RAFFLES INSTITUTION

GIFTED EDUCATION PROGRAMME

ADDITIONAL MATHEMATICS

 

 

ASSIGNMENT 3 

      

  1.        18 persons are employed by a company. 11 of them can do shorthand typing and 12 of them can use the word processor.

            (a)        If every person has at least one of these skills, how many persons have all the skills?

(b)               If  persons have none of the skills, find the greatest possible value of .

 

 

  2.        A number of travellers were interviewed about the transport they used on a particular day. Each of them used once or more of the modes of transport shown in the Venn diagram. Of those interviewed, 6 said that they travelled by bus and MRT only, 2 by MRT and taxi only and 7 by bus, MRT and taxi only.

(a)               Given that 35 people used buses and 25 people used MRT, find

(i)                 the value of ,

(ii)               the number of people who travelled by MRT only,

(iii)             the number of people who travelled by at least two modes of transport.

(b)               Given also that 85 people were interviewed altogether, calculate the number of people who travelled by taxi only.

 

 

  3.        In a community club, a group of 40 women takes part in at least one of the three activities: Cooking, Singing and Dancing. Of the 25 women who choose Cooking, 8 also choose Singing and Dancing, 3 choose Cooking only, 6 choose Dancing but not Singing.

            Of the 15 women who do not choose Cooking,  choose both Singing and Dancing,  choose only Dancing, 5 choose only Singing.

(a)               Draw a Venn diagram to illustrate this information.

(b)               Find the value of .

(c)                How many women choose Cooking and Singing but not Dancing?

 

 

 

  4.        In a school, some of the subjects that are possible to take are Mathematics, Additional Mathematics and Physics. The Venn diagram shows the combinations of these subjects that are possible and the numbers and letters represent the numbers of students in each subset.

 

 

 

 

 

 

(a)               Given that the number of students taking Physics is 123, calculate the value of .

(b)               Given that one-sixth of those taking Mathematics also take Additional Mathematics, calculate the value of and hence find the total number of students taking Mathematics.

 

 

  5.        By drawing a Venn diagram, or otherwise, answer the following questions:

(a)               Given that ,  and , find the least possible value of .

(b)               In a group of 60 people, 33 can speak Spanish and 36 can speak French. Find the greatest possible number of people who can speak Spanish, but not French.