misswelton.weebly.com€¦ · web view3.3. 1a. [4 marks] markscheme (a1)(a1) (ft) (a1)(a1) (ft)...

3.3

1a. [4 marks]

Markscheme

(A1)(A1)(ft)(A1)(A1)(ft) (C4)

Note: Award (A1) for each correct column followed through from the respective columns.

[4 marks]

Examiners report

[N/A]

1b. [2 marks]

Markscheme

neither (A1)(ft)

since the entries in the final column are not all true and not all false (R1) (C2)

Note: Do not award (A1)(R0). Follow through from an incorrect truth table but only if their reasoning

is consistent with the final column.

Award (R1) only if the final column is clearly identified in the justification.

1

[2 marks]

Examiners report

[N/A]

2a. [2 marks]

Markscheme

If my Mathematical Studies homework is not due in tomorrow then today is Wednesday. (A1)(A1)

(C2)

Note: Award (A1) for If… then…

Award (A1) for correct propositions, my Mathematical Studies homework is not due in tomorrow and

today is Wednesday, in the correct order.

Award (A1)(A0) for “If ¬p then q”.

[2 marks]

Examiners report

[N/A]

2b. [3 marks]

Markscheme

(A1)(A1)(A1)

(ft) (C3)

[3 marks]

2

Examiners report

[N/A]

2c. [1 mark]

Markscheme

neither (A1)(ft) (C1)

Note: Follow through from the final column of their truth table.

[1 mark]

Examiners report

[N/A]

3a. [3 marks]

Markscheme

if the baby is happy and wants to play then the baby does not cry (A1)(A1)(A1) (C3)

Note: Award (A1) for “If… then…”; (A1) for “the baby is happy and wants to play”, (A1) for “the baby

does not cry”. Crying must be negated.

[3 marks]

Examiners report

[N/A]

3b. [2 marks]

Markscheme

3

(A1)(A1) (C2)

Note: Award (A1) for each correct column.

[2 marks]

Examiners report

[N/A]

3c. [1 mark]

Markscheme

Neither (A1)(ft) (C1)

Note: Follow through from the last column in their part (b).

[1 mark]

Examiners report

[N/A]

4a. [3 marks]

Markscheme

if the car is less than 2 years old or the car has not been driven more than , then the car is

under warranty (A1)(A1)(A1) (C3)

4

Note: Award (A1) for if …, then …, (A1) for “or”, (A1) for correct statements in correct order. Accept

“If the car has not been driven more than or the car is less than 2 years old, then the car is

under warranty”. Accept logical equivalent wording for each proposition, eg “less than ”.

[3 marks]

Examiners report

[N/A]

4b. [2 marks]

Markscheme

(A1)(A1)(ft) (C2)

Note: Award (A1) for column correct and (A1)(ft) for column correct. Follow

through from their column.

[2 marks]

5

Examiners report

[N/A]

4c. [1 mark]

Markscheme

contrapositive (A1) (C1)

[1 mark]

Examiners report

[N/A]

5a. [1 mark]

Markscheme

I was not paid (A1) (C1)

[1 mark]

Examiners report

[N/A]

5b. [1 mark]

Markscheme

(A1) (C1)

[1 mark]

Examiners report

[N/A]

5c. [2 marks]

Markscheme

6

(A1)(A1) (C2)


[2 marks]

Examiners report

[N/A]

5d. [2 marks]

Markscheme

yes (A1)(ft)

as the last two columns of the truth table are the same (R1)(ft) (C2)

Note: Do not award (A1)(R0). Follow through from part (c)(i).

[2 marks]

Examiners report

[N/A]

6a. [3 marks]

Markscheme

(A1)(A1)(A1)

7

Note: Award (A1) for “ ”.

Award (A1) for “ ” or “ ” (or “ ”or “ ”)

Award (A1) for “ ”.

Award at most (A1)(A1)(A0) if parentheses are missing for .

Award (A0)(A0)(A1) for .

[3 marks]

Examiners report

[N/A]

6b. [3 marks]

Markscheme

is not a multiple of 5 and ( ) is (either) a factor of 60 or ( ) is a multiple of 4, but not both (A1)

(A1)(A1)

Note: Award (A1) for “ is not a multiple of 5”, (A1) for “( ) is a factor of 60 or ( ) is a multiple of 4

but not both”, (A1) for “and” in the correct position. Accept only “but not both” in the second (A1).

Award at most (A1)(A1)(A0) for using extra statements such as “If ...then”, “if and only if” etc.

[3 marks]

Examiners report

[N/A]

6c. [3 marks]

Markscheme

8

(A1)(A1)(A1)(ft)

Note: Award (A1) for each correct column. Last column follows through from previous two.

[3 marks]

Examiners report

[N/A]

6d. [1 mark]

Markscheme

because not all the entries in the column are F (R1)(ft)

Note: If all entries in the last column of their truth table are T, award (R1)(ft) for an answer of “it is a

tautology”. Only award (R1)(ft) if the column is identified in the justification.

[1 mark]

Examiners report

[N/A]

9

6e. [1 mark]

Markscheme

accept one of: 1 OR 2 OR 3 OR 6 (A1)

Note: Award (A1) for any one of the above answers.

[1 mark]

Examiners report

[N/A]

7a. [3 marks]

Markscheme

If Sandi gets up before eight o’clock then Sandi (either) goes for a run or goes for a swim, but not both.

(A1)(A1)(A1) (C3)

Note: Award (A1) for If …… then ……, (A1) for all propositions in the correct order, (A1) for “… or …

but not both” (do not accept “either” as a replacement for “but not both”).

[3 marks]

Examiners report

[N/A]

7b. [2 marks]

Markscheme

10

(A1)(A1)(ft) (C2)

Note: Award (A1) for correct column, and (A1)(ft) for their correct column.

Follow through from their column.

[2 marks]

Examiners report

[N/A]

7c. [1 mark]

Markscheme

tautology (A1)(ft) (C1)

Note: Follow through from part (b).

[1 mark]

Examiners report

[N/A]

8a. [2 marks] 11

Markscheme

(A1)(A1)

Note: Award (A1) for either OR seen. Award (A1) for two correct terms added together.

[2 marks]

Examiners report

[N/A]

8b. [1 mark]

Markscheme

(A1)

Notes: Units not required.

[1 mark]

Examiners report

[N/A]

8c. [1 mark]

Markscheme

(A1)(ft)

Notes: Award (A1)(ft) for equating to their part (b).

Do not accept unless is explicitly defined as their part (b).

12

[1 mark]

Examiners report

[N/A]

8d. [2 marks]

Markscheme

(A1)(ft)(M1)

Note: Award (A1)(ft) for their seen.

Award (M1) for correctly substituting only into a correct part (a).

Award (A1)(ft)(M1) for rearranging part (c) to and substituting for in expression

for .

(AG)

Notes: The conclusion, , must be consistent with their working seen for the (A1)

to be awarded.

Accept as equivalent to .

[2 marks]

Examiners report

[N/A]

8e. [3 marks] 13

Markscheme

(A1)(A1)(A1)

Note: Award (A1) for , (A1) for or , (A1) for .

[3 marks]

Examiners report

[N/A]

8f. [3 marks]

Markscheme

(M1)

Note: Award (M1) for equating their part (e) to zero.

OR (M1)

Note: Award (M1) for isolating .

OR

sketch of derivative function (M1)

with its zero indicated (M1)

(A1)(ft)(G2)

14

[3 marks]

Examiners report

[N/A]

8g. [2 marks]

Markscheme

(M1)

Note: Award (M1) for correct substitution of their part (f) into the given equation.

(A1)(ft)(G2)

[2 marks]

Examiners report

[N/A]

8h. [3 marks]

Markscheme

(M1)

Note: Award (M1) for dividing their part (g) by 2000.

(A1)(ft)

Notes: Follow through from part (g).

15

14 (cans) (A1)(ft)(G3)

Notes: Final (A1) awarded for rounding up their to the next integer.

[3 marks]

Examiners report

[N/A]

9a. [3 marks]

Markscheme

if the teacher is absent then the lesson is cancelled and the students are in the library (A1)(A1)(A1)

(C3)

Note: Award (A1) for If…then.

For Spanish candidates, only accept “Si” and “entonces”.

For French candidates, only accept “Si” and “alors”.

For all three languages these words are from the subject guide.

Award (A1) for “and”,

Award (A1) for correct propositions in correct order.

Examiners report

Question 4: Logic.

All candidates recognized that to fill in a truth table the answer is either true or false. However, given

that there are truth tables in the formula booklet it was surprising that some candidates made mistakes

when negating a given column of the truth table. Most candidates recognized that in a tautology the

column is always true with a small minority confusing tautology and contradiction. Candidates were

able to write a compound proposition in words.

9b. [2 marks]

Markscheme

16

(A1)(A1)(ft) (C2)

Note: Award (A1) for column correct and (A1) for column correct.

Award (A0)(A1)(ft) for a column that correctly follows from an incorrect column.

Examiners report

Question 4: Logic.






9c. [1 mark]

Markscheme

not all of the entries are true (or equivalent) (R1) (C1)

Note: Accept “One entry is false”.

Examiners report

Question 4: Logic.






10a. [4 marks]

17

Markscheme

(A1)(A1)(ft)(A1)(ft)(A1) (C4)

Notes: Award (A1) for each correct column.

For the “ ” follow through from the “ ” column.

For the “ ” column, follow through from the preceding column.

Examiners report

[N/A]

10b. [2 marks]

Markscheme

tautology (A1)(ft)

columns and are identical (R1)(C2)

Notes: Do not award (R0)(A1)(ft). Follow through from their table in part (a).

Award the (R1) for an additional column representing that is

consistent with their table.

18

Examiners report

[N/A]

11a. [3 marks]

Markscheme

(A1)(A1)(A1)

Notes: Award (A1) for conjunction seen, award (A1) for implication seen, award (A1) for correct

simple propositions in correct order (the parentheses are required). Accept .

Examiners report

Forming the statement in part (a) was attainable by the great majority, although the lack of parentheses

was a common fault.

11b. [2 marks]

Markscheme

(A1)(ft)(A1)(ft)

Notes: Award (A1)(ft) for each correct column, follow through to the final column from their

column. For the second (A1)(ft) to be awarded there must be an implication in part (a).

Follow through from part (a).

Examiners report

The truth table in part (b) saw less success and it was clear that some centres simply had not prepared

their candidates in this area of the course.

19

11c. [2 marks]

Markscheme

The argument is not valid since not all entries in the final column are T. (A1)(ft)(R1)

Notes: Do not award (A1)(ft)(R0). Follow through from part (b).

Accept “The argument is not valid since is not a tautology”.

Examiners report

Where the truth table was correctly constructed many candidates were not aware of the conditions

required for an argument to be valid and in part (d) the converse and the inverse were often confused.

11d. [4 marks]

Markscheme

(i) (A1)(ft)(A1)(ft)

OR

(A1)(ft)(A1)(ft)

Notes: Award (A1)(ft) for the negation of their antecedent and the negation of their consequent, (A1)

(ft) for their fully correct answer.

Follow through from part (a). Accept or . Follow through from part

(a).

(ii) if it is not the case that the land has been purchased and the building permit has been obtained

then the land can not be used for residential purposes. (A1)(A1)(ft)

OR

20

if (either) the land has not been purchased or the building permit has not been obtained then the land

can not be used for residential purposes. (A1)(A1)(ft)

Notes: Award (A1) for “if… then…” seen, (A1)(ft) for correct statements in correct order. Follow

through from part (d)(i).

Examiners report

Where the truth table was correctly constructed many candidates were not aware of the conditions

required for an argument to be valid and in part (d) the converse and the inverse were often confused.

12a. [2 marks]

Markscheme

If I do not break my arm, then it will not hurt (A1)(A1) (C2)

Note: Award (A1) for “if… then…”

For Spanish candidates, only accept “Si” and “entonces”.

Award (A1) for “not break my arm” and “not hurt” in correct order.

Examiners report

[N/A]

12b. [2 marks]

Markscheme

(A1)(A1) (C2)


Examiners report

[N/A]

21

12c. [2 marks]

Markscheme

logically equivalent (A1)(ft)

last two columns of the truth table are identical (R1)(ft) (C2)

Notes: Do not award (A1)(ft)(R0).

Follow through from the last two columns of the table in part (a).

Examiners report

[N/A]

13a. [3 marks]

Markscheme

If the food is well cooked and the drinks are chilled then dinner is not spoilt. (A1)(A1)(A1) (C3)

Note: Award (A1) for “If…then” (then must be seen), (A1) for the two correct propositions connected

with “and”, (A1) for “not spoilt”.

Only award the final (A1) if correct statements are given in the correct order.

[3 marks]

Examiners report

[N/A]

13b. [3 marks]

Markscheme

22

(A1)(A1)(A1)(ft) (C3)


The final column must follow through from the previous two columns.

[3 marks]

Examiners report

[N/A]

14a. [2 marks]

Markscheme

If I do not have a bowl of soup then I have an ice cream. (A1)(A1) (C2)

Notes: Award (A1) for If… then…

Award (A1) for correct statements in correct order.

[2 marks]

Examiners report23

Most candidates were able to write the compound proposition in words, however many were not able

to write the converse in symbolic form. While they were able to fill in the third column of the truth

table, many were unable to complete the fourth column correctly.

14b. [2 marks]

Markscheme

(A1)(A1)(ft) (C2)

Note: Follow through from third column to fourth column.

[2 marks]

Examiners report




14c. [2 marks]

Markscheme

(A1)(A1) (C2)

Notes: Award (A1) for .

Award (A1) for and in correct order.

Accept .

24

[2 marks]

Examiners report




15a. [2 marks]

Markscheme

(A1) for third column and (A1)(ft) for fourth column (A1)(A1)(ft) (C2)

Examiners report

This was provocative in the G2 and the comments indicate that candidates found the wording

confusing. Candidates were able to write in words the compound proposition and following

from their truth table the candidates could state if this was true or false.

15b. [2 marks]

Markscheme

is greater than or equal to (not less than) 10 or is greater than 100. (A1)(A1) (C2)

Note: Award (A1) for “greater than or equal to (not less than) 10”, (A1) for “or is greater than 100”.

Examiners report



25

from their truth table the candidates could state if this was true or false. In part (c) many candidates

either stated the correct answer “true” or stated an answer consistent with their truth table and

received follow-through marks. Candidates had difficulty writing down a value of for which is

false.

15c. [1 mark]

Markscheme

True (A1)(ft) (C1)

Note: Follow through from their answer to part (a).

Examiners report



from their truth table the candidates could state if this was true or false. In part (c) many candidates

either stated the correct answer “true” or stated an answer consistent with their truth table and

received follow-through marks. Candidates had difficulty writing down a value of for which \(\neg

p \vee q\]) is false.

15d. [1 mark]

Markscheme

Any value of such that . (A1)(ft) (C1)

Note: Follow through from their answer to part (a).

Examiners report



from their truth table the candidates could state if this was true or false.

16a. [2 marks]

Markscheme

(A1)(A1) (C2)

26

Note: Award (A1) for any 2 correct symbols seen in a statement, (A1) for all 3 correct symbols in

correct order.

Examiners report

[N/A]

16b. [3 marks]

Markscheme

(A1)(A1)(ft)(A1)(ft) (C3)

Note: Award (A1) for each correct column. 4th column is follow through from 3rd, 5th column is follow

through from 4th.

Examiners report

[N/A]

16c. [1 mark]

Markscheme

Not all of last column is F (R1)(ft) (C1)

Note: Award (R1)(ft) if final column does not lead to a contradiction.

Examiners report

27

[N/A]

17a. [2 marks]

Markscheme

(A1)(A1)(ft) (C2)

Notes: Award (A1) for each correct column. Follow through in 4th column from their 3rd column.

[2 marks]

Examiners report

This question was well answered by most of the candidates who could complete the truth table, write

the proposition in symbolic form and write the given proposition in words, although the 'If ' was

sometimes omitted. Where marks were lost on Question 2, it was generally in the second column of the

truth table.

17b. [2 marks]

Markscheme

(A1)(A1) (C2)

Note: Award (A1) for and p in any order, (A1) for .

[2 marks]

Examiners report




truth table.

28

17c. [2 marks]

Markscheme

If I can swim 50 metres (then) I do not take swimming lessons. (A1)(A1) (C2)

Note: Award (A1) for If… (then), (A1) for correct propositions in the correct order.

[2 marks]

Examiners report




truth table.

18a. [4 marks]

Markscheme

(A1)(A1)(A1)(ft)(A1)(ft)

(C4)


Award first (A1)(ft) from their third column in the table.

Award second (A1)(ft) from their fourth and fifth column in the table.

[4 marks]

Examiners report

Weaker candidates had some difficulty here with the majority scoring less than 2 marks on this

question. The more confident candidates were able to score well with most marks being lost only on

29

completing the truth table for . As a consequence, the final column entries of the table were

often incorrect but earned the (A1)(ft) mark. Many candidates went on to correctly identify the correct

(ft) response to (b)(i) and were able to support their answer with a correct reason.

18b. [1 mark]

Markscheme

Tautology (A1)(ft) (C1)

Note: Answer must be consistent with last column in table.

[1 mark]

Examiners report






18c. [1 mark]

Markscheme

All entries (in the final column) are true. (R1)(ft) (C1)

Note: Answer must be consistent with their answer to part (b)(i).

Note: Special case (A1)(R0) may be awarded.

[1 mark]

Examiners report






19a. [3 marks] 30

Markscheme

If I do not choose history then I choose either psychology or I choose art (A1)(A1)(A1) (C3)

Notes: Award (A1) for ‘if… (then)…’

Award (A1) for ‘not choose history.’

Award (A1) for ‘choose (either) psychology or art (or both).’

If the order of the statements is wrong award at most (A1)(A1)(A0).

[3 marks]

Examiners report

Many correct answers were seen in part (a) with only a minority of candidates misinterpreting the

symbol as 'and'. Some candidates left out the word 'if' and consequently lost the first mark.

19b. [1 mark]

Markscheme

(A1) (C1)

[1 mark]

Examiners report

Part (b) was not done as well as expected indicating that some work needs to be done by centres on the

truth table for the logic symbol .

31

19c. [2 marks]

Markscheme

Neither, because not all the entries in the last column are the same. (A1)(ft)(R1) (C2)

Notes: Do not award (R0)(A1). Follow through from their answer to part (b). Reasoning must be

consistent with their answer to part (b).

[2 marks]

Examiners report

Many correct answers of 'neither' were seen in part (c) but the justification was sometimes lacking

definitive reasoning. Without sufficient reasoning, the answer mark was not awarded.

20a. [2 marks]

Markscheme

(A1)(A1) (C2)

Note: Award (A1) for ¬q , (A1) for last column.

[2 marks]

Examiners report

This question was well answered with most candidates able to complete the truth table correctly in

part a) and write the correct compound proposition in symbolic form in part b). A significant number of

candidates could not write the correct contrapositive, although most were awarded one mark for

writing an implication.

32

20b. [2 marks]

Markscheme

(A1)(A1) (C2)

Note: Award (A1) for , (A1) for p and q in the correct order.

[2 marks]

Examiners report





20c. [2 marks]

Markscheme

If Cristina does not do well on the logic test then she does not understand logic. (A1)(A1) (C2)

Note: Award (A1) for If…(then), must be an implication, (A1) for the correct propositions in the correct

order.

[2 marks]

Examiners report





21a. [4 marks]

Markscheme

33

(A1)(A1)(ft)(A1)

(A1)(ft) (C4)

Note: Award (A1) for each correct column (second column (ft) from first, fourth (ft) from third).

Follow through from second column to fourth column for a consistent mistake in implication.

[4 marks]

Examiners report

The truth table was well done by the majority of candidates but significantly fewer could give the

correct reason for whether the compound proposition was a tautology, so many lost 2 marks in this

part of the question.

21b. [2 marks]

Markscheme

Since second and fourth columns are not identical (R1)(ft)

Not a tautology (A1)(ft) (C2)

Note: (R0)(A1) may not be awarded.

[2 marks]

Examiners report

The truth table was well done by the majority of candidates but significantly fewer could give the

correct reason for whether the compound proposition was a tautology, so many lost 2 marks in this

part of the question.

22a. [3 marks]

34

Markscheme

(A1)(A1)(ft)(A1)(ft) (C3)


[3 marks]

Examiners report

The truth table was very well answered and where the table was incorrect a follow through mark could

be given for part (b) for a correct answer resulting from their final column. Some candidates appeared

unsure of the concept of a tautology.

22b. [1 mark]

Markscheme

tautology (A1)(ft) (C1)

Note: Follow through from their last column.

[1 mark]

Examiners report

The truth table was very well answered and where the table was incorrect a follow through mark could

be given for part (b) for a correct answer resulting from their final column. Some candidates appeared

unsure of the concept of a tautology.

22c. [2 marks]

35

Markscheme

(A1)(A1) (C2)

Note: Award (A1) for and p in correct order, (A1) for sign.

[2 marks]

Examiners report

Nearly all candidates could write the proposition in part (c) in symbolic form.

23a. [3 marks]

Markscheme

(A1)(A1)(A1)

Note: Award (A1) for each correct number in the correct position.

[3 marks]

Examiners report

This part was successfully attempted by the great majority. The less familiar form of the Venn diagram

seemed not to cause too many problems, although a common mistake was the failure to add the 20 in

set A in part (b). A surprising number seemed unfamiliar with set notation in (d) and thus were not

able to attempt this part.

23b. [1 mark]

Markscheme36

28 (A1)(ft)

Note: 20 + their 8.

[1 mark]

Examiners report





23c. [1 mark]

Markscheme

59 (A1)(ft)

[1 mark]

Examiners report





23d. [2 marks]

Markscheme

10 + 12 + 20 + 6 (M1)

Note: Award (M1) for use of the correct regions.

= 48 (A1)(ft)(G2)

OR

37

59 − 8 − 3 (M1)

= 48 (A1)(ft)

[2 marks]

Examiners report





23e. [2 marks]

Markscheme

(A1)(A1)

Note: Award (A1) for , (A1) for both statements in the correct order.

[2 marks]

Examiners report

The work on logic also proved accessible to the great majority with a large number of candidates

attaining full marks. The most common errors were the omission of the “If” in the conditional statement

in (b) and the inability to follow the implication in the truth table in (c).

23f. [3 marks]

Markscheme

If it is not snowing and the roads are open (then) we will go skiing. (A1)(A1)(A1)

Note: Award (A1) for “if…(then)”, (A1) for “not snowing and the roads are open”, (A1) for “we will go

skiing”.

[3 marks]38

Examiners report




23g. [3 marks]

Markscheme

(A1)(A1)(ft)(A1)(ft)


[3 marks]

Examiners report




24a. [2 marks]

Markscheme

39

If the sun is shining then I will go swimming. (A1)(A1) (C2)

Note: Award (A1) for “if…then” and (A1) for correct order.

[2 marks]

Examiners report

The most common error was poor use of the “If...then” connective.

24b. [2 marks]

Markscheme

Either the sun is not shining or I will go swimming. (A1)(A1) (C2)

Note: Award (A1) for both correct statements and (A1) for “either” “…or”.

[2 marks]

Examiners report

Confusion between “and” and “or” was rare, however, the use of implication in this part was a little too

common.

24c. [1 mark]

Markscheme

(A1) (C1)

[1 mark]

Examiners report

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Precise, correct terminology was expected in this part.

24d. [1 mark]

Markscheme

They are (logically) equivalent. (A1) (C1)

Note: Do not accept any other answers.

[1 mark]

Examiners report

[N/A]

25a. [2 marks]

Markscheme

(A1)(A1)(ft) (C2)

Note: (A1) for each correct column.

[2 marks]

Examiners report

(a) was generally answered well.

25b. [2 marks]

Markscheme

It is not true that food or drinks may be taken into the cinema.

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Note: (A1) for “it is not true”. (A1) for “food or drinks”.

OR

Neither food nor drinks may be taken into the cinema.

Note: (A1) for “neither”. (A1) for “nor”.

OR

No food and no drinks may be taken into the cinema.

Note: (A1) for “no food”, “no drinks”. (A1) for “and”.

OR

No food or drink may be brought into the cinema. (A2) (C2)

Note: (A1) for “no”, (A1) for “food or drink”. Do not penalize for use of plural/singular.

Note: the following answers are incorrect:

No food and drink may be brought into the cinema. Award (A1) (A0)

Food and drink may not be brought into the cinema. Award (A1) (A0)

No food or no drink may be brought into the cinema. Award (A1) (A0)

[2 marks]

Examiners report

(b) lack of precision in language led to many errors.

25c. [2 marks]

Markscheme

Note: (A1) for both negations, (A1) for conjunction.

OR

(A1)(A1) (C2)

Note: (A1) for negation, (A1) for in parentheses.

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[2 marks]

Examiners report

(a) was generally answered well.

(b) lack of precision in language led to many errors.

26a. [2 marks]

Markscheme

Either Sean is at school or Sean is playing a game on his computer but not both. (A1)(A1) (C2)

Note: (A1) for ‘either ... or but not both’ (A1) for correct statements. ‘Either’ can be omitted.

[2 marks]

Examiners report

The common error in part (a) was not to include “but not both” and for (b), to give the inverse rather

than the converse. The first column in the table (not ) was well done but a number of candidates

answered the implication incorrectly.

26b. [2 marks]

Markscheme

If Sean is not playing a game on his computer then Sean is at school. (A1)(A1) (C2)

Note: (A1) for ‘If ... then’ (A1) for correct propositions in the correct order.

[2 marks]

Examiners report




26c. [2 marks]

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Markscheme

(A1)(A1)(ft) (C2)

Note: (A1) for each correct column.

[2 marks]

Examiners report




27a. [4 marks]

Markscheme

(i)

(A3)

Note: Award (A1) for column correct, (A1)(ft) for column correct, (A1) for last column

correct.

(ii) Yes. (R1)(ft) (C4)

Note: (ft) from their second and the last columns. Must be correct from their table.

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[4 marks]

Examiners report

This question was well answered by many of the candidates. It is an area of the syllabus that is well

taught and many managed to get a follow through mark even though one of the columns in the table

might have been incorrect.

27b. [2 marks]

Markscheme

. (A1)(A1) (C2)

Note: Award (A1) for , (A1) for . Accept or .

[2 marks]

Examiners report

This question was well answered by many of the candidates. It is an area of the syllabus that is well

taught and many managed to get a follow through mark even though one of the columns in the table

might have been incorrect.

28a. [2 marks]

Markscheme

(A2)

(A1) for

(A1) for

(A1)(A0) if brackets are missing.

OR

(A2)

(A1) for both brackets correct, (A1) for disjunctive “or” (A1)(A0) if brackets are missing. (C2)

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[2 marks]

Examiners report

(a) This caused problems for many candidates. They seem to expect to include the implication symbol

somewhere.

28b. [2 marks]

Markscheme

If you choose a salad then you do not choose a dessert. (A2)

(A1) for “if …then…” (A1) for salad and no dessert in the correct order.

OR

If you choose a salad you do not choose a dessert. (A2) (C2)

[2 marks]

Examiners report

(b) Most candidates managed to write this correctly.

28c. [2 marks]

Markscheme

(A1) for each correct column (A1)(A1)(ft) (C2)

[2 marks]

Examiners report

(c) Not all candidates could complete the truth table correctly. Many managed the first column but then

made mistakes in the last column.

29a. [1 mark]

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Markscheme

Both are 'p or q', the first is 'but not both' (A1)

Note: Award mark for clear understanding if wording is poor. (C1)

[1 mark]

Examiners report

a) The majority of candidates were able to explain the difference between inclusive and exclusive

correctly but many used “and” and “or” to distinguish between the two.

29b. [4 marks]

Markscheme

(A1)(A1)(ft)(A1)(A1)

Note: Follow through is for final column. (C4)

[4 marks]

Examiners report

b) Less than half were able to find the truth value of the two disjunctions in the table correctly. Most

candidates did gain some marks but a number of them left at least one cell blank even though it was a

50% chance of getting the correct value.

29c. [1 mark]

Markscheme

Tautology. (A1)(ft) (C1)

[1 mark]

Examiners report

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c) Most candidates answered this part correctly with many receiving follow through for “neither” from

an incorrect table.

30a. [3 marks]

Markscheme

If Alex does not play the flute then he is either a scientist or from Uruguay. (A1)(A1)(A1) (C3)

Note: Award (A1) if… then, correct (A1) antecedent, (A1) correct consequent.

Examiners report

[N/A]

30b. [2 marks]

Markscheme

(A1)(A1) (C2)

Examiners report

[N/A]

30c. [1 mark]

Markscheme

48

Not all entries in the final column are T. (R1) (C1)

Examiners report

[N/A]

Printed for International School of Europe

© International Baccalaureate Organization 2019

International Baccalaureate® - Baccalauréat International® - Bachillerato Internacional®

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