# Mock exam paper B P2 Higher Level

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**PRE – JUNIOR CERTIFICATE EXAMINATION, 2012**

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**MATHEMATICS – HIGHER LEVEL**

**PAPER 2 (300 marks)**

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**TIME: 2 ½ HOURS**

Attempt **ALL** questions.

Each question carries 50 marks.

**Graph paper may be obtained from the superintendent.**

* *The symbol indicates that supporting work must be shown to obtain full marks.

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**1. (a)** A sector has radius length of 6*cm* and subtends and angle of .

45˚

6*cm*

- Find in terms of, the area of the sector.

**(ii) ** Calculate the total length of the perimeter of the sector.

Give your answer correct to one decimal place.

**(b)** A solid cone has a slant height of *cm* and base radius of 3*cm.*

- Find the perpendicular height of the cone.

**(ii)** Find the volume of the cone in , correct to two decimal places, taking .

**(c)** A square is inscribed inside a circle as shown. The radius of the circle is 6*cm*.

**(i)** Calculate the length of the side of the square, giving your answer in the form , where

**(ii)** Find the area of the shaded region. Give your answer correct to one decimal place.

**2. (a)** The line cuts the *x*-axis at *p* and the *y*-axis at *q*.

Find the co-ordinates of *p* and the co-ordinates of *q*.

**(b)** and are two points.** **

**(i)** Find the length of [*ab*]

**(ii)** Find the slope of *ab*.

**(iii)** Find the equation of the line *ab*.

**(c)** *M* is the line and *K* is the line.

**(i)** Verify that *M* is perpendicular to *K*.

**(ii)** Find the co-ordinates of *p*, the point of intersection of *M* and *K*.

**(iii)** *M* contains the point. Find the value of *t*.

**(iv)** Find the image of *p* under, central symmetry in the point *a*.

**3. (a)** Find the measure of the angles *x* and *y* in the diagram below, given that *L**M*.

110˚

*x*˚

50˚

*y*˚

*L*

*M*

**(b) (i)** Construct the triangle *abc* in which , and .

All construction lines must be clearly shown.

**(ii)** Prove that a diagonal bisects the area of a parallelogram.

**(c)** In the, as shown and.

*a*

*y*

*x*

*b*

*c*

**(i) ** Prove that

- Hence, prove

**4. (a) **If *o* is the centre of the circle, find the value of *x*.

*o*

2*x*

4*x*

**(b)** *cd* is a t...