Reference no: EM133074794

CTF3202 Logical Analysis and Problem Solving - University of Leeds

Learning Outcome 1: Apply statistical principles to discern meaningful information based on a given scenario.

Learning Outcome 2: Demonstrate the use of algebra to solve given problems

Section 1 [ALGEBRA AND LOGIC GATES]: Show all necessary calculations.

Question 1. Consider the following list of numbers. Your job is to erase as few of these numbers as possible such that the remaining numbers appear in increasing order. For example, erasing everything except the first two numbers laves an increasing sequence; erasing everything except for the first, third, sixth and eighth numbers does the same.

9 44 32 12 7 42 34 92 35 37 41 8 20 27 83 64 61 28 39 93 29 17 13 14 55 21 66 72 23 73 99 1 2 88 77 5 65 83 84 62 5 11 74 68 76 78 67 75 69 70 22 71 24 25 26

Question 2. Solve the above exercise [1], such that the remaining numbers are in decreasing order

Question 3. Solve the following simultaneous equations for x₁, x₂, x₃, and x₄
E₁: x₁+x₂+0 +3x₄=4
E₂: x₁+x₂-x₃ +x₄=1
E₃: 3x₁-x₂-x₃ +2x₄=-3
E₄: - x₁+2x₂+3x₃-x₄=4

Question 4. A foundation student bought a mobile phone and smart watch for a total of £1,250, excluding VAT (value added tax), paying 3 times as much for the mobile phone
as for the smart watch.
Write an expression to show the total cost in terms of the cost of the smart watch.
What was the cost of each item?
Calculate the VAT on the mobile phone, assuming a VAT rate of 14%

Question 5. Find the value of k to satisfy the equation referring to the discharge of water from a tank

t₁-t₂=2A/a √((1+k)/2g) (√(h₁ )-√(h₂ ))

given that t₂=0.45,t₁=2.6,A=15.6,a=12.57/144 ,g=32.2,h₁=36 and h₂=25

Question 6. Construct a chart giving values of u and v to satisfy the equation 1.2v+0.64u=0.85 the range of u being 5 to 100.(Use Excel)

Question 7. Construct a chart giving values of u and v to satisfy the equation 2u+7v=52 the range of v being 2 to 50. (Use Excel)

Question 8. Consider the following:
An online trading company wants to offer discounts to new customers. The company has recently emailed discount code to the customers. New customer must have a discount code to be eligible but returning customer are not eligible for a discount.
Let
A = Returning Customer
B = Discount Code
(a) Draw a truth table to represent when a customer has a discount.
(b) From your truth table in (a) produce a Boolean expression to represent discounted customer (Q) for the trading company.

Section 2

Question 9. The data below shows the monthly rent for 24 students: 1500, 1350, 350, 1200, 850, 900, 1500, 1150, 1500, 900, 1400, 1100, 1250, 600,610, 960, 890, 1325, 900, 800, 2550, 495, 1200, 690.
(a) Create a relative frequency distribution table using 7 classes
(b) Use your table in (a) to produce a histogram to represent your data

Question 10. The following is a frequency table showing the agesof members of a symphony orchestra for youngadults.

Age        Frequency

15           2

16           5

17           11

18           9

19           14

20           13

21           10

22           13

Find the sample mean and median of the ages of the 77 members of the symphony.

Section 3 [Flowchart and Algorithm Development]

Question 11. Given the following list of steps in the admission process:

1. Search for a school
2. Prepare for the admission test and write test
3. Did you pass the exam?
4. Submit necessary documents and get admission
5. End
6. Are seats available?
7. Start
8. Is there an admission test?

Re-arrange the above steps in the correct order and useMS Visio to draw a flowchart for the admission process.

Question 12. Construct an algorithm that has as input an integer n≥1,n+1points and x₀,x₁,....x_n and a pointx and which produces as output the product
P=(x-x₀ )(x-x₁ ).....(x-x_n )