0606/11 Oct/Nov 2025, Question 2: When a Line Meets, Touches or Misses a Curve
Cambridge IGCSE Additional Mathematics 0606 · Paper 11 (Non-calculator) · Non-calculator · 6 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Determine the range of k values making the line y = kx − 3 intersect y = x² + 2x twice, giving the result with surds simplified.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 6 marks
- 1x² + 2x = kx − 3 ⇒ x² + (2 − k)x + 3 = 0
- 2Two distinct points: (2 − k)² − 12 > 0
- 3k² − 4k − 8 > 0
- 4Critical values k = (4 ± √48)/2 = 2 ± 2√3
- 5k < 2 − 2√3 or k > 2 + 2√3
Answerk < 2 − 2√3, k > 2 + 2√3
Stuck on a step? Read the free lesson: When a Line Meets, Touches or Misses a Curve
Practise more when a line meets, touches or misses a curve questions
Real 0606 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on when a line meets, touches or misses a curve
Also searched as: 0606/11/O/N/25 · 0606_w25_qp_11 · 0606 w25 11 · question 2.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.