Free Simultaneous equations questions for IGCSE Additional Mathematics (0606), part of Algebra. Each question has the answer and the marking points an examiner would look for.
Generate a full Simultaneous Equations worksheet →All Algebra questionsThe line y + 3x = 6 meets the curve xy = 3 at the points A and B.
Find the coordinates of A and B and the length of AB.
| Part | Answer and marking points | Marks |
|---|---|---|
| (1, 3), (1, 3); 0 substitute y = 6 − 3x M1 3x2 − 6x + 3 = 0 A1 solve M1 (1, 3) and (1, 3) A1 distance formula M1 0 A1 | 6 |
Solve the simultaneous equations
y = −2x − 3
x2 + y2 = 5
| Part | Answer and marking points | Marks |
|---|---|---|
| (−2, 1) and (−25, −115) substitute to form a quadratic M1 5x2 + 12x + 4 = 0 A1 solve M1 x = −2, x = −25 A1 y = 1, y = −115 A1 | 5 |
State what is meant by the term tangent condition.
| Part | Answer and marking points | Marks |
|---|---|---|
| A line is a tangent to a curve when the resulting quadratic has a discriminant of zero A line is a tangent to a curve when the resulting quadratic has a discriminant of zero B2 | 2 |
The line y + 4x = 8 meets the curve xy = 4 at the points A and B.
Find the coordinates of A and B and the length of AB.
| Part | Answer and marking points | Marks |
|---|---|---|
| (1, 4), (1, 4); 0 substitute y = 8 − 4x M1 4x2 − 8x + 4 = 0 A1 solve M1 (1, 4) and (1, 4) A1 distance formula M1 0 A1 | 6 |
Solve the simultaneous equations
y = x − 3
x2 + y2 = 45
| Part | Answer and marking points | Marks |
|---|---|---|
| (−3, −6) and (6, 3) substitute to form a quadratic M1 2x2 − 6x − 36 = 0 A1 solve M1 x = −3, x = 6 A1 y = −6, y = 3 A1 | 5 |
The line y + 2x = 4 meets the curve xy = 2 at the points A and B.
Find the coordinates of A and B and the length of AB.
| Part | Answer and marking points | Marks |
|---|---|---|
| (1, 2), (1, 2); 0 substitute y = 4 − 2x M1 2x2 − 4x + 2 = 0 A1 solve M1 (1, 2) and (1, 2) A1 distance formula M1 0 A1 | 6 |
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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