Free Vectors in two dimensions questions for IGCSE Additional Mathematics (0606), part of Vectors & calculus. Each question has the answer and the marking points an examiner would look for.
Generate a full Vectors in Two Dimensions worksheet →All Vectors & calculus questionsA boat travels at 8 m/s in still water. It heads due north across a river flowing at 6 m/s due east.
Find the resultant speed and the angle between the boat’s path and the bank.
| Part | Answer and marking points | Marks |
|---|---|---|
| 10 m/s; 53.1° Pythagoras M1 10 m/s A1 tan θ = 8/6 M1 53.1° A1 | 4 |
p = 4i + 4j and q = −2i − 3j.
Find the unit vector in the direction of p + q.
| Part | Answer and marking points | Marks |
|---|---|---|
| 1√5(2i + j) p + q = 2i + j B1 |p + q| = √5 M1 unit vector A1 | 3 |
State what is meant by the term unit vector.
| Part | Answer and marking points | Marks |
|---|---|---|
| A vector of magnitude 1 A vector of magnitude 1 B1 | 1 |
p = 4i + 5j and q = −5i + 4j.
Find the unit vector in the direction of p + q.
| Part | Answer and marking points | Marks |
|---|---|---|
| 1√82(−i + 9j) p + q = −i + 9j B1 |p + q| = √82 M1 unit vector A1 | 3 |
p = −5i + 2j and q = 4i − 4j.
Find the unit vector in the direction of p + q.
| Part | Answer and marking points | Marks |
|---|---|---|
| 1√5(−i − 2j) p + q = −i − 2j B1 |p + q| = √5 M1 unit vector A1 | 3 |
p = −5i + j and q = −5i + 2j.
Find the unit vector in the direction of p + q.
| Part | Answer and marking points | Marks |
|---|---|---|
| 1√109(−10i + 3j) p + q = −10i + 3j B1 |p + q| = √109 M1 unit vector A1 | 3 |
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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