 0/15 =0.00 
Cosine(C)= 12/15=0.8 
Cosine(A) = 9/15 =0.6 
Tangent Function: 
) = Opposite / Adjacentθtan( 
Tan(B)= 15/9 =1.333 
Tan(A) =12/9 =1.333 
Tan(B) = 9/12 =0.75 
is a right angled triangle.
(ii). Using an appropriate Excel function, demonstrate on a spreadsheet that
A5. Two robots, Alice and Bob are pulling a box as shown on the figure: [P1.3, M1]

Calculate vectors c= a+b.

Calculate magnitude vector c.
= 22.8
Write a pseudo code for calculating magnitude of vector c
);14,18(PVectornew=velocity
);6,5(PVectornew=vector Alice
vector bob(13,20);
void setup() {
;velocityPVector
;positionPVector
LO2: understand the application of Algebraic concepts
B1. A certain British company has three departments. Following sets are showing departments, surnames and annual salaries of employees of this company:
A= (Martin, Marriott, Boast, Preston, Kans
B = (24k, 25k, 26k, 27k, 30k)
C = (production, sales, finance)
Mr Martin and Mrs Marriott are working at production department, Mrs Boast and Mrs Preston working at sales departments and Mr Kans works at Finance department.

B)Find the Cartesian product of set A and set B. (R=A

R(B)Í B, then R(A) ÍIf A

R(B)È B) = R(A) ÈR(A

R(B)Ç R(A) Í B) ÇR(A

Find the Natural join of R and C. (R
= 


Fill in the below table by using provided information:
Employee name 
Department 

production 

Marriott 
production 

B2. A small ICT firm, has three branches in

Redbridge,

Enfield and

Five technicians with following details are working at this company;
Ali (Location; Barnet, age: 25, salary€21,000).
Steve (Location, Redbridge, age: 45, salary: 23,000).
Mike (Location: Barnet, age: 50, Salary 19,000)
Linda (location; Barnet, age 55, salary 24,000
Carol (location; Redbridge, age 43, salary 27,000

Draw required number of tables and fit in the above information there.

List individual satisfying the conditions below.

(Age<46) AND (salary> € 23,000) Carol

(Age>26) OR (salary<€24,000) Mike and Steve

(Age<53) AND (salary>29) OR (location=1) none

(Age>25) XOR (salary>30) OR (locations=2) none
B3. Create a magic square by identifying value of p, q, r, s, t, u, x, y, z in matrix A. [P2.2]
A=
A=
A=
{Show your work step by step}
B4. Show that if
P=
Q=
Then p is the inverse of Q.
=
=
or
, we can follow these steps: To find the inverse of the matrix
Step 1) Find the determinant
. So this means that is of determinant The
Step 2) Swap the values
to get Now switch the highlighted values
Step 3) Change the sign
to get Now change the sign of the highlighted values
Step 4) Multiply by the inverse of the determinant
to get Plug in
to get Multiply by
Step 5) Multiply by every element in the matrix (simplify and reduce if possible)
Reduce each element:
Multiply to get
by EVERY element to get Multiply
LO3: be able to apply the fundamentals of formal methods
C1. Suppose that two sets are A and B. defined by [P3.1]
A= (g, e, r, m, a , n, i)
B= {p, o, l, a, n, d}
Identify the following statements as true or false:

— Truea

— true
b 
— Falsed

u

a 
A =B False

(I, r, a, n) 
– False AUB= 8
C2, suppose we have universal set
21,22,23,24,25,26,27},15,16,17,18,19,20,{1,2,3,4,5,6,7,8,9, 10, 11,12,13,14
Two sets P and O defined as follows:
P= “all multiples of 3”
O= “the first ten even numbers”
O. [P3.1], PUO and PORepresent all of the elements in a Venn diagram and identify the elements in P
C3. For all of the following sets defined in a settheoretic notation, list out all the elements: [P3.1, M3]
x is the element _{— }_{1}
— x is the element_{1}
x is the element_{—}_{1}
x is the element_{— }_{1}
C4. For the circuit shown below, construct a truth table for each intermediate function; hence, find the output function x. [P3.2]

0
0
0
0
0
0
0
0
0
0
0
0
0
0
C5. Suppose that a salesman has 4 differentlylocated customers. [P3.2]

Find the number of differently ways that the salesman can leave home visit two different customers and are then return home.
= 12

Write a pseudo code for calculating the answer for the previous section.
}; // class Tsp_map
return tour;
tour[i] = i;
for(int i = 0; i < size(); ++i) {
vector<int> travel(size());
vector<int> get_default_tour() const {
return home.size();
int size() const {
// # of customers
Point p(x, y);
void add(double x, double y) {
// add a customer at (x, y)
customer.push_back(p);
void add(const Point& p) {
// add a customer at point p
vector<Point> customers;
private:
class Tsp_map {
#include «Point.h»
LO4: be able to apply statistical techniques to analyze data
D1. A research in 157 households found that the number of children per household is
Children 
0 

Household 

Calculate the mean of frequency distribution for the above case.
Mean = 157/6 = 26.17

What is the mode value of number of children’s per household?
The mode value is the number that occurs most in the data and in this case there is no mode.
D2. A company has ten sales territories with approximately the same number of sales people working in each territory. Last month the sales orders achieved were as follows:
For these sales calculate the following:
= 150
= Arithmetic mean =
Mode = 140
,140, 150,150,300140,140Median = 110 120,120, 130,
= 140
Median =
,140, 150,150,300140,140, 130, 120,120Lower quartile = 110
= 120
Lower quartile =
Upper quartile
,300150,150,140, 140,140110 120,120, 130,
= 150
Upper quartile =
Quartile deviation 1/2(Q_3 –Q_1) = ½(150120) =15
Standard deviation
^{2}(x150) 

0 
0 

0 
0 

= 54.37
=
Standard deviation =
= 30
= Mean deviation =
Show all the steps you took to complete your answer.
D3]cIdentify a topic in one of the following areas and conduct a research on it applications in software development. [P4.1
Boolean algebra
There are a number of appropriate sites relating to the use of Boolean algebra for analysing and designing logic gates,