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.

Give your answer correct to one decimal place.

(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

(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 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...

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