Paper Generator › IB Mathematics: Applications & Interpretation › Paper 1 · SL (short questions) · exams to Nov 2028IB · Mathematics: Applications & Interpretation SL & HL · P1S
IB Mathematics: Applications & Interpretation Paper 1 · SL (short questions) · exams to Nov 2028 practice papers SL · 80 marks · 1h 30m · calculator. Each generated paper follows the SL & HL Paper 1 · SL (short questions) · exams to Nov 2028 format, with the same number and style of questions as the real exam, and comes with an IB-style mark scheme.
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Sample Paper 1 · SL (short questions) · exams to Nov 2028 questions Question 1 Structured · 6 marks A* challenge
A company’s monthly sales of a new product start at 2 thousand units and increase by 50% each month.
(a) Find the total sales, in thousands, in the first year.
[2] (b) Find the least number of months after which total sales exceed 10000 thousand units.
[3] (c) Suggest why this model is unlikely to remain valid.
[1] Show answers and mark scheme Part Answer and marking points Marks (a) 515S12 = 2(1.512 − 1) 1.5 − 1 (M1) A1
2 (b) 202(1.5n − 1) 1.5 − 1 (M1) (A1) A1
3 (c) unbounded growthsales cannot grow exponentially for ever (market saturates) R1
1
Question 2 Structured · 5 marks A* challenge
The lengths of leaves are normally distributed with standard deviation 6 mm. A random sample of 49 leaves has mean 51.4 mm.
(a) Find a 95% confidence interval for the mean length.
[3] (b) State how many leaves would be needed to halve the width of the interval.
[1] (c) A botanist claims the mean is 54.08 mm. Comment on this claim.
[1] Show answers and mark scheme Part Answer and marking points Marks (a) 49.72 < μ < 53.08z-interval (M1) A1 A1
3 (b) 196196 A1
1 (c) outside the intervalthe value lies outside the interval, so the claim is not supported R1
1
Question 3 Structured · 5 marks
The population of a town is 48000 at the start of 2025 and decreases by 5% each year.
(a) Find the population at the start of 2030.
[2] (b) Find the first year in which the population at the start of the year is less than 28800.
[3] Show answers and mark scheme Part Answer and marking points Marks (a) 3714148000(0.95)5 (M1) A1
2 (b) 203548000(0.95)n < 28800 (M1) (A1) A1
3
Question 4 Structured · 5 marks
Let M = 10 −3 18 −5
(a) Find the eigenvalues of M.
[3] (b) Find an eigenvector corresponding to λ = 4.
[2] Show answers and mark scheme Part Answer and marking points Marks (a) λ = 4, λ = 1det(M − λI) = 0 M1 2 − 5λ + 4 = 0 A1 A1
3 (b) 1 2 (M − 4I)v = 0 (M1) 1 2 A1
2
Question 5 Structured · 6 marks
The weekly profit, in dollars, from selling x hundred items is modelled by P(x) = −4x2 + 120x − 200.
(b) Find the number of items that maximizes the profit, and the maximum profit.
[3] (c) Find the least number of items that must be sold to make a profit.
[2] Show answers and mark scheme Part Answer and marking points Marks (a) −8x + 120−8x + 120 A1
1 (b) 1500 items; $700P′(x) = 0 (M1) A1 A1
3 (c) 178 itemsP(x) = 0 (M1) A1
2
Question 6 Structured · 6 marks
In a class of 48 students, 21 study French (F), 18 study Spanish (S) and 9 study both.
(a) Find the number of students who study neither.
[1] (b) Find P(F ∪ S) and P(S | F).
[3] (c) Determine whether F and S are independent.
[2] Show answers and mark scheme Part Answer and marking points Marks (a) 1818 A1
1 (b) 30 48 9 21 30 48 A1 (M1) 9 21 A1
3 (c) not independentP(F)P(S) = 0.164, P(F ∩ S) = 0.188 M1 A1
2
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