# Mathematics for Software Development Essay Example

• Category:
Logic & Programming
• Document type:
Coursework
• Level:
• Page:
2
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1229

LO1: understand core mathematical skills form software engineers

A1. Solve the following linear and quadratic equations:

1. 2(3-5x)=15

2. i). 2(3 – 5x) = 15

6-10x =15

10x=15-6 X=0.9 or

+ x -20 = 0 2ii). 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=2y-5Thus

−6y = 3(2y-5) – 4

−6y = 6y-15 − 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]

1. A cube with a length of one side 27 metres

Volume = L x W x H

3Volume = 27 x 27 x 27 = 19,683m

1. A sphere with radius 20 inches

,3Volume = (4/3)*pi*R

3 inches = 33,510.323Volume = (4/3)*pi*20

(9:12:15) is a right-angled triangle. A4. Using Pythagoras theorem, proof that

2= 152+1229

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]

1. Calculate vectors c= a+b. 1. 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.

1. 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

1. Find the Natural join of R and C. (R =
1. Fill in the below table by using provided information:

 Employee name Department production Marriott production

B2. A small ICT firm, has three branches in

1. Redbridge,

2. Enfield and

3. 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

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

2. List individual satisfying the conditions below.

1. (Age<46) AND (salary> € 23,000)- Carol

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

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

4. (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:

1. — True a

2. — true b

3. — False d

4. u

5. a

6. |A| =|B|- False

7. (I, r, a, n)

8. – 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 PO Represent all of the elements in a Venn diagram and identify the elements in P C3. For all of the following sets defined in a set-theoretic 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 differently-located customers. [P3.2]

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

1. Write a pseudo code for calculating the answer for the previous section.

}; // class Tsp_map

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
1. Calculate the mean of frequency distribution for the above case.

Mean = 157/6 = 26.17

1. 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(150-120) =15

Standard deviation

 2(x-150) 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,