Draw a Venn diagram to represent this information. Label A the set that represents The Art Journal readers, B the set that represents The Beartown News readers, and C the set that represents The Currier readers.

Find the percentage of the population that does not read any of the three newspapers.

Find the percentage of the population that reads exactly one newspaper.

Find the percentage of the population that reads The Art Journal or The Beartown News but not The Currier.

A local radio station states that 83 % of the population reads either The Beartown News or The Currier.

Use your Venn diagram to decide whether the statement is true. Justify your answer.

The population of Beartown is 120 000. The local radio station claimed that 34 000 of the town’s citizens read at least two of the local newspapers.

Find the percentage error in this claim.

(A1) for three circles and a rectangle (U need not be seen)

(A1) for 5

(A1) for 3, 8 and 12

(A1) for 16, 26 and 29 OR 32, 46, 54 placed outside the circles.     (A4)

Note: Accept answers given as decimals or fractions.

[4 marks]

100 – (16 + 26 + 29) – (8 + 5 + 3 + 12)     (M1)

100 – 71 – 28

Note: Award (M1) for correct expression. Accept equivalent expressions, for example 100 – 71 – 28 or 100 – (71 + 28).

= 1     (A1)(ft)(G2)

Note: Follow through from their Venn diagram but only if working is seen.

[2 marks]

16 + 26 + 29     (M1)

Note: Award (M1) for 16, 26, 29 seen.

= 71     (A1)(ft)(G2)

Note: Follow through from their Venn diagram but only if working is seen.

[2 marks]

16 + 3 + 26     (M1)

Note: Award (M1) for their 16, 3, 26 seen.

= 45     (A1)(ft)(G2)

Note: Follow through from their Venn diagram but only if working is seen.

[2 marks]

True     (A1)(ft)

100 – (1 –16) = 83     (R1)(ft)

OR

46 + 54 – 17 = 83     (R1)(ft)

Note: Do not award (A1)(R0). Follow through from their Venn diagram.

[2 marks]

28% of 120000     (M1)

= 33600     (A1)

\({\text{%  error}} = \frac{{(34000 - 33600)}}{{33600}} \times 100\)     (M1)

Note: Award (M1) for 28 seen (may be implied by 33600 seen), award (M1) for correct substitution of their 33600 in the percentage error formula. If an error is made in calculating 33600 award a maximum of (M1)(A0)(M1)(A0), the final accuracy mark is lost.

OR

\(\frac{{34000}}{{120000}} \times 100\)     (M1)

= 28.3(28.3333…)     (A1)

\({\text{%  error}} = \frac{{(28.3333... - 28)}}{{28}} \times 100\)     (M1)

= 1.19% (1.19047...)     (A1)(ft)(G3)

Note: % sign not required. Accept 1.07 (1.0714…) with use of 28.3. 1.18 with use of 28.33 and 1.19 with use of 28.333. Award (G3) for 1.07, 1.18 or 1.19 seen without working.

[4 marks]

This question was accessible to the great majority of candidates. The common errors were:

• the lack of a bounding rectangle in (a);
• the lack of subtraction for the entries in the disjoint regions of the type \(A' \cap B' \cap C\) and the subsequent total exceeding 100%;
• the incorrect interpretation of “either ...or” as “exclusive or”. It is of the utmost importance to note that the ambiguity of the “or” statement will be removed and “exclusive or” signalled by the phrase “either ...or....but not both”. Otherwise, “inclusive or” must always be assumed.

A number of candidates were unable to interpret the percentage error question correctly and scored 0/4. This was somewhat disappointing.

This question was accessible to the great majority of candidates. The common errors were:

• the lack of a bounding rectangle in (a);
• the lack of subtraction for the entries in the disjoint regions of the type \(A' \cap B' \cap C\) and the subsequent total exceeding 100%;
• the incorrect interpretation of “either ...or” as “exclusive or”. It is of the utmost importance to note that the ambiguity of the “or” statement will be removed and “exclusive or” signalled by the phrase “either ...or....but not both”. Otherwise, “inclusive or” must always be assumed.

A number of candidates were unable to interpret the percentage error question correctly and scored 0/4. This was somewhat disappointing.

This question was accessible to the great majority of candidates. The common errors were:

• the lack of a bounding rectangle in (a);
• the lack of subtraction for the entries in the disjoint regions of the type \(A' \cap B' \cap C\) and the subsequent total exceeding 100%;
• the incorrect interpretation of “either ...or” as “exclusive or”. It is of the utmost importance to note that the ambiguity of the “or” statement will be removed and“exclusive or” signalled by the phrase “either ...or....but not both”. Otherwise, “inclusive or” must always be assumed.

A number of candidates were unable to interpret the percentage error question correctly and scored 0/4. This was somewhat disappointing.

This question was accessible to the great majority of candidates. The common errors were:

• the lack of a bounding rectangle in (a);
• the lack of subtraction for the entries in the disjoint regions of the type \(A' \cap B' \cap C\) and the subsequent total exceeding 100%;
• the incorrect interpretation of “either ...or” as “exclusive or”. It is of the utmost importance to note that the ambiguity of the “or” statement will be removed and “exclusive or” signalled by the phrase “either ...or....but not both”. Otherwise, “inclusive or” must always be assumed.

A number of candidates were unable to interpret the percentage error question correctly and scored 0/4. This was somewhat disappointing.

This question was accessible to the great majority of candidates. The common errors were:

• the lack of a bounding rectangle in (a);
• the lack of subtraction for the entries in the disjoint regions of the type \(A' \cap B' \cap C\) and the subsequent total exceeding 100%;
• the incorrect interpretation of “either ...or” as “exclusive or”. It is of the utmost importance to note that the ambiguity of the “or” statement will be removed and “exclusive or” signalled by the phrase “either ...or....but not both”. Otherwise, “inclusive or” must always be assumed.

A number of candidates were unable to interpret the percentage error question correctly and scored 0/4. This was somewhat disappointing.

This question was accessible to the great majority of candidates. The common errors were:

• the lack of a bounding rectangle in (a);
• the lack of subtraction for the entries in the disjoint regions of the type \(A' \cap B' \cap C\) and the subsequent total exceeding 100%;
• the incorrect interpretation of “either ...or” as “exclusive or”. It is of the utmost importance to note that the ambiguity of the “or” statement will be removed and“exclusive or” signalled by the phrase “either ...or....but not both”. Otherwise, “inclusive or” must always be assumed.

A number of candidates were unable to interpret the percentage error question correctly and scored 0/4. This was somewhat disappointing.