# Mock Exam Paper D P2 (Project Maths) Higher Level Marking Scheme

Leaving Cert Examination 2014

**Mathematics**

**(Projects Maths – Phase 3)**

Paper II

Ordinary Level

Time hours

300 marks

**Model Solutions – Paper II**

Note the model solutions for each question are not intended to be exhaustive – there may be other correct solutions.

**Instructions**

There are **two **sections in this examination paper.

Section A Concepts and Skills 150 Marks 6 questions

Section B Contexts and Applications 150 Marks 3 questions

Answer **all eight **questions as follows:

In Section A, answer Questions 1 to 5 and

**either** Question 6A **OR ** Question 6B

In Section B, answer Questions 7 to 9.

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 appropriate units of measurement, where relevant.

Answers should be given in simplest form, where relevant.

**Section A Concepts and Skills 150 Marks **

** **

**Question 1 25 Marks**

(a) (i) Find the equations of the two lines through the point whose perpendicular distance

from the origin is 2.

Line containing

distance from to is 2

or

and

(ii) Find the area of the triangle bounded by these two lines and the *y*-axis.

Area

(b) Let *a* and *b* be the points and respectively, and let *p* be any point on the line .

Show that the area of the triangle *abp* is constant.

Area

**Question2 25 marks**

(a) The circle C has centre and radius .

(i) Find the equation of the circle C.

(ii) Verify that the point is on the circle C

Therefore, is on the circle C

(iii) Hence find the equation of the tangent to this circle at the point

Slope from centre t...