Foundation June 2024 Paper 3 Q12
12 At an adventure park, all children participate in three activities, choosing exactly one activity from each of three options.
| Option | Activity |
|---|---|
| 1 | football or golf |
| 2 | bowling or climbing |
| 3 | rafting or swimming or tennis |
On one Monday morning, 100 children visited the adventure park.
The frequency tree shows the number of children choosing some of the activities.
(a) Complete the frequency tree. [3]
(b) Which was the most popular activity out of rafting, swimming and tennis?
Show how you decide. [3]
Show how you decide. [3]
(c) One of the 100 children is picked at random.
Find the probability that this child chose bowling. [2]
(d) Alex says
45% of all children coming to the adventure park choose football.
What assumption has Alex made? [1]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Football, Bowling: 22 Football, Bowling, Tennis: 8 Football, Climbing: 23 Golf: 55 Golf, Climbing, Swimming: 7 | 3 | FT their 22 – 14 for their 8 B2 for 3 correct or B1 for 2 correct | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Tennis and [R =] 37 or \(11 + 12 + 5 + 9\) [S =] 20 or \(3 + 5 + 5 +\) their 7 [T =] 43 or their \(8 + 6 + 25 + 4\) | 3 | FT their (a) even if NR M2 for two from [R =] 37 or \(11 + 12 + 5 + 9\) [S =] 20 or \(3 + 5 + 5 +\) their 7 [T =] 43 or their \(8 + 6 + 25 + 4\) or M1 for one from [R =] 37 or \(11 + 12 + 5 + 9\) [S =] 20 or \(3 + 5 + 5 +\) their 7 [T =] 43 or their \(8 + 6 + 25 + 4\) If 0 or 1 scored, instead award SC2 for Tennis = 43 which is 6 more than R and 23 more than S | Accept their most popular with strict FT from their three correct totals for these sports Sums must be correctly evaluated May be on diagram Accept labelled or in correct order Check \(13 +\) their 7 Check \(35 +\) their 8 If (a) is NR, FT all marks. The values will be: [R =] \(11 + 12 + 5 + 9\) or 37 [S =] \(3 + 5 + 5\) or 13 [T =] \(6 + 25 + 4\) or 35 and the answer R[afting] and the sums or totals seen |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\dfrac{57}{100}\) oe | 2 | FT their 22 or \(11 + 3 +\) their 8 B1 for their \(22 + 35\) correctly evaluated or 57 seen If (a) is NR, award SC1 for answer \(\frac{35}{100}\) oe or answer \(\frac{1}{35}\) | Ignore attempts to change form Accept fraction, decimal (e.g. 0.57) and percentage (e.g. 57%) but not ratio nor in words For B1, condone \(\frac{1}{57}\) as 57 seen |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [That] these [100] children are representative of all children [who attend the adventure park] oe | 1 | See Appendix | Representative sample |
Appendix
Appendix Question 12d
| Assumption | Mark | Reason |
|---|---|---|
| All children choose in the same way as these children | 1 | Has the idea of a representative sample |
| Every group of 100 will chose the same options every time | 1 | BOD does not say “in the same proportion” but implies representative sample |
| 45% of children that weren’t in the 100 would choose football | 1 | Indicates representative sample |
| That every child that turns up for the adventure park will choose the same options as the 100 | 1 | BOD. Does not say “in the same way as the 100” but indicates representative sample |
| The same proportions apply to all other children coming to the park | 1 | Representative sample |
| Because 45 is 45% of every 100 children that come to the park | 1 | Representative sample |
| 45%/0.45 of ALL children will choose football | 0 | Repeats question |