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Section 2: Problem-solving and Program Design

End-of-topic questions 1

1. List the main stages you should go through when trying to solve a generalproblem.

A. Stage 1: Define the problem

Stage 2: Analyse the problemStage 3: Propose and evaluate possible solutions

Stage 4: Select and ustify the optimal solutions

Stage !: "mplementation and revie#

2. Variables and constants are both identifiers. Explain the difference betweenthem.

A. $ariables are identifiers that are capable of changing their values%constants are identifiers that have fi&ed values.

3. What is the difference between an integer and a floating point number

A. "ntegers are #hole numbers' positive or negative #ithout decimal places%floating point or real numbers are positive or negative numbers #ithdecimal values.


1. What is an algorithm

A. An algorithm is a finite number of accurate' unambiguous steps that solvea problem or tas(.

2. List four characteristics of a good algorithm.

A. )he number of steps must be finite% the steps must be precise% the stepsmust be unambiguous% the steps must terminate.

3. What are the three main steps involved in creating an algorithm

A. "nput step% processing step% output step


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!. What is meant by assignment

A. Assignment is #here values are allocated to variables.


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1. "ame three types of control structures that are commonly used inprogramming languages.

A. Se*uencing' selection and repetition.

2. #tate the difference between bounded iteration and unbounded iteration.

A. +ounded iteration is the repetition of a set of instructions a fi&ed number of times% unbounded iteration is repeating a set of steps a number of timesuntil a particular condition becomes false.

3. $ive one example of a statement used in the following control structures%

a. #election

b. &ounded iteration

c. 'nbounded iteration

A. a. if,then,else

b. for,endfor

c. #hile,end#hile


1. (or each of the following problem statements%a. identify the input) output and processing steps.

b. write the algorithm.

- Write an algorithm to read three numbers and find their product.

A. a.

b. Step 1:start

Step 2:read num1'num2' num3

Step 3: product num1-num2-num3

Step 4: #rite product

Step !: stop

"nput Processing utput

)hreenumbers/num1'num2'num30

Accept numbers

alculate product

Store results in product

Display product

Product


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- Write an algorithm that displays the area of a rectangle by acceptinglength and width from the user.

A. a.

b. Step 1:start

Step 2:read length' #idth

Step 3: area length - #idth

Step 4: #rite area

Step !: stop

3. Write an algorithm that will read the radius of a circle and calculate anddisplay its perimeter.

A. a.

b. Step 1:start

Step 2: read radius

Step 3: circumference 2 - 3.14- radius

Step 4: #rite circumference

Step !: stop


length' #idth

Accept length' #idth

alculate area

Store results in area

Display area

Area


radius

Accept radius

alculate circumference

Store results incircumference

Display circumference

circumference


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1. Write a narrative algorithm that will accept the radius of a circle and

calculate and display its area.

A.

Step 1:Start

Step 2: et radius

Step 3: alculate area by using the formula 3.14 - radius - radius and store itin area

Step 4: Display the area

Step !: Stop

2. Write a pseudocode algorithm that will accept three numbers and calculate

and display the largest of the three. A.


)hreenumbers

Accept threenumbers

alculate the total

Store results

Display the result

Sum

ead a' b' c

Sum abc 5rite sum


radius

Accept radius

alculate area

Store results in area

Display area

area


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3. Write a pseudocode algorithm that will accept the mar*s in a test for a groupof 2+ students then calculate and display the average mar*.

A.


)hreenumbers

Accept t#enty,fivenumbers

alculate the total

Store results in sum

alculate the average

Display the average

Average

)otal 6 7

8or " 6 1 to 2! ead mar(

)otal 6 total mar(

9ndfor

Average 6 total2!

5rite average

!. ,dd steps to the previous algorithm so it also displays the highest mar*.

A.

;argest 6 7 8or " 6 1 to 2!

ead mar(

"f mar(


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"#ec$ %our progress 1

1. -raw flowcharts for the following programs%

a. rogram to accept the price of an item and calculate its V,/ at 1+0.

start

read price

vat price -.1!

#rite vat

stop


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b. rogram to accept money in '# dollars and convert it to its euivalentlocal currency.

read us

ec us -2.=1

#rite ec

stop

start


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c. rogram to accept the length and width of a rectangle and calculate itsarea.

read length' #idth

area 6 length - #idth

#rite area

stop

start


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End-of-topic questions

1. -raw flowcharts for the following%

a. , program that accepts 2 numbers and finds their product.

start

product 6 1numcount 67

read num

isnumcount>62

7

product 6 product - numnumcount 6numcount 1

yes

#rite product

no

stop


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b. , program that accepts !+ numbers and finds the number of eroes andnon4eroes in them.

numcount 67 poscount 6 7 negcount 67

read num

is

numcount>64!

yes

#rite product

no

stop

ifnum


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c. , program that accepts a set of integers and finds the number of positiveand negative numbers. /he program stops when the user enters for the

integer value.

numcount 67 poscount 6 7 negcount 67

read num

is

numcount>64!

yes

#rite product

noif

num


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d. , program that accepts a set of numbers and finds the smallest amongthem. /he program stops when the user enters 555 as the number.

read num

no 6 sum num

no =

sum

+

num

isnum6 7555

8snum7smlst

smlst ,1

#rite sum

stop

yes sum num

yes

=

sum

+

num

smlst num

start

read num


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1. 9reate a trace table to determine the output of the following algorithm%

#tep 1% set x ← +

#tep 2% set y ← 1

#tep 3% set ← 3

#tep !% set x ← x:y

#tep +% set y ← x :

#tep ;% set ← x:y:

#tep


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9reate a trace table to determine the output of the following algorithm%

#tep 1% set a← 1

#tep 2% set b← 12

#tep 3% set c← 23

#tep !% set a← a:b:c

#tep +% set b← a4b

#tep ;% set c← b4c

#tep


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1. 9reate a trace table to determine the output of the following algorithm%

#tep 1% set a ← <

#tep 2% set x ← 1

#tep 3% While a67

set x← x : a

set a ← a − 1

#tep !% endwhile

#tep +% write x

A.

a &

=

1

@

14

!

1B

4

23

3

2

2

2@

1

2B

7 )he output #ill be 2B.


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End-of-topic questions !

1. 9reate a trace table to determine the output of the following algorithms%

#tep 1% x ← +

#tep 2% for i← 1 to 1

set x > x : +

endfor

#tep 3% write x

A.

& i

!

1

17

2

1!

3

27

4

2!

!

37

3!

=

47

@

4! B

!7

17

!!

)he output #ill be !!.


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1. What is meant by stepwise refinement or top4down design

A. )op,do#n design or step#ise refinement is converting a bigger probleminto main tas(s and subtas(s. )he maor tas(s are completed first and thesub,tas(s are completed after.

2. List three advantages of using top4down design to solve a problem.

A. eusability C sections of algorithm can be used again in other algorithmsthat re*uire a similar solution' #hich saves time in future development ofalgorithms% 9asy to follo# C as each tas( or subtas( performs only onefunction% 9asy to maintain C as each tas( is by itself' if there is a need for

change in one tas( you need to concentrate on that tas( only.

End-of-topic questions &

1. Explain why a top4down design approach is sometimes used to solveproblems.

A. 5hen #e consider a problem it is often easier to vie# the problem as a#hole' and then brea( it do#n into smaller problems. 5e can thenconcentrate on one of the smaller problems and leave the others untillater.


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2. , hotel wants to have a room boo*ing system. When a guest arrives thereceptionist would be able to see which rooms are free and allocate one to the

guest. When the guest leaves) the room would be mar*ed as free again. Eachday the cleaners would be given a list of the rooms that are in use. ,t any timethe receptionist would be able to use the room number to find the name andhome address of a guest) or could search the room system for a namedguest. -raw a top4down design diagram to show how the room boo*ingsystem could be developed.

A.

Room booking

Room allocation Cleaning tasks Searches

Search for

name and

address of

guest

Search for

room

occupied by

guest


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End-of-section questions

)ultiple-c#oice questions

1. /he following are problem4solving stages

8. analyse the problem

88. suggest possible solutions

888. implement and review

8V. define the problem

V. select the best solution

/he correct order of stages is%

, 8) 8V) 88) 888) V

& 8V) 8) 88) V) 8889 8V) 88) 8) V) 888

- 8) 88) 8V) 888) V

A. +

2. Which one of the following is a variable

, x

& ?x@

9 +

- ?+@

A. A

3. /o store fractional values) use the data type%

, integer

& floating point

9 character

- string

A. +

!. Which of the following is not a characteristic of a good algorithm , precise

& finite number of steps

9 ambiguous

- logical flow of control

A.


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+. -iagrammatic representation of an algorithm is%

, flowchart

& data flow diagram

9 algorithm design

- pseudocode

A. A

;. Which of the following isAare control structures

, selection

& seuencing

9 repetition

- all of the above A. D

y9 x7y and x>y

- x6 7y

A.


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1.9onsider the following algorithm segment%

x > x:y

y > x − y

write y) x

#uppose x > 1 and y > 1+) after the completion of the above statements) thevalues of x and y will be%

, 2+ and 1

& 1 and 2+

9 1 and 4+

- 4+ and 1

A. +


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Structured questions

1 a. List the main stages of problem4solving process for computer4basedproblem4solving.

b. (or each of the stages identified in 1a above) briefly describe the activitiesthat are involved in it.

A. a. Stage 1: Definition of the problem

Stage 2: Analyse the problem

Stage 3: Propose and evaluate possible solutions

Stage 4: Develop and represent an algorithm

Stage !: )est and validate the algorithm

Stage : "mplement the algorithm

b. Stage 1: Definition of the problem

"n this stage' the problem is loo(ed at carefully and if it is not phrased properly' it is modified to ensure that it is clearly stated.

Stage 2: Analyse the problem

"n this stage' identify the inputs to be used' outputs re*uired' values tobe stored /if any0' and the processing that needs to be done to get thecorrect outputs.

Stage 3: Propose and evaluate possible solutions

ere identify solutions to the problem and evaluate each option to see

#hich is most appropriate and choose the best option.Stage 4: Develop and represent an algorithm

"n this stage' brea( do#n the problem into simple manageable stepscalled algorithm so that they can be handled easily.

Stage !: )est and validate the algorithm

ere' chec( the algorithm #ritten using some values to ensure that it produces the re*uired results.

Stage : "mplement the algorithm

"n this stage' #rite the steps of algorithm using a programming language so that computer can operate on it.


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2. 8C diagrams can be used to brea* down a problem into its components.

a. #tate what is meant by ?8C diagrams@

b. 9reate an 8C chart for the following problem statement% ?,ccept thevalues of length and width of a rectangle and calculate its area@

A. a. An "P diagram is a table #ith three columns sho#ing the input' outputand processing parts of the problem.

b.

"nput Processing output

length and#idth

Accept length and#idth

alculate area

Store results in areaDisplay area

Area

3. a. #tate the difference between%

i. constants and variablesii. integer data type and floating point data type

iii. character data type and string data type

b. -efine the following terms%

i. identifier

ii. literal

A. a. i. ?9onstants are fixed values while variables identify a memory locationthat is capable of storing values that can be changed.@

ii. "ntegers are #hole numbers' positive or negative #ithout decimal places' e.g. ,4!' and 12% floating point or real numbers are positiveor negative numbers #ith decimal values' e.g. ,!. and .=.

iii. haracters are anything that you can (ey in from a (eyboard such asletters' numbers and special characters% string is a linear group ofcharacters to be stored as one.

b. i. "dentifier is the name used for identifying a variable or a constant.

ii. ;iterals are constants that are #ritten literally as itself rather than as a

value.

!. 9reate a narrative algorithm that will prompt the user to enter two numbersand find their difference.

A. Step 1: Start

Step 2: et t#o numbers

Step 3: Subtract second number from the first number

Step 4: Store the results in difference

Step !: Display difference


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+. Write a pseudocode that prompts the user to enter a value and display itssuare and cube values.

A. Step 1: start Step 2: read num

Step 3: s*uare num - num

Step 4: cube num - num- num

Step!: #rite s*uare' cube

Step : stop

;. -raw a flowchart and write a pseudocode that will prompt the user to entertwo numbers and display their product.

A.

read n1'n2

prod 6 n1 - n2

#rite prod

stop

start


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length FwidthG

A.

Step 1: start

Step 2: read length' #idth

Step 3: area length - #idth

Step 4: #rite area

Step !: stop

read length' #idth

area 6 length - #idth

#rite area

stop

start


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=. Write a pseudocode that will accept 2+ integers and displays the numberof positive and negative numbers.

A. Step 1: start Step 2: poscount 7' negcount 7

Step 3: for i 1 to 2!

Step 3: read num

Step 4: if num


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17

3!

17

b. )he algorithm #ill print 17 3! 17

1.a. -raw a trace table for the following algorithm.

b. What is the output of this algorithm

x > 1y > 1+

> 2

x> x:y

y > x:

> x:y:

if x 7y then

x > x :+

else

x > x B 3endif

if y 6 then

y > y:1

else

y > y B 1

endif

print x) y)

A. a.

& y ?

17

1!

2 7

2 !

4

!


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2 2

! !

b. )he output #ill be 22 !! B7

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