A-level COMPUTER SCIENCE Paper

You are advised to spend no longer than 45 minutes on this section. Type your answers to Section A in your Electronic Answer Document. You must save this document at regular intervals. Figure 1 shows two vectors a and b and the angle between them, . Figure 1 a = [4, 3] b = [4, 0] The magnitude of a vector, represented as an arrow, is the length of the arrow. The magnitude of vector a is 5 because �42+32 = 5 . What is the magnitude of vector b? [1 mark] . Calculate the dot product of vectors a and b. You should show your working. [2 marks] The angle between two vectors cannot be larger than 180o. If the angle is measured as being greater than 180o then this angle is subtracted from 360o to find the actual angle between the two vectors. Example: if an angle between two vectors represented as arrows is measured as being 240o then the angle between the two vectors is 360o – 240o = 120o . Describe what will happen to the angle and the magnitude of vector a when vector a is multiplied by the scalar 2 [2 marks] . Describe what will happen to the angle and the magnitude of vector a when vector a is multiplied by the scalar -1 [2 marks] Turn over for the next question Turn over ► A regular language is a language that can be defined by a regular expression. . Complete the unshaded cells of Table 1 to show which of the statements about regular languages are true and which are false. Table 1 Statement True or False? All regular languages can be represented using a finite state machine without outputs. The set of strings defined by a regular language is always finite in size. There are some languages which can be represented in Backus- Naur Form (BNF) that are not regular languages. Copy the contents of the unshaded cells in Table 1 into the table in your Electronic Answer Document. [2 marks] Figure 2 shows a set of Backus-Naur Form (BNF) rules that are used to define a language. Figure 2 sentence ::= npv sentence ::= vnp np ::= dn n ::= human | dog | cat | baby d ::= a | the v ::= ate | slept | drank | cuddle c ::= and | but | or . There are two rules in Figure 2 with sentence on the left-hand side that are used to define what a valid sentence is in the language. Write a single rule that could replace these two rules. Your new rule must not change what a valid sentence is. [1 mark]