# Mock exam paper E Paper 2 Marking Scheme

Pre-Junior Cert Examination

Mathematics

Paper 2

Higher Level

Marking Scheme

Page 1 of 22

Question 1 (10 mins)

1. A sector has radius length of 4.5 cm and subtends and angle of 45 .
1. Find in terms of , the area of the sector.

Area = r2

360

• (4:5)2 60 360
• 278 cm2
1. Calculate the total length of the perimeter of the sector. Give your answer correct to one decimal place.
 Perimeter = length of sector + 2 radii = (2)( )(4:5) 360 + 4:5 + 4:5 60 = 13:7 cm (b) A solid cone has a slant height of p 65 cm and base radius of 4 cm.
1. Find the perpendicular height of the cone.

p 2

h2 = 65 (4)2

• 65 16
• 49

h = 7 cm

1. Find the volume of the cone in , correct to two decimal places, taking = 3:142.

Volume = 13 r2h

• 13 (4)2(7)
• 117:30 cm3

Page 2 of 22

Question 2 (5 mins)

1. Six people, John, Patrick, Laura, Avril, Emer and Danny, leave for the same place of work at the same time. They all arrive for work at di erent times.
1. How many di erent ways can the six people arrive at work.

6 5 4 3 2 1 = 720

1. If John arrives rst and Avril arrives last, how many di erent ways can the other people arrive at work?

1 4 3 2 1 1 = 24

Page 3 of 22

Question 3 (5 mins)

A sample of eggs from two farms are taken and each egg is weighed (in grams). The results are as follows:

Farm I 60, 72, 58, 61, 57, 56, 62, 54, 48, 59, 70, 58, 57, 49, 52, 55, 61, 49 Farm II 49, 56, 74, 67, 55, 72, 64, 75, 77, 78, 68, 69, 70, 59, 58, 72, 71, 80

1. Represent this data on a back-to-back stem-and-leaf diagram.
 Farm 1 Farm 2 9 9 8 4 9 9 8 8 7 7 6 5 4 2 5 5 6 8 9 2 1 1 0 6 4 7 8 9 2 0 7 0 1 2 2 4 5 7 8 8 0 Key: 41
1. How many eggs were tested in total? 36 eggs were tested in total.
2. What was the range of weights for each farm

Farm 1 = 24

Farm 2 = 31

1. One of the farms tested was completely free range and organic. Based on the data supplied which farm do you think it was? Give a reason for your answer.

Farm 2 was free range. The eggs produced on this farm are generally bigger than Farm 1

Page 4 of 22

Question 4 (5 mins)

A survey is conducted by the board of management of a school to nd out about the students' choices in bread at lunch time. The ...