Mock Exam Paper D P1 (Project Maths) Higher Level
Pre-Leaving Cert Examination 2014
(Projects Maths – Phase 3)
For Examiners use only
There are two sections in this examination paper:
Section A Concept and skills 150 marks 6 questions
Section B Contexts and Applications 150 marks 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 paper clearly with the question number and part.
The superintendent will give you a copy of the booklet of Formulae and Tables. You must return is at the end of the examination. You are not allowed to bring your won 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 mark and model of your calculator(s) here:
Section A Concepts and Skills 125 marks
Answer all four questions from this section.
Question 1 25 marks
(a) Sketch the region which satisfies
(b) Given that express the following in terms of k
(i) Find the values of m and c where , and
(ii) Find a value for such that
(d) If, for all x, , find the value of c.
Question 2 25 marks
(a) The complex number z has modulus 4 and argument
The complex number w has modulus 2 and argument
(i) Express z and w in the form , where a and b are integers or surds.
(ii) Mark on an Argand diagram the complex numbers z and w.
(b) Use De Moivre’s Theorem to prove that
Question 3 25 marks
(a) Prove that for all and
(b) Given that and that a and b are positive integers, find the value of a and b.
(c) Using a geometric series express in the form , where
Question 4 25 marks
(a) Using mathematical inductio...