Designing algorithms: flowcharts, pseudocode, trace tables, errors – GCSE Computer Science exam questions with mark scheme

1Grade 6–75 marks

The flowchart shows an algorithm.

(a) Complete a trace table with columns n, count and output for the algorithm when the input is 6. [4]

(b) State the output when the input is 1. [1]

(a) count starts at 0 and n values 3, 10, 5 in order(1)
(a) n values 16, 8, 4 in order(1)
(a) n values 2, 1 in order (loop then ends)(1)
(a) count increases by 1 with each new n value, reaching 8, and the only output is 8. Follow through if one earlier n value is wrong but the count matches the number of rows.(1)
(b) 0 (the loop never runs because 1 > 1 is false)(1)
Answer: (a) n: 6, 3, 10, 5, 16, 8, 4, 2, 1; count: 0 to 8; output 8. (b) 0
Examiner tip: Follow the loop arrow back to the n > 1 decision every time. Students often stop one step early or forget the count update.

2Grade 4–55 marks

Look at the algorithm below.

nums = [4, 7, 2, 9, 5]
x = nums[0]
for i = 1 to 4
    if nums[i] > x then
        x = nums[i]
    endif
next i
print(x)

(a) Complete a trace table with columns i, x and output. [4]

(b) State the purpose of the algorithm. [1]

(a) x is 4 at the start (before the loop)(1)
(a) i = 1, x = 7 and i = 2, x stays 7(1)
(a) i = 3, x = 9 and i = 4, x stays 9(1)
(a) Output 9 (once, after the loop)(1)
(b) It finds (and outputs) the largest / maximum value in the array.(1)
Answer: (a) x: 4, 7, 7, 9, 9 for i = 1 to 4; output 9. (b) Finds the largest number.
Examiner tip: OCR arrays start at index 0, so nums[0] is 4. The loop begins at i = 1 because the first value has already been used.

3Grade 6–75 marks

The algorithm below uses the MOD and DIV operators.

num = int(input("Enter a number"))
total = 0
while num > 0
    digit = num MOD 10
    total = total + digit
    num = num DIV 10
endwhile
print(total)

(a) Complete a trace table with columns num, digit, total and output when the input is 507. [4]

(b) Describe the purpose of the algorithm. [1]

(a) num 507 and total 0 at the start(1)
(a) digit 7, total 7, num 50(1)
(a) digit 0, total 7, num 5 then digit 5, total 12, num 0(1)
(a) Output 12 only, after the loop ends(1)
(b) Adds up / outputs the sum of the digits of the number entered.(1)
Answer: (a) digits 7, 0, 5; totals 7, 7, 12; num 50, 5, 0; output 12. (b) Sums the digits.
Examiner tip: MOD gives the remainder and DIV gives the whole-number quotient. If you mix them up, every later row in the table is wrong.

4Grade 1–34 marks

The diagram shows four flowchart symbols labelled A to D.

State what each symbol is used for. [4]

A (parallelogram): input / output(1)
B (diamond): decision / selection (e.g. yes/no question)(1)
C (rectangle): process (e.g. a calculation or assignment)(1)
D (rounded rectangle): start / end (terminal)(1)
Answer: A input/output; B decision; C process; D start/end
Examiner tip: Keep the parallelogram (input/output) and the rectangle (process) apart. Mixing them up is the most common lost mark.

5Grade 8–96 marks

A teacher wants a program that lets them enter test scores one at a time. Entering -1 stops the input. The program must then output the mean score and the highest score.

Write an algorithm for the program, using OCR Exam Reference Language or a high-level programming language. [6]

Initialises a total, a count and a highest value (e.g. highest = -1, 0, or the first score) before the loop(1)
Inputs a score (as an integer or real) before the loop and again inside it, or uses a loop that inputs each time (e.g. do ... until)(1)
Uses a condition-controlled loop that stops when -1 is entered (while or do ... until). In a high-level language, allow an infinite loop (e.g. while True) that exits with break when -1 is entered.(1)
Adds each score to the total and adds 1 to the count inside the loop (-1 must not be included)(1)
Compares each score with highest and updates highest if it is bigger(1)
After the loop, calculates the mean as total / count and outputs the mean and the highest. A check for count = 0 is not required for the mark.(1)

Answer:

total = 0
count = 0
highest = -1
score = int(input("Enter score"))
while score != -1
    total = total + score
    count = count + 1
    if score > highest then
        highest = score
    endif
    score = int(input("Enter score"))
endwhile
if count > 0 then
    print("Mean: " + str(total / count))
    print("Highest: " + str(highest))
else
    print("No scores entered")
endif

Examiner tip: A common lost mark is letting -1 get added to the total. Input the next score at the end of the loop, so the check happens before anything is used.

Still losing marks on this topic?

Book a free introductory session and we'll find exactly which step is costing you.

Book a free intro