# Mock exam paper A P2 Higher Level

**PRE-JUNIOR CERTIFICATE EXAMINATION, 2011**

______________________________________

**MATHEMATICS – HIGHER LEVEL**

**Paper II (300 marks)**

______________________________________

Time: hours

____________________________________________________________

Attempt **ALL** questions.

Each question carries 50 marks.

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

____________________________________________________________

**Q.1** (a) A cone has a base radius of 5 *cm *and a slant height of 13 *cm*.

5 *cm*

*h*

13 *cm*

(i) Find *h*, the perpendicular height.

(ii) Find the volume of the cone in terms of .

(b) (i) Calculate, in terms of , the volume of a solid sphere of diameter 9 *cm* .

(ii) The sphere is melted down and recast as a cylindrical rod of radius

. Calculate the length of the rod.

(c) A ladle in the shape of a hemispherical bowel has a diameter 24 *cm*.

(i) If it is full of liquid, calculate, in terms of , the volume of liquid in the

ladle.

The liquid is then poured into a cylindrical container with internal diameter of 16 *cm*.

(ii) Calculate the height of the liquid in the cylindrical container.

**Q.2 (a)** Find the image of the point under the central symmetry in the point

.

** (b)** The three points are all on a straight line.

**(i)** Calculate the ratio

**(ii)** Find the equation of the line *L* through *b* which is perpendicular to *ac*.

**(c) (i)** The line is perpendicular to the line .

Find the value of *k*.

**(ii)** The slope containing the points and is .

Find the value of *t.*

**Q.3 (a)** The line *L* is parallel to the line *M*.

*L*

*x*

*y*

*L*

Calculate the value of *x* and *y* in

the diagram.

**(b) (i)** Construct a line segment [*ab*] where .

Show how to divide this line segment into three equal parts.

All construction lines must be shown.

**(ii)** Prove that if two sides of a triangle are equal in measure, then the angles

opposite these sides are equal in measure.

*b*

*y*

*c*

*a*

** (c)** In the diagram

**(i)** Prove that

**(ii)** If ,

prove

*x*

*c*

*b*

*a*

*4*

*m*

*5*

*3*

*n*

**Q.4 (a)** In the triangle *abc*, *mn* is parallel t...