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

a) Programmes A, B &C, give out notifications every 3 days, every 4 days & every 6 days. when will they give out notifications at the same time during the course of two month

b) 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

c) A teacher has three computer science classes. Each class has 120, 72, and 184 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.

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

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

g) 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. Based on the number calculated in previous task ( i.e. modular value 1 directed to server 1).given below are some of the outputs of hash function and determine which server they are belong to

i. 2048

ii. 3987

iii. 2675

h) Find the multiplicative inverse of 2675modn whereas “n” is the number of servers

Task 3

a) 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)

i. Find the length of the line AC without using the diagram

ii. Find the area of the polygon without using the diagram

iii. Convert the given coordinates to polar coordinates

b) 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

a) 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:

. -

( ) =

Where is the voltage, is the time in seconds, and is the initial voltage which is equal to 2V.

Learning Outcomes and Assessment Criteria

Distinction

101 Use applied number theory in practicai computing scenanos i

Dl produce detailed written

a

explanation of the importance of prime numbers within the field

Pi Calculate the greatest common divisor and least common multiple of a given pair of numbers,

P2 Use relevant theory to sum arithmetic arpd geometric progressions. of computing. Ml identify multiplicative inverses in moduar arithmetic.

L02 Analyse events using probability theory and probability distributions D2 Evaluate probability theory to an example involving hashing and load balancing.

3

D Construct the scaling of

simple shapes that are described by vector Co-ordinates.

P3 Deduce the conditional probability of different events occurring within independent trials,

P4 Identify the expectationvariables, of an event occurring from a discrete, random

variable. M2 Calculate probabilities within both binomially distributed and normally distributed random

L03 Determine solutions of graphical examples using geometry and vector methods

P5 identify simple shapes using co-ordinate geometry.

P6 Determine shape parameters using appropriate vector methods. M3 Evaluate the co- ordinateordinatesystem used in programming a simple output device.

L04 evaluate problems concerning differentlal and integral calculus 4

D Justify, by further

differentiation, that a value is a minimum.

P7 Determine the rate of change within an algebraic function,

P8 Use integral calculus to solve practical problems involving area. M4 Analyse maxima and minima of increasing and decreasing functions using

higher order Jeri tives,

va

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 shape parameters using appropriate vector methods.

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

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

a) Programmes A, B &C, give out notifications every 3 days, every 4 days & every 6 days. when will they give out notifications at the same time during the course of two month

b) 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

c) A teacher has three computer science classes. Each class has 120, 72, and 184 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.

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

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

g) 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. Based on the number calculated in previous task ( i.e. modular value 1 directed to server 1).given below are some of the outputs of hash function and determine which server they are belong to

i. 2048

ii. 3987

iii. 2675

h) Find the multiplicative inverse of 2675modn whereas “n” is the number of servers

Task 3

a) 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)

i. Find the length of the line AC without using the diagram

ii. Find the area of the polygon without using the diagram

iii. Convert the given coordinates to polar coordinates

b) 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

a) 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:

. -

( ) =

Where is the voltage, is the time in seconds, and is the initial voltage which is equal to 2V.

Learning Outcomes and Assessment Criteria

Distinction

101 Use applied number theory in practicai computing scenanos i

Dl produce detailed written

a

explanation of the importance of prime numbers within the field

Pi Calculate the greatest common divisor and least common multiple of a given pair of numbers,

P2 Use relevant theory to sum arithmetic arpd geometric progressions. of computing. Ml identify multiplicative inverses in moduar arithmetic.

L02 Analyse events using probability theory and probability distributions D2 Evaluate probability theory to an example involving hashing and load balancing.

3

D Construct the scaling of

simple shapes that are described by vector Co-ordinates.

P3 Deduce the conditional probability of different events occurring within independent trials,

P4 Identify the expectationvariables, of an event occurring from a discrete, random

variable. M2 Calculate probabilities within both binomially distributed and normally distributed random

L03 Determine solutions of graphical examples using geometry and vector methods

P5 identify simple shapes using co-ordinate geometry.

P6 Determine shape parameters using appropriate vector methods. M3 Evaluate the co- ordinateordinatesystem used in programming a simple output device.

L04 evaluate problems concerning differentlal and integral calculus 4

D Justify, by further

differentiation, that a value is a minimum.

P7 Determine the rate of change within an algebraic function,

P8 Use integral calculus to solve practical problems involving area. M4 Analyse maxima and minima of increasing and decreasing functions using

higher order Jeri tives,

va

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 shape parameters using appropriate vector methods.

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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