- a) Let A = {a, b, c} and B = {1, 2, 3, 4}. Determine whether each of the following is TRUE or FALSE:
- b) (124 mod 6 = 4) → (5 | 16). c) , domain is the set of integers.
- Q−2: [5×1 marks] Determine whether each of the following is TRUE or FALSE:
- b) Using the truth table, determine whether or not the proposition is a tautology.
- a) Find a proposition using only and the connective ˅ with the following truth table:
- M131: Discrete Mathematics
- c) Show that the first three column vectors are linearly independent. Explain.
- b) Determine whether the fourth column vector forms a linear combination with the first three column vectors.
- a) Find a matrix B that is row equivalent to A.
- Q−6:[2+1+1 marks]Consider a linear system whose augmented matrix is of the form: . For what values of a and b will the system have: a) No Solution; b) A unique solution; c) Infinitely many solutions.
- Q−6:[2+1+1 marks]Consider a linear system whose augmented matrix is of the form:
- c) Find the matrix B such that .
- b) Find a matrix C such that .
- a) Write the linear system in matrix form .
- Q¬−5:[1 + 2 + 2 marks]. Consider the linear system: .
- b) Solve the system by applying the Gaussian elimination method.
- a) Write the augmented matrix for the system.
- Q−3:[1+4 marks]Consider the linear system:
- c) Compute |-2A.AT.A-1|
- a) Write the coefficient matrix A of the system
- Q−2: [1+3+2 marks]For the system:
- e) The vectors form a linear combination with .
- d) The vectors are linearly independent.
- c) If AB = 0, thenA = B = 0.
- b) If (c1 , c2) is a solution of the 2 x 2 system , then, for any real number k, the ordered pair (kc1 , kc2) is a solution.
- a) If m1 ≠m2 in the system , where m1 , m2 , b1 , and b2 are constants, then the system has a unique solution.
- M132: Linear algebra
- e) Estimate the population in the year 2020.
- d) What was the population in 1960?
- c) What is the growth constant?
- b) What was the initial population (the population in 1950) ?
- a) Find the formula for P(t).
- Q¬−8: [5×1 Marks] Let P(t) be the population (in millions) of a certain city t years after 1950, and suppose that P(t) satisfies the differential equation P′(t) = 0.017 P(t), P(0)= 2560
- b) Use the logarithmic differentiation to differentiate the function
- a) Differentiate the function
- A window is being built and the bottom is a rectangle and the top is a semicircle. If there is 12 m of framing materials what must the dimensions of the window be to let in the most light
- e) Find the points of inflection, if any.
- d) Find the intervals on which the graph of f (x) is concave up or concave down.
- c) Find the local maximum and minimum of f (x), if any.
- b) Find the intervals on which f (x) is increasing or decreasing.
- Q¬−4: [2+3 Marks] Use the definition of the derivative to find f ′(x) if
- Use the definition of the derivative to find f ′(x) if
- Find the slope of the tangent line to the following curves at the designated points
- c) Describe the domains of f (x) and g(x).
- b) Find g (f (x)), and describe its domain
- a) Find f (g(x)) and describe its domain.
- Q−2: [2+2+1 Marks] Let .
- b) Find the points of intersection, if any, of the graphs of y = f (x) and y = -4 .
- a) Find the zeros of g(x) and h(x).
- Q−1: [4+1 Marks] let
- Find the probability of accident rain or no rain.
- Suppose that city records produced the following probability data on a driver being an accident on the last day of a Memorial Day Weekend
- A committee of 3 juniors and 3 seniors is to be formed from the members of a club having 18 juniors and 15 seniors. How many different committees are possible?
- How many permutations are there of the letters in the word BANANA?
- You are considering 10 different colleges. Before you decide to apply to the colleges, you want to visit some or all of them. In how many orders you can visit:
- Why might the range be an unhelpful measure of spread for these particular data?
- a) Find the range of the earnings.
- Calculate the standard deviation of the earnings.
- Calculate the lower and upper quartiles, and find the inter-quartile range.
- Calculate the mean, median and mode.
- Below are the earnings, for a particular week, of 15 staff (including the owner) working in a small business
- e) Find the cumulative distribution function.
- d) Find the mean and standard deviation.
- The density function for a random variable X is given by where k is a constant
- Q-6: [2+2+2+3+3Marks] The density function for a random variable X is given by where k is a constant
- e) Calculate the variance and standard deviation of the random variable X.
- d) Find the mean of the random variable X.
- b) Find the probability distribution and the cumulative distribution of the random variable X.
- a) List the possible elements of the sample space S for the three tosses of the coin and to each sample point assign a value x of X.
- Q-5: A coin is tossed three times. Let X be a random variable representing the number of heads in three tosses of a coin. The coin is unbalanced and a head has a 60% chance of occurrence.
- Q-5: [2+2+3+2+3Marks] A coin is tossed three times. Let X be a random variable representing the number of heads in three tosses of a coin. The coin is unbalanced and a head has a 60% chance of occurrence.
- d) If the product is not defective, what is the probability that it was made by machine ?
- c) If the product is defective, what is the probability it was made by machine ?
- b) What is the probability that it is not defective
- a) What is the probability that it is defective
- A manufacturer has 3 machines , make 20%, 30% and 50%, respectively, of the products. It is known from past experience that 2%, 3% and 4% of the products made by each machine respectively are defective. If a finished product is randomly selected
- Q-4: [2+2+3+3Marks] A manufacturer has 3 machines , make 20%, 30% and 50%, respectively, of the products. It is known from past experience that 2%, 3% and 4% of the products made by each machine respectively are defective. If a finished product is ra
- d) Find the probability of an accident, given rain.
- c) Find the probability of an accident and rain.
- b) Find the probability of rain, accident or no accident.
- a) Find the probability of accident rain or no rain.
- Accident (A) No accident (A’) Total Rain (R) 0.025 0.335 0.360 No rain (R’) 0.015 0.625 0.640 Total 0.040 0.960 1.00
- Q-3: [3+3+1+3Marks] Suppose that city records produced the following probability data on a driver being an accident on the last day of a Memorial Day Weekend.
- c) A committee of 3 juniors and 3 seniors is to be formed from the members of a club having 18 juniors and 15 seniors. How many different committees are possible?
- b) How many permutations are there of the letters in the word BANANA?
- i- 6 of the colleges ii- All ten colleges
- a) You are considering 10 different colleges. Before you decide to apply to the colleges, you want to visit some or all of them. In how many orders you can visit:
- e) Why might the range be an unhelpful measure of spread for these particular data?
- c) Calculate the standard deviation of the earnings.
- Calculate the lower and upper quartiles, and find the inter-quartile range.
- a) Calculate the mean, median and mode.
- Weekly earnings (£) 280 370 305 285 480 1,260 210 340 280 290 315 325 370 360 280
- Q−1: [2+3+3+1+1 Marks] Below are the earnings, for a particular week, of 15 staff (including the owner) working in a small business:
- Below are the earnings, for a particular week, of 15 staff (including the owner) working in a small business
- Microcontroller A: - The clock speed of the processor is 33.554432 MHz - 25-bit counter/timer. - 1024 bytes RAM. - 256 bytes non-volatile, read-write memory. - Watchdog timer
- Microcontroller B: - The clock speed of the processor is 131.072 KHz - 18-bit counter/timer. - 512 bytes RAM. - 128 bytes non-volatile, read-write memory. - Watchdog timer
- Which microcontroller would you choose from the above two if you need to generate clock pulse every 2 seconds? (Give reasons).
- Microcontroller A: - The clock speed of the processor is 33.554432 MHz - 25-bit counter/timer. - 1024 bytes RAM. - 256 bytes non-volatile, read-write memory. - Watchdog timer Microcontroller B: - The clock speed of the processor is 131.072 KHz - 18-b
- (ii) State if 2’s complement overflow has occurred. Justify your answer.
- (i) Add these two numbers in binary. Show the carry bits in your working.
- (b) The following two 8-bit binary code words both represent 2’s complement integers: 0101 1010 0110 1111
- (b) The following two 8-bit binary code words both represent 2’s complement integers:
- (ii) Work out what this code word represents if it is instead the code for a signed integer using 2’s complement representation. Show your work.
- (i) Write down what this code word represents if it is the code for a text character using 7-bit ASCII code with a zero inserted in the leftmost position. (2 marks)
- (a) This part relates to the 8-bit binary code word 0101 0001
- e. What does the loop do? Do not give a description on an instruction-by- instruction level; give the overall task of the loop in brief
- d. Why is the following instruction: “add immediate rB 0000 “used?
- c. The loop reads successive data items from a block of locations in data memory. What are the lowest and highest addresses (in hexadecimal) of the locations in this block?
- b. How many times in total will the set of instructions within the loop be executed?
- a. The subroutine includes a loop. Which register is being used as the loop counter?
- load immediate r1 0000 load immediate r3 0012 load immediate rA 0500 load register-indirect via rA rB add immediate rB 0000 jump if zero relative 0001 jump relative 0001 add immediate r1 0001 add immediate rA 0001 subtract immediate r3 0001 jump if z
- In this question, all numbers are in hexadecimal. This part of the question refers to the following subroutine for the T224 simulated processor:
- This question carries 25% of the assignment marks. It enables you to demonstrate your mastery of Learning Outcomes 4, 5, 10, 13 and 19 of Block 2.
- The processor needs to find out whether the patient has pressed a button to change the desired temperature. It does this examining the state of the two buttons. If one has been pressed, the stored value for the desired temperature is changed appropri
- Draw a flowchart for this part of the total task, assuming that a button will not have been pressed more than once
- b. The processor needs to find out whether the patient has pressed a button to change the desired temperature. It does this examining the state of the two buttons. If one has been pressed, the stored value for the desired temperature is changed appro
- Draw the flowchart that corresponds to the above list using appropriate shapes for the boxes and drawing appropriate linking lines. Note that the flowchart includes at least one loop.
- - Input actual temperature.
- - Output the valve settings.
- - Does actual temperature equal desired temperature?
- The new desired temperature will be shown on the display. - The processor in the computer will compare the temperature inside the lounge with the desired temperature
- - Switch fan off.
- - Switch fan on.
- and if they are not the same it will switch on a fan to supply air of an appropriate temperature to the interior of the lounge. The processor controls the temperature of this air supply by setting a valve to a hot air supply and a valve to a cool air
- - Workout the valve settings.
- a. The processor’s task in this climate-control system includes the following items:
- a. The processor’s task in this climate-control system includes the following items: - Workout the valve settings. - Switch fan on. - Switch fan off. - Does actual temperature equal desired temperature? - Output the valve settings. - Input actual te
- The processor controls the temperature of this air supply by setting a valve to a hot air supply and a valve to a cool air supply appropriately. Each of these valves has a number of settings, ranging from fully shut to fully open.
- button labeled UP will cause the desired temperature to increase by 1°C and pressing the button labeled DOWN will cause the desired temperature to decrease by 1°C
- The desired temperature will be factory pre-set to 25 °C. The patient will be able to change this temperature by means of two buttons. Pressing the button labeled UP will cause the desired temperature to increase by 1°C and pressing the button labele
- - There will be a small display to show the desired temperature. It will consist of two 7-segment displays showing the digits, plus a pre-set display showing the “°C”.
- Some lounges in medical centers incorporate climate control, whereby a computer is used to maintain the temperature inside the lounge at a setting chosen by the patient. The climate control will be computer-controlled and will operate as follows
- T224: Computers and Processors
- ááÈíÚ:Apple iPhone 5S/5C+Apple iPad Air - Silver - 32GB
- 1. What is the function of the following: a. Control Unit. b. Main Memory. c. Compiler.
- Consider an image of size 1000 X 720 pixels which requires 2160000 bytes to be stored inside the computer. Find the number of bits used to represent each pixel, the pixel amplitude and the coloring system used for the image
- Show all the steps required to convert the decimal value 1980 to its octal representation
- Show all the steps required to convert the binary value 111000101 to its decimal representation
- Any feature of the analogue world can be taken inside the boundary of the computer using two-steps process. Mentions the two steps with brief explanation giving an example that illustrates the steps
- Explain the advantage of complex representations using the traffic signs as an example
- From your understanding of the term “complex representation”, briefly explain why traffic signs are considered to be complex representations
- Representations play a central role in facilitating communication by establishing a relationship between some form and some meaningful content subject to some convention; mention the two conditions for effective representation
- Define a search engine. Give examples on two search engines you use
- Explain the difference between the Internet and the Web
- b. How can you avoid plagiarism when writing your TMAs?
- a. Briefly define the term plagiarism.
- One showing the case when the user selected to buy a white laptop.
- One showing the case when the user selected to buy a black laptop.
- One showing the case when the user selected to buy a PC.
- Test your program and run it to make sure it works properly. In your Solution document insert three screenshots for the output
- Assume that all strings used in the program and entered by a user are in small letters.
- Print the user selection, price and discounted price in the output window
- Give the following discount on the price and calculate the discounted price as follows: - PC: 20%. - Black laptop: 15%. - White laptop: 10%.
- Calculate the price of the user selection as follows: - PC: 1700$. - Black laptop: 2500$. - White laptop: 3000$.
- If the user selected a "laptop" then ask the user to select which color he wants "white" or "black". Read the answer from the user and store it in a variable.
- Ask the user if he wants to buy a "pc" or a "laptop". Read the answer from the user and store it in a variable.
- a. Using nested if-else statement, write JavaScript program that works according to the following specifications:
- Calculate the area and volume of the cube using the following formulas: Area = 6 *(edge length)2 volume = (edge length)3
- Read the edge length of a cube
- a. Write JavaScript program to calculate area and volume of a cube. The program should work according to the following specifications: [
- What is the exact output after these instructions have been executed? You need to draw a simple tracing table that shows how you got your answer.
- How many times will the loop be executed
- The condition, the loop body, and any instruction(s) that is (are) not in the loop body
- The following flowchart diagram shows a loop structure program
- Not (a and not b) not a or b
- Use truth tables to show whether the following two Boolean expressions are equivalent or not
- c. Compiler.
- Main Memory.
- Control Unit
- What is the function of the following
- Consider an image of size 1000 X 720 pixels which requires 2160000 bytes to be stored inside the computer. Find the number of bits used to represent each pixel, the pixel amplitude and the coloring system used for the image.
- Show all the steps required to convert the decimal value 1980 to its octal representation
- Show all the steps required to convert the binary value 111000101 to its decimal representation.
- Any feature of the analogue world can be taken inside the boundary of the computer using two-steps process. Mentions the two steps with brief explanation giving an example that illustrates the steps
- Explain the advantage of complex representations using the traffic signs as an example
- From your understanding of the term “complex representation”, briefly explain why traffic signs are considered to be complex representations? Explain the advantage of complex representations using the traffic signs as an example.
- Representations play a central role in facilitating communication by establishing a relationship between some form and some meaningful content subject to some convention; mention the two conditions for effective representation
- Define a search engine. Give examples on two search engines you use
- Explain the difference between the Internet and the Web
- b. How can you avoid plagiarism when writing your TMAs?
- M150 Data, computing and information
- a. Briefly define the term plagiarism.
- Print the array elements in the output window
- Ask the user to enter any 10 numbers and fill them in the array
- Define JavaScript function occurrence(anArray,num), that takes an array anArray and a number num as arguments. The function returns the number of occurrences of num in anArray
- Declare an array of 10 elements
- Define a JavaScript function occurrence(anArray,num), that takes an array anArray and a number num as arguments. The function returns the number of occurrences of num in anArray
- In the context of UI design, define and briefly explain (using your own understanding) the terms: visibility, affordance, tolerance and consistency
- What is a user interface? Give two examples of user interfaces you use in your daily life.
- Briefly define the term HCI. What's the purpose of this kind of study?
- one showing the program prompting for the game name, with you having entered the name but not yet pressed OK
- Use an appropriate methods to: − Increment the game by two chances. − Print the game information
- Create a game instance and initialize its properties by the values entered by the user. Chance should be set to 1.
- Prompt the user for values of name and level of a game he wants to create
- Implement the methods getName(),getLevel (), getChance(), and displayInfo() according to the above specifications.
- Write the Game constructor function Game(aName, aLevel, aChance)
- displayInfo(): a method that displays the name, level and the chance of the game in an alert box, using the three methods: getName() and getLevel() and getChance().
- moveForward(): a method that gives the next chance (i.e. increments chance by 1) only if the chance is less than 6. Otherwise, set it to 1.
- getChance(): a method that returns the chance of playing the game
- getLevel(): a method that returns the level selected of the game
- getName(): a method that returns the name of the game
- The Game object type has the following methods
- The Game object can go forward to further chances, however, the maximum value of chance is 6.
- chance: a number (from 1 to 6) representing the chance of playing the game.
- level: a string representing the level of the game, such as easy, moderate, difficult.
- name: a string representing the name of the Game.
- You are required to model a new user-defined object type, Game. The Game object type has the following properties:
- What information do we usually find in function specifications?
- Provide a copy of the specifications of all the functions you’ve used in writing your program.
- Insert a screenshot that shows the resulted output of parts c and d.
- Change the state to be 30 December 2000. You should not create a new date. - Display the day name. - Display it in long form
- Display the day name. - Display it in long form.
- Change the state to be 30 December 2000. You should not create a new date.
- For the Date object you've created in a. do the following
- Calculate the difference in years between the two dates and print it in the output window
- Create another Date object representing the date 13 November 2013
- Create a Date object representing the date 2 June 1950.
- In unit9, page 21 you were introduced to the methods associated with Date object. In the same unit, section 4.2 you learned how to use functions from the "dateLibrary.js" in JavaScript programs. The specifications for all the functions in t
- Run your program two times: one where the number 0 is an element on the array and another time where the number 0 is not in the array. Provide two screenshots of the two required outputs of your program. This should also show the arrays elements
- Run your program two times: one where the number 0 is an element on the array and another time where the number 0 is not in the array
- Using the function occurrence(), display on the screen the number of occurrences of number 0 in the array. If the number 0 doesn’t exist in the array, you should display a suitable message also
- Print the array elements in the output window.
- Ask the user to enter any 10 numbers and fill them in the array
- Declare an array of 10 elements
- Define a JavaScript function occurrence(anArray,num), that takes an array anArray and a number num as arguments. The function returns the number of occurrences of num in anArray.
- M150 Data, computing and information
- Íá æÇÌÈ m256 tma answer assignment solution m256
- M256, Software development with Java Fall 2013 2014
- Consider the following use case for this system. List Department’s Tutors The administrator identifies abranch, the system displays all departmentsof that branch, and then the administrator selects one of the displayed departments, the system display
- department20anddepartment2, assume that the object department20is selected which has the tutorsrepresented by the objectstutor7, tutor11, tutor20andtutor3
- the administrator selects one of the displayed departments, the system displays the tutors of that department
- For this question you should use a scenario based on a branch represented by an object branch4 which has a number of departments represented by the objects department3, department20anddepartment2, assume that the object department20is selected which
- List Department’s Tutors The administrator identifies abranch, the system displays all departmentsof that branch, and then the administrator selects one of the displayed departments, the system displays the tutors of that department.
- Consider the following use case for this system.
- The following is a use case description and a class diagramfor the Arab Open University (AOU) system.
- Write the corresponding core code of the sequence diagram you drew in part(d).
- On the basis of cascading design, construct a walk-through and a sequence diagram for this scenario.
- Write down a specification for the coordinating method(s) for this use case.
- Draw a sequence diagram showing just the communication between the userinterfaceobjectand the coordinatingobject(aOUCoord)for this scenario. You should assume that the user interface has already identified the relevant branch object.
- Draw an object diagram illustrating the relevant objects and the links for this scenario.
- a. Draw an object diagram illustrating the relevant objects and the links for this scenario.
- b. Draw a sequence diagram showing just the communication between the userinterfaceobjectand the coordinatingobject(aOUCoord)for this scenario. You should assume that the user interface has already identified the relevant branch object.
- d. On the basis of cascading design, construct a walk-through and a sequence diagram for this scenario.
- e. Write the corresponding core code of the sequence diagram you drew in part(d).
- State an invariant mentioned explicitly in the requirements document which can’t be implemented on the class diagram.
- State an invariant mentioned explicitly in the requirements documentwhich can’t be implemented on the class diagram.
- Give the class descriptions, including a brief comment for each class and attribute.
- Construct a class diagram including all class diagram entities (classes, multiplicities and associations) and including any generalization relationship if needed.
- Classify the conceptual classes identified in part (a) as tangible entity, role, event, organizational unit, or abstract entity.
- Identify the conceptual classes of the Arab Open Universitysystem, and then write their names according to UML conventions.