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Programming Constructs and Operators: Question 3

Syllabus 8.1

Structured 8 marks

A weekend fundraiser records the donation made by each of 6 donors, together with whether the donation was made in cash. This pseudocode algorithm totals all of the donations, and also counts how many donations were both at least $20 and made in cash.

01 DECLARE Donation : REAL
02 DECLARE IsCash : BOOLEAN
03 DECLARE Total : REAL
04 DECLARE BigCashCount : INTEGER
05 DECLARE Counter : INTEGER
06 Total ← 0
07 BigCashCount ← 0
08 FOR Counter ← 1 TO 6
09     INPUT Donation
10     INPUT IsCash
11     Total ← Total + Donation
12     IF Donation >= 20 AND IsCash = TRUE THEN
13         BigCashCount ← BigCashCount + 1
14     ENDIF
15 NEXT Counter
16 OUTPUT Total
17 OUTPUT BigCashCount

The algorithm is run once, using this donation data, entered in the order shown:

Donor Donation ($) IsCash
1 15 TRUE
2 25 TRUE
3 30 FALSE
4 20 TRUE
5 50 FALSE
6 22 TRUE

(a) State the line number of the statement that performs totalling, and the line number of the statement that performs counting. Explain how you identified each one. [2]

(b) Complete a full trace table showing the value of Total and BigCashCount after each pass of the loop, for the data given above. [4]

(c) State the values output for Total and BigCashCount when the algorithm finishes. [2]

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Worked solution

Part (a): Identifying totalling and counting

  • Totalling. Line 11: Total ← Total + Donation adds the actual value of Donation to the running total on every single pass of the loop (it is not inside the IF), so Total ends up holding the sum of all 6 donations.
  • Counting. Line 13: BigCashCount ← BigCashCount + 1 always adds exactly 1, never the value of Donation itself, and it only runs when the IF condition on line 12 is true. This is the signature of a counting statement: it counts how many times something happens, not how much. [2 marks]: [1] for correctly identifying each line, [1] for a correct explanation of the totalling/counting distinction.

Part (b): Tracing the FOR loop

The loop runs once for Counter = 1 through Counter = 6 inclusive. Total starts at 0 and BigCashCount starts at 0 (lines 06–07). On each pass, Total always increases by Donation. BigCashCount only increases when Donation >= 20 AND IsCash = TRUE.

CounterDonationIsCashDonation >= 20 AND IsCash = TRUE?TotalBigCashCount
115TRUE15 >= 20 is false → false150
225TRUE25 >= 20 and TRUE → true401
330FALSE30 >= 20 but FALSE → false701
420TRUE20 >= 20 and TRUE → true902
550FALSE50 >= 20 but FALSE → false1402
622TRUE22 >= 20 and TRUE → true1623

[4 marks]: [1] for a correct running Total column, [1] for correctly totalling all 6 donations to 162, [1] for correctly applying the AND condition on each row (in particular, recognising that Donor 4’s exact $20 donation still satisfies >= 20), [1] for a correct final BigCashCount of 3.

Note that Donor 1 (cash, but only 15)andDonor6(15) and Donor 6 (22, cash) are the kind of pair that distinguishes AND from OR: under AND, both parts of the condition must be true, so Donor 1 fails on the amount even though the payment method matches.

Part (c): Final output

After Counter reaches 6 and the loop ends, line 16 outputs Total and line 17 outputs BigCashCount:

  • Total = 162
  • BigCashCount = 3

[2 marks]: [1] for each correctly stated final value.

Final answers

  • (a) Line 11 totals the donations; line 13 counts them (adds 1 each time the condition is met).
  • (b) Trace table as shown above. Total rises 15, 40, 70, 90, 140, 162; BigCashCount rises 0, 1, 1, 2, 2, 3.
  • (c) Total = 162, BigCashCount = 3.