Higher National Certificate/Diploma in

Computing

Assessment Brief

Student Name/ID Number

Unit Number and Title 11: Maths for Computing

Academic Year 2019

Unit Tutor M.T.M. Ramees

Assignment Title Application of number theory , probability ,Vector geometry & calculus in computing

Issue Date 22/12/2019

Submission Date 2/2/2020

IV Name & Date Supun Walpita 11/12/2019

Submission Format

This assignment should be submitted at the end of your lesson, on the week stated at the front of this brief. The assignment can either be word-processed or completed in legible handwriting.

If the tasks are completed over multiple pages, ensure that your name and student number are present on each sheet of paper.

Unit Learning Outcomes

LO1 Use applied number theory in practical computing scenarios

LO2 Analyse events using probability theory and probability distributions

LO3 Determine solutions of graphical examples using geometry and vector methods

LO4 Evaluate problems concerning differential and integral calculus.

Assignment Brief and Guidance

Suppose that you work for a company which operates in multidisciplinary streams such as hardware & software development, sales, networking, resources management etc. you have been recruited by the company and it is required for you to work in all the disciplines during the first year probationary period, in order to gain minimum competence in each area. Following tasks asses your mathematics knowledge, skills and its application in relevant areas of work that you are about to get involved.

Task 1

Programmes A, B & C, give out notifications every 2 days, every 5 days & every 6 days. when will they give out notifications at the same time during the course of two month

Computer store A sells a package of 12 CPU’s for half price while Computer store B sells a package of 9 Desktop monitors for half price. Suppose that you intend to buy CPU’s and monitors to set up a gaming zone and find What is the least number of CPU’s and Desktop monitors you need to buy in order to make sure you are not left with a surplus

A teacher has three computer science classes. Each class has 102, 72, and 120 students respectively. He wants to divide each class into groups (members should be from the same class) In order to give a common assignment so that every group in every class has the same number of students. For the convenience of marking, the teacher expect to set up less number of groups as possible. Find the number of students can put into each group.

Suppose you have two hard disks with different disk space’s 512 GB and 604 GB. If you are required to partition both disks into equal capacity that are as large as possible, find the space that should be allocated for each partition?

Describe importance of prime numbers in detail within the field of computing.

Task 2

It was determined that 75% of spam emails have “check this out” in the subject line while 10% of non-spam emails have this sentence in the subject line. If you see a mail contains “”check this out” by your filter, what is the probability that it is an actual spam?

Suppose that the company created an Image processing programme which can classify people according to their hairstyle (long or short) through CCTV images. It is known that 90% males and only 20% females have short hair. If the population comprised of 60% female & 40% male, find the probability of being a male if the programme identifies a person with long hair.

The probability that a visitor to a Web site provides contact data for additional information is 0.01. Assume that 2000 visitors to the site behave independently. Determine the following probabilities

No visitor provides contact data

Exactly 100 visitors provide contact data

More than 3 visitors provide contact data.

What is the expected number of visitors provide contact data

The time until recharge for a battery in a laptop computer under common conditions is normally distributed with a mean of 250 minutes and a standard deviation of 40 minutes.

What is the probability that a battery lasts more than four hours?

What are the quartiles (the 25% and 75% values) of battery life?

What value of life in minutes is exceeded with 95% probability?

Suppose that a server can only handle 500 requests at a time. Find out how many servers you need in order to accommodate requests without any interruption for a confidence level of 95%, if load balancing is done evenly

Discuss the use of modular arithmetic’s in the field of computing

A hash function will be used in directing users to servers whereas the modular value of the output will be used in determining the relevant server (i.e. modular value 1 directed to server 1) based on the number calculated in part e). Given below are some of the outputs of hash function and determine which server they belong to

2048

3987

2675

Find the multiplicative inverse of 2675 (mod n) whereas “n” is the number of servers

Task 3

Plot following points Cartesian coordinates and enclose it to make a polygon ABCDEA such as A(0,2) ; B(4,8); C(15,5); D(12,4) ;E(6,2)

Find the length of the line AC without using the diagram

Find the area of the polygon without using the diagram

Convert the given coordinates to polar coordinates

Draw a view port P(0,0) ,Q(0,10),R(16,10), S(16,0) and assume it as the output screen of the computer zoomed at 100 %.Suppose that you have zoomed out to 40% keeping the same aspect ratio ,redraw the image that can be visualized in the screen and also define the new boundaries of the viewport.

Task 4

You have been asked to analyse a motherboard to assess the lifespan of the capacitors. When a charged capacitor is connected to a resistor to form an RC (resistor-capacitor) circuit, the capacitor discharge follows the equation:

V(t)=V_max ?Cos?(2t) .e?^(-t)

Where V is the voltage, t is the time in seconds, and V_max is the initial voltage which is equal to 3V.

Determine how long it will take for a capacitor in this circuit to discharge to Half of its initial charge

Find the rate of discharge at t=2s

A monitor to be made with 864cm2 display area with 2cm margins from top & bottom and 3cm margins in sides. Find the dimensions of the monitor with least total area.

A software office complex has the space to accommodate 250 employees. For every person they employ (x) then their monthly profit, in rupees, can be approximated by the equation:

P(x)=-8x^2+3200x-80000

Find How many people should they employ in order to maximise their profits?

Task 5

Find the area enclosed by f(x)=-x^2+4x+96 , g(x)=-x^3 + 27, x=-1 and x=2

The rate at which the depletion of charge of a portable computer battery is directly proportional to the charge of the battery at any given instance. Suppose that it was charged to 100% before use. After one hour of usage, it was reduced to 70%. Find the percentage charge after three hours

Power supply in a particular computer converts the A/C input voltage to D/C output whereas the input can be given as function of current

V(t)= Vmax Sin(t)

If the output average voltage is 240v then find the value of the Vmax in the input

Achievement Summary

Criteria Reference Pass criteria Achieved?

(tick)

LO1 P1 Calculate the greatest common divisor and least common multiple of a given pair of numbers.

P2 Use relevant theory to sum arithmetic and geometric progressions.

LO2 P3 Deduce the conditional probability of different events occurring within

independent trials.

P4 Identify the expectation of an event occurring from a discrete, random variable.

LO3 P5 Identify simple shapes using co-ordinate geometry

P6 Determine shape parameters using appropriate vector methods.

LO4 P7 Determine the rate of change within an algebraic function

P8 Use integral calculus to solve practical problems involving area.

Higher Grade achievements

Grade descriptor

Achieved?

(tick)

Grade descriptor

Achieved?

(tick)

M1 D1

M2 D2

M3 D3

M4

Assessors Feedback

Computing

Assessment Brief

Student Name/ID Number

Unit Number and Title 11: Maths for Computing

Academic Year 2019

Unit Tutor M.T.M. Ramees

Assignment Title Application of number theory , probability ,Vector geometry & calculus in computing

Issue Date 22/12/2019

Submission Date 2/2/2020

IV Name & Date Supun Walpita 11/12/2019

Submission Format

This assignment should be submitted at the end of your lesson, on the week stated at the front of this brief. The assignment can either be word-processed or completed in legible handwriting.

If the tasks are completed over multiple pages, ensure that your name and student number are present on each sheet of paper.

Unit Learning Outcomes

LO1 Use applied number theory in practical computing scenarios

LO2 Analyse events using probability theory and probability distributions

LO3 Determine solutions of graphical examples using geometry and vector methods

LO4 Evaluate problems concerning differential and integral calculus.

Assignment Brief and Guidance

Suppose that you work for a company which operates in multidisciplinary streams such as hardware & software development, sales, networking, resources management etc. you have been recruited by the company and it is required for you to work in all the disciplines during the first year probationary period, in order to gain minimum competence in each area. Following tasks asses your mathematics knowledge, skills and its application in relevant areas of work that you are about to get involved.

Task 1

Programmes A, B & C, give out notifications every 2 days, every 5 days & every 6 days. when will they give out notifications at the same time during the course of two month

Computer store A sells a package of 12 CPU’s for half price while Computer store B sells a package of 9 Desktop monitors for half price. Suppose that you intend to buy CPU’s and monitors to set up a gaming zone and find What is the least number of CPU’s and Desktop monitors you need to buy in order to make sure you are not left with a surplus

A teacher has three computer science classes. Each class has 102, 72, and 120 students respectively. He wants to divide each class into groups (members should be from the same class) In order to give a common assignment so that every group in every class has the same number of students. For the convenience of marking, the teacher expect to set up less number of groups as possible. Find the number of students can put into each group.

Suppose you have two hard disks with different disk space’s 512 GB and 604 GB. If you are required to partition both disks into equal capacity that are as large as possible, find the space that should be allocated for each partition?

Describe importance of prime numbers in detail within the field of computing.

Task 2

It was determined that 75% of spam emails have “check this out” in the subject line while 10% of non-spam emails have this sentence in the subject line. If you see a mail contains “”check this out” by your filter, what is the probability that it is an actual spam?

Suppose that the company created an Image processing programme which can classify people according to their hairstyle (long or short) through CCTV images. It is known that 90% males and only 20% females have short hair. If the population comprised of 60% female & 40% male, find the probability of being a male if the programme identifies a person with long hair.

The probability that a visitor to a Web site provides contact data for additional information is 0.01. Assume that 2000 visitors to the site behave independently. Determine the following probabilities

No visitor provides contact data

Exactly 100 visitors provide contact data

More than 3 visitors provide contact data.

What is the expected number of visitors provide contact data

The time until recharge for a battery in a laptop computer under common conditions is normally distributed with a mean of 250 minutes and a standard deviation of 40 minutes.

What is the probability that a battery lasts more than four hours?

What are the quartiles (the 25% and 75% values) of battery life?

What value of life in minutes is exceeded with 95% probability?

Suppose that a server can only handle 500 requests at a time. Find out how many servers you need in order to accommodate requests without any interruption for a confidence level of 95%, if load balancing is done evenly

Discuss the use of modular arithmetic’s in the field of computing

A hash function will be used in directing users to servers whereas the modular value of the output will be used in determining the relevant server (i.e. modular value 1 directed to server 1) based on the number calculated in part e). Given below are some of the outputs of hash function and determine which server they belong to

2048

3987

2675

Find the multiplicative inverse of 2675 (mod n) whereas “n” is the number of servers

Task 3

Plot following points Cartesian coordinates and enclose it to make a polygon ABCDEA such as A(0,2) ; B(4,8); C(15,5); D(12,4) ;E(6,2)

Find the length of the line AC without using the diagram

Find the area of the polygon without using the diagram

Convert the given coordinates to polar coordinates

Draw a view port P(0,0) ,Q(0,10),R(16,10), S(16,0) and assume it as the output screen of the computer zoomed at 100 %.Suppose that you have zoomed out to 40% keeping the same aspect ratio ,redraw the image that can be visualized in the screen and also define the new boundaries of the viewport.

Task 4

You have been asked to analyse a motherboard to assess the lifespan of the capacitors. When a charged capacitor is connected to a resistor to form an RC (resistor-capacitor) circuit, the capacitor discharge follows the equation:

V(t)=V_max ?Cos?(2t) .e?^(-t)

Where V is the voltage, t is the time in seconds, and V_max is the initial voltage which is equal to 3V.

Determine how long it will take for a capacitor in this circuit to discharge to Half of its initial charge

Find the rate of discharge at t=2s

A monitor to be made with 864cm2 display area with 2cm margins from top & bottom and 3cm margins in sides. Find the dimensions of the monitor with least total area.

A software office complex has the space to accommodate 250 employees. For every person they employ (x) then their monthly profit, in rupees, can be approximated by the equation:

P(x)=-8x^2+3200x-80000

Find How many people should they employ in order to maximise their profits?

Task 5

Find the area enclosed by f(x)=-x^2+4x+96 , g(x)=-x^3 + 27, x=-1 and x=2

The rate at which the depletion of charge of a portable computer battery is directly proportional to the charge of the battery at any given instance. Suppose that it was charged to 100% before use. After one hour of usage, it was reduced to 70%. Find the percentage charge after three hours

Power supply in a particular computer converts the A/C input voltage to D/C output whereas the input can be given as function of current

V(t)= Vmax Sin(t)

If the output average voltage is 240v then find the value of the Vmax in the input

Achievement Summary

Criteria Reference Pass criteria Achieved?

(tick)

LO1 P1 Calculate the greatest common divisor and least common multiple of a given pair of numbers.

P2 Use relevant theory to sum arithmetic and geometric progressions.

LO2 P3 Deduce the conditional probability of different events occurring within

independent trials.

P4 Identify the expectation of an event occurring from a discrete, random variable.

LO3 P5 Identify simple shapes using co-ordinate geometry

P6 Determine shape parameters using appropriate vector methods.

LO4 P7 Determine the rate of change within an algebraic function

P8 Use integral calculus to solve practical problems involving area.

Higher Grade achievements

Grade descriptor

Achieved?

(tick)

Grade descriptor

Achieved?

(tick)

M1 D1

M2 D2

M3 D3

M4

Assessors Feedback

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