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Numeracy Foundation November 2017 Unit 2 Q5

WJECFoundationCurrent spec5 marksSets

5. The Headteacher of Ysgol Maes Newydd gave option forms to all Year 9 pupils.

The form asked which foreign languages the pupils would like to study in Year 10.

There were 4 languages listed on the form: French, German, Spanish and Mandarin.
The pupils could select as many of the languages as they wished.
All pupils completed and returned the option form.

The Headteacher displayed the results in a Venn diagram, as shown below.

Venn diagram with universal set and four circles: Mandarin, Spanish, German, French. Mandarin only 7, Spanish only 2, German only 14, French only 1; Mandarin and Spanish only 22; Mandarin and German only 8; Mandarin and French only 5; Spanish and French only 27; German and French only 7; Mandarin, Spanish and French 0; Mandarin, German and French 3; outside all circles 0
(a) How many pupils did not select at least one of the four languages?
Circle your answer. [1]

0    1    3    5    7

(b) How many pupils are there in Year 9?
Circle your answer. [1]

92    94    96    98    100

(c) How many pupils selected only one language? [1]
(d) The Headteacher can offer only 2 out of these 4 languages in Year 10.
She writes the timetable so that as many as possible of the pupils who chose 2 languages are able to study those 2 languages.
Which two languages will the Headteacher offer in Year 10?
You must show all your working and give a reason for your answer. [2]
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