国外数学试卷21

2014. S234

Coimisiún na Scrúduithe Stáit

State Examinations Commission

Junior Certificate Examination 2014

Mathematics

(Project Maths – Phase 2)

Paper 1

Higher Level

Friday 6 June – Afternoon, 2:00 to 4:30

300 marks

For examiner

Question Mark Question Mark

1 11

2 12

3 13

4 14

5

6

7

8

9

10 Total

Instructions

There are 14 questions on this examination paper. Answer all questions.

Questions do not necessarily carry equal marks. To help you manage your time during this examination, a maximum time for each question is suggested. If you remain within these times you should have about 10 minutes left to review your work.

Question 14 carries a total of 50 marks.

Write your answers in the spaces provided in this booklet. You may lose marks if you do not do so. There is space for extra work at the back of the booklet. You may also ask the superintendent for more paper. Label any extra work clearly with the question number and part.

The superintendent will give you a copy of the Formulae and Tables booklet. You must return it at the end of the examination. You are not allowed to bring your own copy into the examination.

You will lose marks if all necessary work is not clearly shown.

Answers should include the appropriate units of measurement, where relevant.

Answers should be given in simplest form, where relevant.

(a) Place the following numbers in order, starting with the smallest:

3

2

1·4

(b) Which one of the following is not a rational number? Explain your answer.

13

7

3·142

227

π

(c) (i)

Find the values of 241

,13

n + where {}17, 19, 21.n ∈

(ii) State which one of your answers is a natural number, and explain your choice.

Page running

(a) John He sa He a (i)

(ii)

(b) The S

the e value

Expl

n thinks that ays that if h lso says tha Complete

Give two r Swiss math expression es of n less ain why it d he has a m he uses the f at these form the table.

p 0 1 2 3 4 5

reasons why hematician a 2

41n n −+ than 41.

does not giv ethod for fi formulas in mulas will g 6p +1y his metho and physicis gives a prim ve a prime n

nding all pr the table be generate onl + 1

od is not full st, Euler, fir me number number for rime numbe elow, he wi ly the prime 6p +5ly correct.

rst noticed (for all posi 41.n = ers. ll generate t e numbers. + 5 5

(in 1772) tha itive integer the prime n at r numbers.