Mathematics (Project Maths – Phase 3)
2012. M327 S
Coimisi?n na Scr?duithe St?it State Examinations Commission
Leaving Certificate Examination, 2012 Sample Paper
Mathematics (Project Maths ? Phase 3)
Paper 1 Ordinary Level Time: 2 hours, 30 minutes
300 marks
Examination number Centre stamp
Running total
For examiner
Question
Mark
1
2
3
4
5
6
7
8
9
Total
Grade
Instructions
There are two sections in this examination paper:
Section A
Concepts and Skills
Section B
Contexts and Applications
150 marks 150 marks
6 questions 3 questions
Answer all nine questions.
Write your answers in the spaces provided in this booklet. 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 booklet of Formulae and Tables. You must return it at the end of the examination. You are not allowed to bring your own copy into the examination.
Marks will be lost 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.
Write the make and model of your calculator(s) here:
Leaving Certificate 2012 ? Sample Paper
Page 2 of 19
Project Maths, Phase 3 Paper1 ? Ordinary Level
Section A
Concepts and Skills
Answer all six questions from this section.
Question 1
1
(a) Write 6-2 and 812 without using indices.
6-2 =
1
812 =
150 marks
(25 marks)
(b) Express 224 in the form a ?10n , where 1 a < 10 and n , correct to three significant figures.
(a )a 3
(c) Show that a4 simplifies to a .
(d) Solve the equation 49x = 72+x and verify your answer.
Leaving Certificate 2012 ? Sample Paper
Page 3 of 19
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Project Maths, Phase 3 Paper1 ? Ordinary Level
Question 2
(25 marks)
(a) A sum of 5000 is invested in an eight-year government bond with an annual equivalent rate (AER) of 6%. Find the value of the investment when it matures in eight years' time.
(b) A different investment bond gives 20% interest after 8 years. Calculate the AER for this bond.
Leaving Certificate 2012 ? Sample Paper
Page 4 of 19
Project Maths, Phase 3 Paper1 ? Ordinary Level
Question 3 Two complex numbers are u = 3 + 2i and v = -1+ i , where i2 = -1 .
(a) Given that w = u - v - 2 , evaluate w.
(25 marks)
(b) Plot u, v, and w on the Argand diagram below. 4 Im(z)
3
2
1
-4 -3 -2 -1 -1
Re(z) 1234
-2
-3
-4
(c) Find 2u + v . w
Leaving Certificate 2012 ? Sample Paper
Page 5 of 19
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Project Maths, Phase 3 Paper1 ? Ordinary Level
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