Stage 9 - Q1 - 2 marks
An activity club charges USD 10 per visit with no membership fee. Write its cost \(P\) for \(n\) visits.
Hint
There is no fixed charge.
Stage 9 - Q2 - 3 marks
Pay-as-you-go: USD 10 per visit; Flex: USD 22 plus USD 6 per visit; Unlimited: USD 90 for the whole period. Which is cheapest for 2 visits?
Hint
A small per-visit price may be outweighed by a membership fee.
Stage 9 - Q3 - 4 marks
Pay-as-you-go: USD 10 per visit; Flex: USD 22 plus USD 6 per visit; Unlimited: USD 90 for the whole period. Complete a comparison table for 0,5,10,15 visits.
Hint
The unlimited cost remains constant even at zero visits.
Stage 9 - Q4 - 4 marks
Pay-as-you-go: USD 10 per visit; Flex: USD 22 plus USD 6 per visit; Unlimited: USD 90 for the whole period. Find where Pay and Flex costs match, then the first whole visit count at which Flex is cheaper than Pay.
Hint
Do not round a non-integer crossing to the nearest visit.
Stage 9 - Q5 - 4 marks
Pay-as-you-go: USD 10 per visit; Flex: USD 22 plus USD 6 per visit; Unlimited: USD 90 for the whole period. Advise a member expecting 9 visits. Give all costs and a justified recommendation.
Hint
A pairwise crossover may not determine the cheapest of three plans.
Stage 9 - Q6 - 5 marks
Pay-as-you-go: USD 10 per visit; Flex: USD 22 plus USD 6 per visit; Unlimited: USD 90 for the whole period. For whole visit counts from 0 to 20, state the cheapest plan on every interval, including ties.
Hint
Check the neighbouring integer counts around each crossing.
Stage 9 - Q7 - 4 marks
Pay-as-you-go: USD 10 per visit; Flex: USD 22 plus USD 6 per visit; Unlimited: USD 90 for the whole period. Find the first whole visit count at which Unlimited is strictly cheaper than both alternatives.
Hint
Checking only one competing plan is insufficient.
Stage 9 - Q8 - 4 marks
Pay-as-you-go: USD 10 per visit; Flex: USD 22 plus USD 6 per visit; Unlimited: USD 90 for the whole period. With a budget of USD 85, compare the maximum whole visits on the affordable plans.
Hint
The same budget must cover the fixed and variable charges.
Stage 9 - Q9 - 4 marks
Pay costs USD 11 per visit. Choose a Flex fee with USD 6 per visit and an Unlimited price so all three costs tie at 12 visits. Find the two fixed prices and explain the graph.
Hint
A shared intersection does not mean the lines are identical.
Stage 9 - Q10 - 6 marks
Challenge: Pay costs USD 12/visit. Flex costs an unknown whole-dollar fee \(F\) plus USD 6/visit. Unlimited costs \(U\) whole dollars. Find all \(F\) and \(U\) making Pay uniquely cheapest for 0–4 visits, Flex for 5–8, and Unlimited for every \(n\ge9\). Justify the strict boundaries.
Hint
Compare the two plans on each side of a required integer switch, then intersect the resulting inequalities.