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Numeracy Intermediate November 2017 Unit 2 Q2

WJECIntermediateCurrent spec8 marksSets

2. 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 circles Mandarin, Spanish, German and French inside a universal set; region values 7, 22, 2, 8, 0, 5, 3, 27, 14, 7, 1 and 0 outside the circles
(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) Which was the most popular language selected?
You must show all your working. [3]
(e) 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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