# 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 6cm and subtends and angle of .

45˚

6cm

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

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

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

1. 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 6cm.

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

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 LM.

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

1. Hence, prove

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

o

2x

4x

(b) cd is a t...