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Unit 11 Maths for Computing, Assignments of Technology

Technology

It's about HND computing for maths document.

Typology: Assignments

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Higher Nationals
Internal verification of assessment decisions – BTEC (RQF)
INTERNAL VERIFICATION – ASSESSMENT DECISIONS
Programme title
BTEC Higher National Diploma in Computing
Assessor
Internal Verifier
Unit(s)
Unit 11 : Maths for Computing
Assignment title
Importance of Maths in the Field of Computing
Student’s name
List which assessment
criteria the Assessor
has
awarded.
Pass
Merit Distinction
INTERNAL VERIFIER CHECKLIST
Do the assessment criteria awarded
match
those shown in the
assignment brief? Y/N
Is the Pass/Merit/Distinction grade awarded
justified
by the assessor’s comments on the
student work?
Y/N
Has the work been assessed
accurately? Y/N
Is the feedback to the student:
Give details:
•
Constructive?
•
Linked to relevant assessment
criteria?
•Identifying opportunities for
improved performance?
•
Agreeing actions?
Y/N
Y/N
Y/N
Y/N
Does the assessment decision need
amending? Y/N
Assessor signature
Date
Internal Verifier signature Date
Programme Leader signature (if
required)
Date
pf3
pf4
pf5
pf8
pf9
pfa
pfd
pfe
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Higher Nationals

Internal verification of assessment decisions – BTEC (RQF)

INTERNAL VERIFICATION – ASSESSMENT DECISIONS Programme title BTEC Higher National Diploma in Computing Assessor Internal Verifier Unit(s) Unit 11 : Maths for Computing Assignment title Importance of Maths in the Field of Computing Student’s name List which assessment criteria the Assessor has awarded. Pass Merit Distinction INTERNAL VERIFIER CHECKLIST Do the assessment criteria awarded match those shown in the assignment brief? Y/N Is the Pass/Merit/Distinction grade awarded justified by the assessor’s comments on the student work? Y/N Has the work been assessed accurately? Y/N Is the feedback to the student: Give details:

  • Constructive?
  • Linked to relevant assessment criteria?
  • Identifying opportunities for improved performance?
  • Agreeing actions? Y/N Y/N Y/N Y/N Does the assessment decision need amending? Y/N Assessor signature Date Internal Verifier signature Date Programme Leader signature (if required) Date

Confirm action completed Remedial action taken Give details: Assessor signature Date Internal Verifier signature Date Programme Leader signature (if required) Date

Pearson

Higher Nationals in

Computing

Unit 11 : Maths for Computing

General Guidelines

  1. A Cover page or title page – You should always attach a title page to your assignment. Use previous page as your cover sheet and be sure to fill the details correctly.
  2. This entire brief should be attached in first before you start answering.
  3. All the assignments should prepare using word processing software.
  4. All the assignments should print in A4 sized paper, and make sure to only use one side printing.
  5. Allow 1” margin on each side of the paper. But on the left side you will need to leave room for binging. Word Processing Rules
  6. Use a font type that will make easy for your examiner to read. The font size should be 12 point, and should be in the style of Time New Roman.
  7. Use 1.5 line word-processing. Left justify all paragraphs.
  8. Ensure that all headings are consistent in terms of size and font style.
  9. Use footer function on the word processor to insert Your Name, Subject, Assignment No, and Page Number on each pag e. This is useful if individual sheets become detached for any reason.
  10. Use word processing application spell check and grammar check function to help edit your assignment. Important Points:
  11. Check carefully the hand in date and the instructions given with the assignment. Late submissions will not be accepted.
  12. Ensure that you give yourself enough time to complete the assignment by the due date.
  13. Don’t leave things such as printing to the last minute – excuses of this nature will not be accepted for failure to hand in the work on time.
  14. You must take responsibility for managing your own time effectively.
  15. If you are unable to hand in your assignment on time and have valid reasons such as illness, you may apply (in writing) for an extension.
  16. Failure to achieve at least a PASS grade will result in a REFERRAL grade being given.
  17. Non-submission of work without valid reasons will lead to an automatic REFERRAL. You will then be asked to complete an alternative assignment.
  18. Take great care that if you use other people’s work or ideas in your assignment, you properly reference them, using the HARVARD referencing system, in you text and any bibliography, otherwise you may be guilty of plagiarism.
  19. If you are caught plagiarising you could have your grade reduced to A REFERRAL or at worst you could be excluded from the course.

Student Name /ID Number Unit Number and Title Unit 11 : Maths for Computing Academic Year 2017/ Unit Tutor Assignment Title Importance of Maths in the Field of Computing Issue Date Submission Date IV Name & Date 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:

Activity 01

Part 1

  1. Mr.Steve has 120 pastel sticks and 30 pieces of paper to give to his students. a) Find the largest number of students he can have in his class so that each student gets equal number of pastel sticks and equal number of paper. b) Briefly explain the technique you used to solve (a).
  2. Maya is making a game board that is 16 inches by 24 inches. She wants to use square tiles. What is the largest tile she can use? Part 2
  3. An auditorium has 40 rows of seats. There are 20 seats in the first row, 21 seats in the second row, 22 seats in the third row, and so on. Using relevant theories, find how many seats are there in all 40 rows?
  4. Suppose you are training to run an 8km race. You plan to start your training by running 2km a week, and then you plan to add a ½km more every week. At what week will you be running 8km?
  5. Suppose you borrow 100,000 rupees from a bank that charges 15% interest. Using relevant theories, determine how much you will owe the bank over a period of 5 years. Part 3
  6. Find the multiplicative inverse of 8 mod 11 while explaining the algorithm used. Part 4
  7. Produce a detailed written explanation of the importance of prime numbers within the field of computing.

Activity 02

  1. Differentiate between ‘Discrete’ and ‘Continuous’ random variables.
  2. Two fair cubical dice are thrown: one is red and one is blue. The random variable M represents the score on the red die minus the score on the blue die. (a) Find the distribution of M. (b) Write down E(M). (c) Find Var(M).
  3. Two 10p coins are tossed. The random variable X represents the total value of each coin lands heads up. (a)Find E(X) and Var(X). The random variables S and T are defined as follows: S = X-10 and T = (1/2)X- (b)Show that E(S) = E(T). (c)Find Var(S) and Var (T). (d) Susan and Thomas play a game using two 10p coins. The coins are tossed and Susan records her score using the random variable S and Thomas uses the random variable T. After a large number of tosses they compare their scores. Comment on any likely differences or similarities.
  4. A discrete random variable X has the following probability distribution: x 1 2 3 4 P(X=x) 1/3 1/3 k 1/ where k is a constant. (a) Find the value of k. (b) Find P(X ≤3). Part 3
    1. In a quality control analysis, the random variable X represents the number of defective products per each batch of 100 products produced. Defects (x) 0 1 2 3 4 5 Batches 95 113 87 64 13 8 (a) Use the frequency distribution above to construct a probability distribution for X. (b) Find the mean of this probability distribution. (c) Find the variance and standard deviation of this probability distribution.
  5. A surgery has a success rate of 75%. Suppose that the surgery is performed on three patients.

(a) What is the probability that the surgery is successful on exactly 2 patients? (b) Let X be the number of successes. What are the possible values of X? (c) Create a probability distribution for X. (d) Graph the probability distribution for X using a histogram. (e) Find the mean of X. (f) Find the variance and standard deviation of X.

  1. Colombo City typically has rain on about 16% of days in November. (a) What is the probability that it will rain on exactly 5 days in November? 15 days? (b) What is the mean number of days with rain in November? (c) What is the variance and standard deviation of the number of days with rain in November?
  2. From past records, a supermarket finds that 26% of people who enter the supermarket will make a purchase. 18 people enter the supermarket during a one-hour period. (a) What is the probability that exactly 10 customers, 18 customers and 3 customers make a purchase? (b) Find the expected number of customers who make a purchase. (c) Find the variance and standard deviation of the number of customers who make a purchase. 14.On a recent math test, the mean score was 75 and the standard deviation was 5. Shan got 93. Would his mark be considered an outlier if the marks were normally distributed? Explain. 15.For each question, construct a normal distribution curve and label the horizontal axis and answer each question. The shelf life of a dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days. (a) About what percent of the products last between 9 and 15 days? (b) About what percent of the products last between 12 and 15 days? (c) About what percent of the products last 6 days or less? (d) About what percent of the products last 15 or more days? 16.Statistics held by the Road Safety Division of the Police shows that 78% of drivers being tested for their licence pass at the first attempt. If a group of 120 drivers are tested in one centre in a year, find the probability that more than 99 pass at the first attempt, justifying the most appropriate distribution to be used for this scenario. Part 4 17.Evaluate probability theory to an example involving hashing and load balancing.

Activity 04

Part 1

  1. Find the function whose tangent has slope 4x + 1 for each value of x and whose graph passes through the point (1, 2).
  2. Find the function whose tangent has slope 3x^2 + 6x − 2 for each value of x and whose graph passes through the point (0, 6). Part 2
  3. It is estimated that t years from now the population of a certain lakeside community will be changing at the rate of 0.6t 2 + 0.2t + 0.5 thousand people per year. Environmentalists have found that the level of pollution in the lake increases at the rate of approximately 5 units per 1000 people. By how much will the pollution in the lake increase during the next 2 years?
  4. An object is moving so that its speed after t minutes is v(t) = 1+4t+3t 2 meters per minute. How far does the object travel during 3rd minute? Part 3
  5. Sketch the graph of f(x) = x − 3x 2/3^ , indicating where the graph is increasing/decreasing, concave up/down, and any asymptotic behavior.
  6. Draw the graph of f(x)= 3x^4 -6X^3 +3x^2 by using the extreme points from differentiation. Part 4
  7. For the function f(x) = cos 2x, 0.1 ≤ x ≤ 6, find the positions of any local minima or maxima and distinguish between them.
  8. Determine the local maxima and/or minima of the function y = x^4 −1/3x^3
  9. By further differentiation, identify lines with minimum y = 12 x 2 − 2x, y = x 2 + 4x + 1, y = 12x − 2x 2 , y = −3x 2 + 3x + 1.

Grading Rubric Grading Criteria Achieved Feedback LO1 : Use applied number theory in practical computing scenarios 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. M1 Identify multiplicative inverses in modular arithmetic. D1 Produce a detailed written explanation of the importance of prime numbers within the field of computing. LO2 Analyse events using probability theory and probability distributions 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 random variables. D2 Evaluate probability theory to an example involving hashing and load balancing. LO3 Determine solutions of graphical examples using