10 free IGCSE Additional Mathematics Geometry & Trigonometry questions written in the style of Cambridge Additional Mathematics papers, each with its answer and mark scheme. 4 of them are A* challenge questions, built to catch the mistakes strong students still make.
This topic covers Straight-line graphs, Coordinate geometry of the circle, Circular measure, Trigonometry. Work through the questions below, then generate a full Geometry & Trigonometry paper with a fresh set every time.
Generate a full Geometry & Trigonometry paper →The points A(−2, 1), B(6, 5) and C(4, k) are such that angle ABC = 90°.
Find the value of k.
Find the area of triangle ABC.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | k = 9 gradient AB = ½ B1 gradient BC = −2: (k − 5) ÷ (4 − 6) = −2 M1 k = 9 A1 | 3 |
| (b) | 20 AB = √80, BC = √20 M1 ½ × √80 × √20 = 20 A1 | 2 |
Solve 2 sec2y = 5 tan y for 0° ≤ y ≤ 360°.
| Part | Answer and marking points | Marks |
|---|---|---|
| 26.6°, 63.4°, 206.6°, 243.4° sec2y = 1 + tan2y M1 2tan2y − 5 tan y + 2 = 0 A1 tan y = 2 or ½ A1 26.6°, 63.4° A1 206.6°, 243.4° A1 | 5 |
The diagram shows a sector of radius 12 cm and angle π3 radians.
Find the exact perimeter and the exact area of the sector.
| Part | Answer and marking points | Marks |
|---|---|---|
| 24 + 4π cm; 24π cm² arc = rθ M1 24 + 4π A1 ½r2θ M1 24π A1 | 4 |
A circle has centre C(2, 3) and passes through the point P(6, 7).
Find the equation of the circle.
Find the equation of the tangent to the circle at P.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | (x − 2)2 + (y − 3)2 = 25 radius 5 B1 (x − 2)2 + (y − 3)2 = 25 B1 | 2 |
| (b) | tangent gradient CP = 1 B1 tangent gradient −1 M1 y − 7 = −1(x − 6) A1 | 3 |
A circle has equation x2 + y2 − 2x + 4y − 31 = 0.
Find the centre and the radius of the circle.
| Part | Answer and marking points | Marks |
|---|---|---|
| centre (1, −2); radius 6 completing the square M1 centre (1, −2) A1 radius 6 A1 | 3 |
A is (−1, −1) and B is (5, 3).
Find the equation of the perpendicular bisector of AB, giving your answer in the form ax + by = c, where a, b and c are integers.
| Part | Answer and marking points | Marks |
|---|---|---|
| 6x + 4y = 16 midpoint (2, 1) B1 gradient AB = 23 B1 perpendicular gradient −32 M1 6x + 4y = 16 (or a multiple) A1 | 4 |
Show that sin x1 − cos x − sin x1 + cos x = 2tan x.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | shown common denominator 1 − cos2x M1 sin x(1 + cos x) − sin x(1 − cos x) M1 2 sin x cos xsin2x A1 = 2 cos xsin x = 2tan x AG A1 | 4 |
A sector OAB of a circle has radius 5 cm and angle AOB = 1.2 radians.
Find the perimeter of the sector.
Find the area of the segment cut off by the chord AB.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 16 cm rθ M1 16 A1 | 2 |
| (b) | 3.35 cm² ½r2θ M1 ½r2 sin θ M1 3.35 A1 | 3 |
A sector has radius 6 cm and angle π4 radians. Find the arc length, in terms of π.
Find the area of the sector, in terms of π.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 32π cm s = rθ M1 32π A1 | 2 |
| (b) | 92π cm² A = ½r2θ M1 92π A1 | 2 |
Solve 2 sin2x = 1 + cos x for 0° ≤ x ≤ 360°.
| Part | Answer and marking points | Marks |
|---|---|---|
| 60°, 180°, 300° use of identity M1 2cos2x + cos x − 1 = 0 A1 cos x = ½ or −1 A1 60°, 180°, 300° A1 | 4 |
In the 0606 syllabus, Geometry & Trigonometry covers Straight-line graphs, Coordinate geometry of the circle, Circular measure, Trigonometry.
This page has 10 Geometry & Trigonometry questions with answers. For more, the free generator on mentorriyaz.in builds a new Geometry & Trigonometry paper with a full mark scheme each time you click.
Riyaz Shaikh has mentored IGCSE, IB and A Level students for 15+ years, one-on-one, online and in Mumbai. The hardest questions on this site are the ones he uses to find a student's weak points.
Meet Riyaz →Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in