IB Mathematics: Analysis & Approaches Paper 1 · HL (no calculator) · 2029 syllabus practice papers
2029 syllabus · HL · 100 marks · 2h · Section A short + Section B long. Each generated paper follows the SL & HL Paper 1 · HL (no calculator) · 2029 syllabus format, with the same number and style of questions as the real exam, and comes with an IB-style mark scheme.
Sample Paper 1 · HL (no calculator) · 2029 syllabus questions
Question 1Structured · 7 marks
The plane Π has equation −x + 2y − z = 1. The line L has equation r = −5−812 + λ13−3.
(a)
Find the coordinates of the point where L meets Π.
[4]
(b)
Find the shortest distance from the point (0, 0, 0) to the plane Π.
[3]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
(−2, 1, 3)
substituting the parametric form of L into the equation of Π M1 −23 + 8λ = 1 A1 λ = 3 A1 (−2, 1, 3) A1
4
(b)
1√6
distance = |d| ÷ |n| for the plane r·n = d (M1) |n| = √6 (A1) 1√6A1
3
Question 2Structured · 5 marks
The graph of y = f(x) passes through the point P(5, 3).
(a)
The graph of y = f(x) is translated by −3−2. Find the image of P.
[2]
(b)
The graph of y = f(x) is transformed to y = 2f(x − 1). Find the image of P.
[2]
(c)
Describe fully a transformation that maps y = f(x) onto y = f(−x).
[1]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
(2, 1)
x-coordinate 2 A1 y-coordinate 1 A1
2
(b)
(6, 6)
x: 6 A1 y: 6 A1
2
(c)
reflection in the y-axis
reflection in the y-axis A1
1
Question 3Structured · 4 marks
Prove that the sum of any four consecutive integers is never divisible by 4.
[4]
Show answers and mark scheme
Part
Answer and marking points
Marks
proof
n + (n + 1) + (n + 2) + (n + 3) M1 = 4n + 6 A1 = 4(n + 1) + 2 A1 which leaves remainder 2 on division by 4, so is never divisible by 4 R1
4
Question 4Structured · 7 marks
The point P(0, −1) lies on the graph of y = f(x). The graph of y = f(x) is transformed to the graph of y = −f(2x − 2) − 4.
(a)
Find the coordinates of the image of P.
[3]
(b)
Describe fully a sequence of transformations that maps the graph of y = f(x) onto this graph.
[4]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
(1, −3)
2x − 2 = 0 (M1) x = 1 A1 y = −3 A1
3
(b)
horizontal stretch, scale factor 12, then horizontal translation of 1; reflection in the x-axis and no vertical stretch; vertical translation of −4
horizontal stretch, scale factor 12A1 followed by a horizontal translation of 1 (or: translation of 2 first, then the stretch) A1 reflection in the x-axis and no vertical stretch A1 vertical translation of −4 (after the vertical stretch) A1
4
Question 5Structured · 5 marks
The angles A and B are acute, with tan A = 23 and tan B = 17.
(a)
Find the exact value of tan(A + B).
[3]
(b)
Find the exact value of cos A.
[2]
Show answers and mark scheme
Part
Answer and marking points
Marks
(a)
1719
tan A + tan B1 − tan A tan B(M1) 17/2119/21(A1) 1719A1
3
(b)
3√13
right-angled triangle with opposite 2, adjacent 3 (M1) cos A = 3√13A1
2
Question 6Structured · 6 marks
The probability distribution of a discrete random variable X is given by P(X = x) = kx2, for x ∈ {1, 2, 3, 4}.
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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