Home / IB Math Analysis & Approaches Question bank-Topic: SL 4.3- Effect of constant changes to the original data SL Paper 1

IB Math Analysis & Approaches Question bank-Topic: SL 4.3- Effect of constant changes to the original data SL Paper 1

Question

A city hired 160 employees to work at a festival. The following cumulative frequency curve shows the number of hours employees worked during the festival.

M17/5/MATME/SP1/ENG/TZ2/08.a.ii

The city paid each of the employees £8 per hour for the first 40 hours worked, and £10 per hour for each hour they worked after the first 40 hours.

Find the median number of hours worked by the employees.

[2]
a.i.

Write down the number of employees who worked 50 hours or less.

[1]
a.ii.

Find the amount of money an employee earned for working 40 hours;

[1]
b.i.

Find the amount of money an employee earned for working 43 hours.

[3]
b.ii.

Find the number of employees who earned £200 or less.

[3]
c.

Only 10 employees earned more than £\(k\). Find the value of \(k\).

[4]
d.
Answer/Explanation

Markscheme

evidence of median position     (M1)

eg\(\,\,\,\,\,\)80th employee

40 hours     A1     N2

[2 marks]

a.i.

130 employees     A1     N1

[1 mark]

a.ii.

£320     A1     N1

[1 mark]

b.i.

splitting into 40 and 3     (M1)

eg\(\,\,\,\,\,\)3 hours more, \(3 \times 10\)

correct working     (A1)

eg\(\,\,\,\,\,\)\(320 + 3 \times 10\)

£350     A1     N3

[3 marks]

b.ii.

valid approach     (M1)

eg\(\,\,\,\,\,\)200 is less than 320 so 8 pounds/hour, \(200 \div 8,{\text{ }}25,{\text{ }}\frac{{200}}{{320}} = \frac{x}{{40}}\),

18 employees     A2     N3

[3 marks]

c.

valid approach     (M1)

eg\(\,\,\,\,\,\)\(160 – 10\)

60 hours worked     (A1)

correct working     (A1)

eg\(\,\,\,\,\,\)\(40(8) + 20(10),{\text{ }}320 + 200\)

\(k = 520\)     A1     N3

[4 marks]

d.

Question

The following box-and-whisker plot shows the number of text messages sent by students in a school on a particular day.

Find the value of the interquartile range.

[2]
a.

One student sent k text messages, where k > 11 . Given that k is an outlier, find the least value of k.

[4]
b.
Answer/Explanation

Markscheme

recognizing Q1 or Q3 (seen anywhere)     (M1)

eg    4,11 , indicated on diagram

IQR = 7     A1 N2

[2 marks]

a.

recognizing the need to find 1.5 IQR     (M1)

eg   1.5 × IQR, 1.5 × 7

valid approach to find    (M1)

eg   10.5 + 11, 1.5 × IQR + Q3

21.5     (A1)

k = 22     A1 N3

Note: If no working shown, award N2 for an answer of 21.5.

[4 marks]

b.
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