plumiScalar and vector quantities: Edexcel International GCSE Further Maths questions
Edexcel International GCSE Further Maths past-paper questions on 7 Scalar and vector quantities, 2019–2025, with mark schemes and examiner’s reports where available.
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All 29 questions on Scalar and vector quantities, as a list
- June 2025 (R), Paper 1, Q6 (9 marks): Referred to a fixed origin O, the position vector of the point A is 9 a b 12 and the position vector of the point B is 2a p b where a b =1 = Given that AB = 25
- June 2025 (R), Paper 2, Q1 (4 marks): The points A, B, C and D are the vertices of a quadrilateral ABCD such that a b a b a b 3 2 2 5 5 3 Show that ABCD is a parallelogram. (4)
- June 2025, Paper 2, Q8 (11 marks): Diagram NOT accurately drawn A 3u + v O B Figure 2 Figure 2 shows triangle OAB with = 3u v u 2 v + = (a) Find as a simplified expression in terms of u and v (2)
- November 2024, Paper 2, Q8 (12 marks): D Diagram NOT A accurately drawn C O B Figure 2 Figure 2 shows triangle AOB b b b where | a | = | b| = 1 4 a 5 8a 15 a 10 (a) (i) Find in terms of a and b (ii)
- June 2024 (R), Paper 1, Q8 (10 marks): 3a B C Diagram NOT accurately drawn 2b A D 5a Figure 3 Figure 3 shows a trapezium ABCD a a b BC 3 AD 5 CD 2 → as a simplified expression in terms of a and b (a)
- June 2024 (R), Paper 2, Q3 (6 marks): O, A and B are fixed points such that OA AB i a j OB i a j 3 5 3 7 2 Given that a > 0 (a) find the value of a (4) → (b) Hence find a unit vector parallel to OA
- June 2024, Paper 2, Q10 (11 marks): The points A, B, C and D are the vertices of a quadrilateral such that a b a b a b AB AC AD 3 4 7 9 4 5 (a) Show that ABCD is a parallelogram. (3) BC is extende
- November 2023, Paper 2, Q11 (9 marks): A Diagram NOT accurately drawn O B M C Figure 3 Figure 3 shows quadrilateral OABC where = 4p + 5q = 3p + q = 2p - 4q The point M is the midpoint of OC as a simp
- June 2023 (R), Paper 1, Q10 (11 marks): A Diagram NOT accurately drawn M Y O B X Figure 5 a b and M is the midpoint of OA. In Figure 5, OA 2 , OB 4 The point Y lies on AB such that AY : YB = 3 : 1 The
- June 2023 (R), Paper 2, Q4 (6 marks): O, A and B are fixed points such that → = 5i + 7j AB → = ai + 16j and ½OB →½ = 5 29 OA (a) Find the possible values of a (4) Given that a > 0 → (b) find a unit
- June 2023, Paper 1, Q10 (10 marks): O, A and B are fixed points such that → = (b + 1)i + bj OA → = 3i AB → is 17 34 [(3a + 2)i + bj] The unit vector parallel to OB Given that a and b are constants
- January 2023 (R), Paper 1, Q4 (12 marks): O, A and B are fixed points such that → = pi + 2pj → = 5i + 9pj OA OB → is parallel to (i – 2j) Given that AB (a) find the value of p (6) → as a simplified expr
- January 2023, Paper 1, Q11 (10 marks): A Diagram NOT accurately drawn M X O N B Figure 3 → = a and OB → = b Figure 3 shows triangle OAB with OA M is the midpoint of OA. N is the point on OB such that
- June 2022 (R), Paper 1, Q9 (10 marks): B C Diagram NOT accurately drawn D A Figure 3 Figure 3 shows quadrilateral ABCD such that → = 2a + b BC → = 1 → = –4a – b 3 b BD AD → is parallel to DC → (a) Pr
- June 2022 (R), Paper 2, Q1 (5 marks): The position vector of the point A is (3i – 2j), referred to a fixed origin O. → = (6i + 8j) The point B is such that AB (a) Find the position vector of B as a
- June 2022, Paper 1, Q10 (14 marks): A Diagram NOT accurately drawn M P N O B Figure 4 Figure 4 shows triangle OAB in which → = a and OB → = b OA The point P lies on AB such that AP : PB = 3 : 1 Th
- June 2022, Paper 2, Q3 (9 marks): O, A and B are fixed points such that → = ( pi – 4j) OB → = i + (2p + 1) j OA 2 |OA →| = |OB →| and p > 0 Given that (a) find the value of p (4) Using this valu
- January 2022 (R), Paper 1, Q6 (10 marks): The points P, Q, R and S are the vertices of a quadrilateral PQRS such that → → → = 2i + 3j PR −i + 18j PS = −3i +15j PQ (a) Show that PQRS is a parallelogram.
- January 2022 (R), Paper 2, Q11 (13 marks): A Diagram NOT accurately drawn N P B M C O Figure 3 → → Figure 3 shows triangle OAB with OA = a and OB = b The point C lies on OB such that OC : CB = 2 : 1 The
- January 2022, Paper 2, Q9 (13 marks): A Diagram NOT accurately drawn 2a O B 4b Figure 3 Figure 3 shows the triangle OAB with → = 2a and OB → = 4b OA → in terms of a and b (a) Find AB (2) The point P
- November 2021, Paper 1, Q8 (15 marks): b A B Diagram NOT accurately drawn a O C E D Figure 3 → = a and AB → = b Figure 3 shows the regular hexagon OABCDE with OA → in terms of a and b (a) Find OB (1)
- June 2021, Paper 1, Q10 (14 marks): A Diagram NOT accurately drawn D F O B C Figure 1 Figure 1 shows triangle OAB and triangle OCD. → = 5p AB → = 3q OC → = 3 → OD → = 3 → OA 2 OB 5 OA → as a simpl
- November 2020 (R), Paper 1, Q11 (13 marks): X Diagram NOT accurately drawn A Z O B Y Figure 1 Figure 1 shows a triangle OXY → = 2a and OY → = 3b OX A is the midpoint of OX and B is the point on OY such th
- November 2020, Paper 1, Q11 (13 marks): A Diagram NOT accurately drawn D O C B Figure 5 → = a and OB → = b In Figure 5, OA The point C divides OB in the ratio 1 : 3 The point D is the midpoint of AC (
- January 2020 (R), Paper 1, Q10 (11 marks): A B Diagram NOT accurately drawn 2a − b –a + 3b 3a + b O C Figure 1 Figure 1 shows quadrilateral OABC with → = 2a − b OB → = 3a + b BC → = –a + 3b OA → as a sim
- January 2020, Paper 1, Q10 (13 marks): M A B X a N Diagram NOT accurately drawn c O C Figure 3 Figure 3 shows the parallelogram OABC → = a OC → = c OA The midpoint of AB is M and the midpoint of BC i
- January 2020, Paper 2, Q4 (7 marks): The points A, B, C and D are the vertices of a quadrilateral ABCD such that → = 7i + pj AC → = 11i – pj AD → = 4i – 2pj AB (a) Show that, for all values of p, A
- June 2019 (R), Paper 1, Q7 (8 marks): O, A, B and C are fixed points such that o i í j OB o = 15i í j OC o i + j OA o as a simplified expression in terms of i and j (a) Find BC (2) o (b) Find a unit
- June 2019, Paper 2, Q1 (4 marks): Referred to a fixed origin O, the point A has position vector (4i + 3j) and the point B has position vector (i + 7j) ĺ as a simplified expression in terms of i
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