# 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)

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

_{Area =} _{r}2

360

_{(4:5)}2^{60}360^{27}_{8}cm^{2}

- 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 | ||||||||

65 cm and base radius of 4 cm. |

- Find the perpendicular height of the cone.

p 2

h^{2} = 65 (4)^{2}

- 65 16
- 49

h = 7 cm

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

Volume = ^{1}_{3} r^{2}h

^{1}_{3}(4)^{2}(7)- 117:30 cm
^{3}

Page 2 of 22

Question 2 (5 mins)

- 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.
- How many di erent ways can the six people arrive at work.

6 5 4 3 2 1 = 720

- 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

- 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 |

- How many eggs were tested in total? 36 eggs were tested in total.
- What was the range of weights for each farm

Farm 1 = 24

Farm 2 = 31

- 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 ...