6 (a) The factorial of an integer number is the product of all the integers from that number down to 1. In general, the factorial of n is n × (n-1) × ... x 2 x 1 For example, the factorial of 5 is 5 × 4 × 3 × 2 × 1 = 120 In this question, n will be referred to as the BaseNumber. A function FindBaseNumber() will: • be called with a positive, non-zero integer value as a parameter • return BaseNumber if the parameter value is the factorial of the BaseNumber • return -1 if the parameter value is not a factorial. For example: Parameter value Value returned 120 5 12 -1 6 3 1 1 FindBaseNumber(12) will return -1 because 12 is not a factorial. You may use the rest of this page for rough working.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

1. [7] (a) Example by repeated multiplication: Mark as follows (multiplication solution), (Max 7): 1 Function heading and ending including parameter and return type 2 Declaration and initialisation of local Num 3 Any conditional loop 4 Conditional loop until ThisValue found or Try out of range 5 Multiply Try by Num in a loop 6 Compare Try with ThisValue and set termination if the same in a loop 7 Increment Num and repeat in a loop 8 Attempt to Return Num if ThisValue is a factorial or -1 otherwise FUNCTION FindBaseNumber(ThisValue : INTEGER) RETURNS INTEGER DECLARE Num, Try : INTEGER DECLARE Found : BOOLEAN Num <- 0 Found <- FALSE Try <- 1 WHILE Try <= ThisValue AND Found = FALSE Num <- Num + 1 Try <- Try * Num IF Try = ThisValue THEN //BaseNumber found Found <- TRUE ENDIF ENDWHILE IF Found = TRUE THEN RETURN Num ELSE RETURN -1 ENDIF ENDFUNCTION Alternative FOR LOOP solution. Mark as follows: 1 Function heading and ending including parameter and return type 2 Declaration of local Integer value for Num and Try 3 Count-controlled Loop from 1 to ThisValue 4 Multiply Try by Num in a loop 5 Compare Try with ThisValue in a loop 6 ...Immediate return of Num if they are the same in a loop 7 Return -1 if ThisValue not found after loop FUNCTION FindBaseNumber(ThisValue : INTEGER) RETURNS INTEGER DECLARE Num, Try : INTEGER Try <- 1 FOR Num <- 1 TO ThisValue Try <- Try * Num IF Try = ThisValue THEN //BaseNumber found RETURN Num ENDIF NEXT Num RETURN -1 ENDFUNCTION
2. [4] (b) One mark per row. Examples of invalid strings: 1 Non-numeric but not "End" // contains space or other non-numeric characters 2 Real number 3 Integer value out of range (i.e. <= 0) 4 Empty string 5 Correct word but wrong case e.g. "end" rather than "End" Input Reason for choice "Aardvark" Non-numeric (and not "End") "27.3" Numeric but not an integer "-3" // "0" A non-positive integer "" An empty string