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Session: September 2021
BTEC Higher National Diploma (HND) in Computing
Unit number and title
Maths for Computing (L4)
Assignment number & title
1 of 1
Final assignment submission deadline
10-15 January 2022
Late submission deadline
17-22 January 2022
The learners are required to follow the strict deadline set by the College for submissions of assignments in accordance with the BTEC level 4 – 7 submission guidelines and College policy on submissions.
Formative feedback will be available in class during the semester.
Final feedback will be available within 2 – 3 weeks of the assignment submission date.
You are strongly advised to read “Preparation guidelines of the Coursework Document” before answering your assignment.
Aim & Objective
This assignment is designed so that it enables the student to demonstrate their understanding of the mathematical concepts covered in the module through answering various practical problems; divided into four parts. The coursework should be submitted as one document in a report format in final submission.
The GCD (greatest common divisor), LCM (lowest common multiple) and prime numbers is used for a variety of applications in number theory, particularly in modular arithmetic and thus encryption algorithms such as RSA. It is also used for simpler applications, such as simplifying fractions. This makes the GCD, LCM and prime numbers a rather fundamental concept to number theory, and as such several algorithms have been discovered to efficiently compute it. Primes are the set of all numbers that can only be equally divided by 1 and themselves, with no other even division possible. Numbers like 2, 3, 5, 7, and 11 are all prime numbers.
Demonstrate the concepts of greatest common divisor and least common multiple of a given pair of numbers with an example. To support the evidence of your understanding on LCM and GCD, you should present with pseudocode and a computer program in python to compute LCM and GCD based on user’s input. It is desirable, to support your findings by identifying multiplicative inverses in modular arithmetic with an example. Produce a detailed written explanation of the importance and application of prime numbers in RSA encryption (Rivest–Shamir–Adleman). To support the evidence of your understanding on the use of prime numbers, you are required to develop a computer program in C/ C++ or python to demonstrate the asymmetric cryptography algorithm.
Arithmetic progressions are used in simulation engineering and in the reproductive cycle of bacteria. Some uses of AP’s in daily life include uniform increase in the speed at regular intervals, completing patterns of objects, calculating simple interest, speed of an aircraft, increase or decrease in the costs of goods, sales and production and so on. Geometric progressions (GP’s) are used in compound interest and the range of speeds on a drilling machine. In fact, GPs are used throughout mathematics, and they have many important applications in physics, engineering, biology, economics, computer science, queuing theory and finance.
To support the evidence of your understanding on AP and GP, solve the following 4 problems.
Probability theory and probability distributions
The probability of something to happen is the likelihood or a chance of it happening. Values of probability lie between 0 and 1, where 0 represents an absolute impossibility and 1 represent an absolute certainty. The probability of an event happening usually lies somewhere between these two extreme values and it is expressed either as a proper a decimal fraction.
2.1 To support the evidence of your understanding on probability theory and probability distributions, solve the following problems.
i) all of them are blue.
ii) two is white and the third is red.
a) less than 19.5 hours?
b) between 20 and 22 hours?
a) What percent of people earn less than £30,000?
b) What percent of people earn between £35,000 and £45,000?
c) What percent of people earn more than £50,000?
It is also desirable to support your findings by producing a brief evaluation report on the use of probability theory in hashing and load balancing.
Forces, velocities, and various other quantities are vectors functions find their applications in engineering, physics, fluid flow, electrostatics, computational maths and so on. The engineer must understand these fields as the basis of the design and construction of systems, such as airplanes, laser generators, thermodynamically system, or robots. In three dimensions, geometrical ideas become influential, enriching the theory. Thus, many geometrical quantities can be given by vectors.
To support the evidence of your understanding on geometry and vectors, solve the following problems
3.1 Find the equation of the line passing through (5, 7) and parallel to the line 5x – 7y = 4.
3.2 What is an equation of the line that goes through (−1, −3) and is perpendicular to the line 2x+7y+5=0?
3.3 Discover the estimation of h for which the lines 6x+5y+8=0 and 5x-hy+8= 0 are
(i) perpendicular to each other
(ii) parallel to each other
3.4 Explain the concepts of vector graphics in a computer system.
To present your further understanding on coordinate systems, you are required to evaluate the coordinate system used in programming a simple output device (Use a computer screen as an example of the output device in your evaluation). You should also present your findings on how to construct the scaling of simple shapes; like Triangle, circle, or a straight line in vector coordinates and visually by programming and simulating in Python or any other programming language. Unit 11: Maths for Computing
Calculus (Differential and integral calculus) is deeply integrated in every branch of the physical sciences, such as physics and biology. It is found in computer science, statistics, and engineering, in economics, business, and medicine. Among the many applications in computer science, numerical calculations, systems modelling and problems involving the performance of algorithm can be cited as examples. In this task you will demonstrate your understanding of differential and integral calculus.
To support the evidence of your understanding on Calculus, solve the following problems
4.1 Suppose that x = f(t) = ¼*t2 - t + 2 denotes the position of a bus at time t.
(a) Find the velocity as a function of time; plot its graph.
(b) Find and plot the speed as a function of time.
(c) Find the acceleration.
4.2 Sand is pouring out of a tube at 5 cubic cm per second. It forms a pile which has the shape of a cone. The height of the cone is equal to the radius of the circle at its base. How fast is the sandpile rising when it is 10 cm high?
4.3 Find the maximum and minimum value of the function
x3 - 3x2 - 9x + 12
4.4 Find the dimensions of a rectangle with perimeter 1000 metres so that the area of the rectangle is a maximum.
4.5 If the region bounded above by the graph of the function f(x)= x2 - 6x + 9 and below by the graph of the function g(x)=x+3 over the interval [x, y] is represented as R, find the area of Region R.
4.6 Find the area between the two curves y = x2 and y = 2x – x2
To gain a Pass in a BTEC HND Unit, you must meet ALL the Pass criteria; to gain a Merit, you must meet ALL the Merit and Pass criteria; and to gain a Distinction, you must meet ALL the Distinction, Merit and Pass criteria. Unit 11: Maths for Computing
1. Learning Outcomes and Assessment Criteria
Learning Outcomes and Assessment Criteria - Unit 11: Maths for Computing
LO1 Use applied number theory in practical computing scenarios
D1 Produce a detailed written explanation of the importance of prime numbers within the field of computing.
P1Calculate the greatest common divisor and least common multiple of a given pair of numbers.
P2 Use relevant theory to sum arithmetic and geometric progressions.
M1 Identify multiplicative inverses in modular arithmetic.
LO2 Analyse events using probability theory and probability distributions
D2 Evaluate probability theory to an example involving hashing and load balancing.
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.
M2 Calculate probabilities within both binomially distributed and normally distributed
LO3 Determine solutions of graphical examples using geometry and vector methods
D3 Construct the scaling of simple shapes that are described by vector coordinates.
P5 Identify simple shapes using co- ordinate geometry.
P6 Determine shape parameters using appropriate vector methods.
M3 Evaluate the coordinate system used in programming a simple output device.
LO4 Reflect on the application of research methodologies and concepts
D4 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 derivatives.
2. Preparation guidelines of the Coursework Document
3. Plagiarism and Collusion
Any act of plagiarism or collusion will be seriously dealt with according to the College regulations. In this context the definitions and scope of plagiarism and collusion are presented below
Plagiarism is presenting somebody else’s work as your own. It includes copying information directly from the Web or books without referencing the material, submitting joint coursework as an individual effort.
Collusion is copying another student’s coursework, stealing coursework from another student and submitting it as your own work.
Suspected plagiarism or collusion will be investigated and if found to have occurred will be dealt with according to the College procedure (For details on Plagiarism & Collusion please see the Student Handbook).
5. Good practice
6. Extension and Late Submission
Submit to: Online to the ICON VLE only
Analyse: Break an issue or topic into smaller parts by looking in depth at each part. Support each part with arguments and evidence for and against (Pros and cons)
Evaluate: When you evaluate you look at the arguments for and against an issue.
Critically Evaluate/Analyse: When you critically evaluate you look at the arguments for and against an issue. You look at the strengths and weaknesses of the arguments. This could be from an article you read in a journal or from a textbook
Discuss: When you discuss you look at both sides of a discussion. You look at both sides of the arguments. Then you look at the reason why it is important (for) then you look at the reason why it is important (against).
Explain: When you explain you must say why it is important or not important.
Describe: When you give an account or representation of in words. Identify: When you identify you look at the most important points. Define: State or describe the nature, scope or meaning.
Implement: Put into action/use/effect Compare: Identify similarities and differences Explore: To find out about
Recommend: Suggest/put forward as being appropriate, with reasons why
The price includes Python software work as well.
Unit 11: Maths for Computing
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