Every IB Mathematics: Applications & Interpretation topic, with free past-paper-style questions and full mark schemes. Pick a chapter to practise its questions, or generate a complete SL & HL-format paper in seconds, from easy warm-ups to A*-level "brutal" papers.
A mixed set from across the syllabus. Questions marked A* challenge come from the hardest bank.
Question 1Structured · 5 marksA* challenge
A set of 16 marks has mean 69 and standard deviation 7.
(a)
Each mark is multiplied by 3 and then 10 is added. Find the new mean and standard deviation.
[3]
(b)
A second group of 22 students has a mean mark of 76 on the original test. Find the mean mark of all 38 students.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
mean 217, sd 21
mean = 3 × 69 + 10 = 217 A1 adding does not change the sd (M1) sd = 21 A1
3
(b)
73.053
(16 × 69 + 22 × 76)/38 (M1) 73.053 A1
2
Question 2Structured · 6 marks
Two mobile phone masts are at A(6, 2) and B(8, 8). A phone connects to the nearest mast.
(a)
Find the equation of the perpendicular bisector of AB, giving your answer in the form y = mx + c.
[4]
(b)
A phone is at P(6, 4). Determine which mast it connects to.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
y = −13x + 223
midpoint (7, 5) A1 gradient of AB = 3 A1 perpendicular gradient −13(M1) y = −13x + 223A1
4
(b)
A
PA = 2.00, PB = 4.47 (M1) A A1
2
Question 3Structured · 6 marks
Each day is either sunny (S) or rainy (R). If today is sunny, the probability that tomorrow is sunny is 0.7. If today is rainy, the probability that tomorrow is sunny is 0.4.
(a)
Write down the transition matrix T, with columns representing today’s weather.
[2]
(b)
Given that today is sunny, find the probability that it is sunny in two days’ time.
[2]
(c)
Find the long-term proportion of sunny days.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
0.7 0.40.3 0.6
correct structure (M1) 0.7 0.40.3 0.6A1
2
(b)
0.610
T2(M1) 0.610 A1
2
(c)
0.571
steady state: Tv = v (M1) 0.571 A1
2
Question 4Structured · 6 marks
A particle moves in a straight line with velocity v(t) = t2 − 7t + 10 m s−1, for 0 ≤ t ≤ 7.
(a)
Find the times when the particle changes direction.
[2]
(b)
Find the total distance travelled.
[2]
(c)
Find the displacement at t = 7.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
t = 2, t = 5
v(t) = 0 with a sign change (M1) t = 2, t = 5 A1
2
(b)
21.8 m
∫07|v|dt (M1) 21.8 m A1
2
(c)
12.8 m
∫07v dt (M1) 12.8 m A1
2
Question 5Structured · 5 marks
The number of calls to a helpline follows a Poisson distribution with a mean of 3 calls per ten minutes.
(a)
Find the probability of exactly 3 calls in a ten-minute period.
[2]
(b)
Find the probability of at least 10 calls in a 30-minute period.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
0.224
X ~ Po(3) (M1) 0.224 A1
2
(b)
0.413
Y ~ Po(9) (A1) 1 − P(Y ≤ 9) (M1) 0.413 A1
3
Question 6Structured · 5 marks
The pH of a solution is given by pH = −log10[H+], where [H+] is the hydrogen ion concentration in mol dm−3.
(a)
Find [H+] for a solution with pH 5.3. Give your answer in standard form.
[2]
(b)
Find how many times greater [H+] is in a solution of pH 5.3 than in a solution of pH 6.6.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
5.01 × 10−6
10−5.3(M1) 5.01 × 10−6A1
2
(b)
20.0
10−5.310−6.6(M1) 101.3(A1) 20.0 A1
3
Frequently asked questions
Are these real SL & HL past paper questions?
No. They are original questions written to match the IB Mathematics: Applications & Interpretation SL & HL syllabus and the style of real IB papers, so you can practise beyond the past papers you have already done.
Do the Mathematics: Applications & Interpretation questions have answers?
Yes. Every question on these pages has its answer, and every generated paper comes with a full IB-style mark scheme you can download as a PDF.
Can I make a full IB Mathematics: Applications & Interpretation practice paper?
Yes. Choose the paper (Paper 1 SL (short questions) · 2029 syllabus, Paper 2 SL (long questions) · 2029 syllabus, Paper 1 HL (short questions) · 2029 syllabus, Paper 2 HL (long questions) · 2029 syllabus, Paper 3 HL problem solving · 2029 syllabus, Paper 1 SL (short questions) · exams to Nov 2028, Paper 2 SL (long questions) · exams to Nov 2028, Paper 1 HL (short questions) · exams to Nov 2028, Paper 2 HL (long questions) · exams to Nov 2028, Paper 3 HL problem solving · exams to Nov 2028), the topics, the marks and the difficulty, and the generator builds a fresh paper with the same number and style of questions as the real exam.
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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