# Mock exam paper A P2 Higher Level

PRE-JUNIOR CERTIFICATE EXAMINATION, 2011

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MATHEMATICS – HIGHER LEVEL

Paper II (300 marks)

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Time: hours

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Attempt ALL questions.

Each question carries 50 marks.

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

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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

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...