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Linear models: IB Mathematics: Applications & Interpretation questions with answers Free Linear models questions for IB Mathematics: Applications & Interpretation (SL & HL), part of Functions. Each question has the answer and the marking points an examiner would look for.
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Linear models practice questions Question 1 Structured · 7 marks A* challenge
Plan A costs $8 per month plus $5 per GB of data. Plan B costs $35 per month, which includes 10 GB, and $9 for each additional GB.
(a) Write down the cost of each plan for 8 GB.
[2] (b) Write down an expression for the cost of plan B when x > 10.
[1] (c) Find the range of values of x for which plan B is cheaper.
[4] Show answers and mark scheme Part Answer and marking points Marks (a) A: $48, B: $35$48 A1 A1
2 (b) 35 + 9(x − 10)35 + 9(x − 10) A1
1 (c) 5.40 < x < 15.88 + 5x = 35 (M1) A1 (M1) A1
4
Question 2 Structured · 6 marks
The cost $C of a taxi journey of d km is modelled by C = md + c. A journey of 5 km costs $12.00 and a journey of 17 km costs $33.60.
(a) Find the value of m and the value of c.
[3] (b) Interpret the value of m in this context.
[1] (c) Find the greatest distance that can be travelled for $30.
[2] Show answers and mark scheme Part Answer and marking points Marks (a) m = 1.8, c = 3two equations or gradient from two points (M1) A1 A1
3 (b) cost per kmeach additional km costs $1.80 A1
1 (c) 15.0 km1.8d + 3 = 30 (M1) A1
2
Question 3 Structured · 4 marks
A taxi charges a fixed fee of $5 plus $1.5 per kilometre.
(a) Write down a linear model for the cost C of a journey of d km.
[1] (b) A second taxi charges $2 per kilometre with no fixed fee. Find the distance for which both cost the same.
[2] (c) State what the gradient of the first model represents.
[1] Show answers and mark scheme Part Answer and marking points Marks (a) C = 1.5d + 5C = 1.5d + 5 A1
1 (b) 10.0 kmequating (M1) A1
2 (c) cost per kmcost per kilometre R1
1
Question 4 Structured · 7 marks A* challenge
Plan A costs $10 per month plus $4 per GB of data. Plan B costs $30 per month, which includes 10 GB, and $8 for each additional GB.
(a) Write down the cost of each plan for 8 GB.
[2] (b) Write down an expression for the cost of plan B when x > 10.
[1] (c) Find the range of values of x for which plan B is cheaper.
[4] Show answers and mark scheme Part Answer and marking points Marks (a) A: $42, B: $30$42 A1 A1
2 (b) 30 + 8(x − 10)30 + 8(x − 10) A1
1 (c) 5.00 < x < 15.010 + 4x = 30 (M1) A1 (M1) A1
4
Question 5 Structured · 6 marks
The cost $C of a taxi journey of d km is modelled by C = md + c. A journey of 8 km costs $18.40 and a journey of 18 km costs $36.40.
(a) Find the value of m and the value of c.
[3] (b) Interpret the value of m in this context.
[1] (c) Find the greatest distance that can be travelled for $40.
[2] Show answers and mark scheme Part Answer and marking points Marks (a) m = 1.8, c = 4two equations or gradient from two points (M1) A1 A1
3 (b) cost per kmeach additional km costs $1.80 A1
1 (c) 20.0 km1.8d + 4 = 40 (M1) A1
2
Question 6 Structured · 4 marks
A taxi charges a fixed fee of $3 plus $1.5 per kilometre.
(a) Write down a linear model for the cost C of a journey of d km.
[1] (b) A second taxi charges $2 per kilometre with no fixed fee. Find the distance for which both cost the same.
[2] (c) State what the gradient of the first model represents.
[1] Show answers and mark scheme Part Answer and marking points Marks (a) C = 1.5d + 3C = 1.5d + 3 A1
1 (b) 6.00 kmequating (M1) A1
2 (c) cost per kmcost per kilometre R1
1
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Meet Riyaz → Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in