Date | May 2021 | Marks available | 2 | Reference code | 21M.2.SL.TZ2.3 |
Level | Standard Level | Paper | Paper 2 | Time zone | Time zone 2 |
Command term | Find | Question number | 3 | Adapted from | N/A |
Question
A new concert hall was built with seats in the first row. Each subsequent row of the hall has two more seats than the previous row. The hall has a total of rows.
Find:
The concert hall opened in . The average number of visitors per concert during that year was . In , the average number of visitors per concert increased by .
The concert organizers use this data to model future numbers of visitors. It is assumed that the average number of visitors per concert will continue to increase each year by .
the number of seats in the last row.
the total number of seats in the concert hall.
Find the average number of visitors per concert in .
Determine the first year in which this model predicts the average number of visitors per concert will exceed the total seating capacity of the concert hall.
It is assumed that the concert hall will host concerts each year.
Use the average number of visitors per concert per year to predict the total number of people expected to attend the concert hall from when it opens until the end of .
Markscheme
recognition of arithmetic sequence with common difference (M1)
use of arithmetic sequence formula (M1)
A1
[3 marks]
use of arithmetic series formula (M1)
A1
[2 marks]
OR (M1)
A1
Note: Award M0A0 if incorrect used in part (b), and FT with their in parts (c) and (d).
[2 marks]
recognition of geometric sequence (M1)
equating their th geometric sequence term to their (M1)
Note: Accept inequality.
METHOD 1
EITHER
A1
A1
A1
OR
A1
A1
A1
METHOD 2
11th term (M1)A1
12th term (M1)A1
A1
Note: The last mark can be awarded if both their 11th and 12th correct terms are seen.
[5 marks]
seen (A1)
EITHER
(M1)
multiplying their sum by (M1)
OR
sum of the number of visitors for their and their seven years (M1)
multiplying their sum by (M1)
OR
(M1)(M1)
THEN
A1
Note: Follow though from their from part (b).
[4 marks]