Scalars and vectors
1.4What the syllabus asks of you
- understand the difference between scalar and vector quantities and give examples of scalar and vector quantities included in the syllabus
- add and subtract coplanar vectors
- represent a vector as two perpendicular components
Read the notes first
Chapter 1: Scalars and vectors
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Every question on Scalars and vectors, untimed, marked as you go.
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79 questions
1May / June 2026 · Paper 11 · Q4Show mark scheme →
A1 N
B5 N
C7 N
D13 N
Mark scheme
2May / June 2026 · Paper 12 · Q1Show mark scheme →
Ascalar quantities: energy and work; vector quantities: momentum and power
Bscalar quantities: energy and momentum; vector quantities: force and power
Cscalar quantities: energy and power; vector quantities: force and momentum
Dscalar quantities: momentum and power; vector quantities: force and velocity
Mark scheme
3May / June 2026 · Paper 13 · Q1Show mark scheme →
Adensity
Bmass
Cpressure
Dweight
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4May / June 2026 · Paper 13 · Q4Show mark scheme →
A14 N
B16 N
C17 N
D18 N
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5Oct / Nov 2025 · Paper 11 · Q1Show mark scheme →
Aacceleration: scalar, charge: vector, kinetic energy: vector, wavelength: scalar
Bacceleration: vector, charge: vector, kinetic energy: scalar, wavelength: scalar
Cacceleration: scalar, charge: scalar, kinetic energy: scalar, wavelength: vector
Dacceleration: vector, charge: scalar, kinetic energy: scalar, wavelength: scalar
Mark scheme
6Oct / Nov 2025 · Paper 11 · Q4Show mark scheme →
A6.0 N
B7.9 N
C10 N
D12 N
Mark scheme
7Oct / Nov 2025 · Paper 13 · Q1Show mark scheme →
Aacceleration: scalar, charge: vector, kinetic energy: vector, wavelength: scalar
Bacceleration: vector, charge: vector, kinetic energy: scalar, wavelength: scalar
Cacceleration: scalar, charge: scalar, kinetic energy: scalar, wavelength: vector
Dacceleration: vector, charge: scalar, kinetic energy: scalar, wavelength: scalar
Mark scheme
8Oct / Nov 2025 · Paper 13 · Q4Show mark scheme →
A6.0 N
B7.9 N
C10 N
D12 N
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9May / June 2025 · Paper 11 · Q1Show mark scheme →
Apressure
Btemperature
Cweight
Dwork
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10May / June 2025 · Paper 11 · Q4Show mark scheme →
AX + Y: horizontal arrow to the right; X − Y: vertical arrow downwards
BX + Y: horizontal arrow to the right; X − Y: vertical arrow upwards
CX + Y: horizontal arrow to the left; X − Y: vertical arrow downwards
DX + Y: horizontal arrow to the left; X − Y: vertical arrow upwards
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11May / June 2025 · Paper 13 · Q1Show mark scheme →
A1 N upwards
B2 kg decrease
C3 K cooler
D4 s later
Mark scheme
12May / June 2025 · Paper 14 · Q4Show mark scheme →
A2.4 N
B3.2 N
C4.8 N
D6.4 N
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13Feb / March 2025 · Paper 12 · Q1Show mark scheme →
Aforce
Bmomentum
Cvelocity
Dwork
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14Oct / Nov 2024 · Paper 11 · Q2Show mark scheme →
AAcceleration of free fall is a vector quantity because it has a constant magnitude.
BTemperature in °C is a vector quantity because it can be positive or negative.
CTime is a vector quantity because it can only go in the forwards direction.
DWeight is a vector quantity because it has a direction.
Mark scheme
15May / June 2024 · Paper 11 · Q3Show mark scheme →
Avector A
Bvector B
Cvector C
Dvector D
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16May / June 2024 · Paper 11 · Q5Show mark scheme →
Acurrent × time
Bfinal displacement – initial displacement
C\frac{\text{work done}}{\text{time}}
D\frac{1}{2} \times \text{mass} \times (\text{speed})^2
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17May / June 2024 · Paper 11 · Q16Show mark scheme →
A3/5 T
B6/5 T
C8/5 T
D2T
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18May / June 2024 · Paper 12 · Q1Show mark scheme →
Aa quantity that can be represented as two perpendicular components
Ba quantity that does not require a unit
Ca quantity without a direction
Da quantity without a magnitude
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19May / June 2024 · Paper 12 · Q9Show mark scheme →
A5 m s⁻¹ to the left
B5 m s⁻¹ to the right
C11 m s⁻¹ to the left
D11 m s⁻¹ to the right
Mark scheme
20May / June 2024 · Paper 13 · Q4Show mark scheme →
A(force) × (displacement of an object in the direction of the force)
B(mass) × (acceleration of the mass)
C(pressure) × (area on which the pressure acts)
D(velocity) × (time for which an object has that velocity)
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21Feb / March 2024 · Paper 12 · Q5Show mark scheme →
A5.5 m s⁻¹
B6.1 m s⁻¹
C12 m s⁻¹
D14 m s⁻¹
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22Oct / Nov 2023 · Paper 11 · Q4Show mark scheme →
A
B
C
D
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23Oct / Nov 2023 · Paper 13 · Q4Show mark scheme →
Aθ = 42°, v = 4.5 m s⁻¹
Bθ = 42°, v = 7.2 m s⁻¹
Cθ = 48°, v = 4.5 m s⁻¹
Dθ = 48°, v = 7.2 m s⁻¹
Mark scheme
24May / June 2023 · Paper 11 · Q4Show mark scheme →
A5 N
B10 N
C17 N
D20 N
Mark scheme
25May / June 2023 · Paper 12 · Q4Show mark scheme →
A
B
C
D
Mark scheme
26May / June 2023 · Paper 13 · Q4Show mark scheme →
Adiagram A
Bdiagram B
Cdiagram C
Ddiagram D
Mark scheme
27Oct / Nov 2022 · Paper 11 · Q4Show mark scheme →
Amomentum
Bspeed
Ctemperature
DYoung modulus
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28Oct / Nov 2022 · Paper 12 · Q4Show mark scheme →
AA scalar quantity has direction but a vector quantity does not.
BA scalar quantity has magnitude but a vector quantity does not.
CA vector quantity has direction but a scalar quantity does not.
DA vector quantity has magnitude but a scalar quantity does not.
Mark scheme
29Oct / Nov 2022 · Paper 13 · Q4Show mark scheme →
Adensity
Bmass
Cvolume
Dweight
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30May / June 2022 · Paper 11 · Q4Show mark scheme →
Ahorizontal component 9.73 N, vertical component 0.534 N
Bhorizontal component 9.73 N, vertical component 10.2 N
Chorizontal component 18.0 N, vertical component 0.534 N
Dhorizontal component 18.0 N, vertical component 10.2 N
Mark scheme
31May / June 2022 · Paper 12 · Q4Show mark scheme →
A
B
C
D
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32May / June 2022 · Paper 13 · Q5Show mark scheme →
A0 N
B5 N
C8 N
D13 N
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33Feb / March 2022 · Paper 12 · Q4Show mark scheme →
AA scalar quantity has direction but not magnitude.
BA scalar quantity has magnitude but not direction.
CA vector quantity has direction but not magnitude.
DA vector quantity has magnitude but not direction.
Mark scheme
34Oct / Nov 2021 · Paper 11 · Q3Show mark scheme →
Aθ = 14°, resultant velocity = 770 km h⁻¹
Bθ = 14°, resultant velocity = 820 km h⁻¹
Cθ = 76°, resultant velocity = 770 km h⁻¹
Dθ = 76°, resultant velocity = 820 km h⁻¹
Mark scheme
35Oct / Nov 2021 · Paper 12 · Q3Show mark scheme →
Av sinθ
Bv_y cosθ
Cv_y sinθ
D(v² − v_y²)^(1/2)
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36Oct / Nov 2021 · Paper 13 · Q3Show mark scheme →
Aacceleration, displacement, force, weight
Bdensity, energy, frequency, velocity
Cdistance, pressure, temperature, time
Dmomentum, power, volume, wavelength
Mark scheme
37May / June 2021 · Paper 11 · Q3Show mark scheme →
A10 cos 30° – 5 | 10 cos 30°
B10 sin 30° – 5 | 10 cos 30°
C10 – 5 cos 30° | 5 sin 30°
D10 – 5 sin 30° | 5 cos 30°
Mark scheme
38May / June 2021 · Paper 12 · Q3Show mark scheme →
A15 N at 15° to the vertical
B15 N at 18° to the vertical
C7.7 N at 37° to the vertical
D6.6 N at 36° to the vertical
Mark scheme
39May / June 2021 · Paper 13 · Q3Show mark scheme →
A12 N
B16 N
C25 N
D27 N
Mark scheme
40Feb / March 2021 · Paper 12 · Q3Show mark scheme →
Anortherly 38, easterly 38
Bnortherly 38, easterly 65
Cnortherly 65, easterly 38
Dnortherly 65, easterly 65
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41Oct / Nov 2020 · Paper 11 · Q3Show mark scheme →
Adiagram A
Bdiagram B
Cdiagram C
Ddiagram D
Mark scheme
42Oct / Nov 2020 · Paper 12 · Q3Show mark scheme →
AGraph A: P starts at maximum at θ = 0 and decreases to 0 at θ = 90°
BGraph B: P starts at 0 at θ = 0 and increases to maximum at θ = 90°
CGraph C: P starts at 0 at θ = 0 and increases to maximum at θ = 90°
DGraph D: P starts at maximum at θ = 0 and decreases to 0 at θ = 90°
Mark scheme
43Oct / Nov 2020 · Paper 13 · Q3Show mark scheme →
Adisplacement and distance
Bforce and momentum
Ctorque and time
Dweight and pressure
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44May / June 2020 · Paper 11 · Q3Show mark scheme →
Ascalars: displacement, time; vectors: force, power
Bscalars: power, work; vectors: displacement, force
Cscalars: power, force; vectors: displacement, work
Dscalars: work, time; vectors: power, displacement
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45May / June 2020 · Paper 12 · Q2Show mark scheme →
Aacceleration
Bforce
Ckinetic energy
Dmomentum
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46May / June 2020 · Paper 13 · Q3Show mark scheme →
Adirection only
Bmagnitude and direction
Cmagnitude and unit
Dunit only
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47Feb / March 2020 · Paper 12 · Q3Show mark scheme →
Aacceleration and momentum
Bcharge and resistance
Ckinetic energy and mass
Dtemperature and velocity
Mark scheme
48Oct / Nov 2019 · Paper 11 · Q3Show mark scheme →
Adiagram A
Bdiagram B
Cdiagram C
Ddiagram D
Mark scheme
49Oct / Nov 2019 · Paper 12 · Q3Show mark scheme →
Aarea, length, displacement
Bkinetic energy, speed, power
Cpotential energy, momentum, time
Dvelocity, distance, temperature
Mark scheme
50Oct / Nov 2019 · Paper 12 · Q12Show mark scheme →
A[diagram A: triangle with resultant F]
B[diagram B: triangle with resultant F]
C[diagram C: triangle with resultant F]
D[diagram D: triangle with resultant F]
Mark scheme
51Oct / Nov 2019 · Paper 13 · Q3Show mark scheme →
Adiagram A
Bdiagram B
Cdiagram C
Ddiagram D
Mark scheme
52May / June 2019 · Paper 11 · Q3Show mark scheme →
Amagnitude of V: √(Vv² + Vh²), θ: tan⁻¹(Vh/Vv)
Bmagnitude of V: √(Vv² + Vh²), θ: tan⁻¹(Vv/Vh)
Cmagnitude of V: √(Vv² − Vh²), θ: tan⁻¹(Vh/Vv)
Dmagnitude of V: √(Vv² − Vh²), θ: tan⁻¹(Vv/Vh)
Mark scheme
53May / June 2019 · Paper 12 · Q4Show mark scheme →
Ahorizontal component / N: 9.73, vertical component / N: 0.534
Bhorizontal component / N: 9.73, vertical component / N: 10.2
Chorizontal component / N: 18.0, vertical component / N: 0.534
Dhorizontal component / N: 18.0, vertical component / N: 10.2
Mark scheme
54May / June 2019 · Paper 13 · Q3Show mark scheme →
A3.1 kN
B5.2 kN
C7.0 kN
D7.3 kN
Mark scheme
55Feb / March 2019 · Paper 12 · Q3Show mark scheme →
A23.0° east of north
B23.0° west of north
C25.2° east of north
D25.2° west of north
Mark scheme
56Oct / Nov 2018 · Paper 11 · Q3Show mark scheme →
Aeast 4.0, north 4.0
Beast 4.0, north 6.9
Ceast 4.6, north 6.9
Deast 6.9, north 4.0
Mark scheme
57Oct / Nov 2018 · Paper 12 · Q3Show mark scheme →
Aacceleration, momentum, velocity, weight
Barea, current, force, work
Cdistance, kinetic energy, power, pressure
Dmass, temperature, time, speed
Mark scheme
58Oct / Nov 2018 · Paper 12 · Q4Show mark scheme →
A
B
C
D
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59Oct / Nov 2018 · Paper 13 · Q3Show mark scheme →
Aacceleration, displacement, speed
Bacceleration, work, electric field strength
Cdisplacement, force, velocity
Dpower, electric field strength, force
Mark scheme
60May / June 2018 · Paper 11 · Q2Show mark scheme →
Akinetic energy and force
Bmomentum and time
Cvelocity and electric field strength
Dweight and temperature
Mark scheme
61May / June 2018 · Paper 11 · Q3Show mark scheme →
A80 N
B170 N
C270 N
D320 N
Mark scheme
62May / June 2018 · Paper 12 · Q15Show mark scheme →
Aarrow pointing down-left
Barrow pointing down-right
Carrow pointing up-left
Darrow pointing up-right
Mark scheme
63May / June 2018 · Paper 13 · Q2Show mark scheme →
Adisplacement and acceleration
Bforce and kinetic energy
Cpower and speed
Dwork and potential energy
Mark scheme
64May / June 2018 · Paper 13 · Q3Show mark scheme →
Ahorizontal component: F cosθ; vertical component: F cos (90° – θ)
Bhorizontal component: F cosθ; vertical component: F sin (90° – θ)
Chorizontal component: F sinθ; vertical component: F cosθ
Dhorizontal component: F sinθ; vertical component: F cos (90° – θ)
Mark scheme
65Feb / March 2018 · Paper 12 · Q3Show mark scheme →
Atowards the north-east
Btowards the north-west
Ctowards the south-east
Dtowards the south-west
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66Oct / Nov 2017 · Paper 11 · Q2Show mark scheme →
A5 N
B10 N
C17 N
D20 N
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67Oct / Nov 2017 · Paper 11 · Q6Show mark scheme →
A37° east of north
B37° west of north
C53° east of north
D53° west of north
Mark scheme
68Oct / Nov 2017 · Paper 12 · Q2Show mark scheme →
A3.0 km
B3.8 km
C4.0 km
D5.0 km
Mark scheme
69Oct / Nov 2017 · Paper 13 · Q3Show mark scheme →
A12 N
B16 N
C20 N
D27 N
Mark scheme
70May / June 2017 · Paper 11 · Q2Show mark scheme →
A27°
B30°
C45°
D60°
Mark scheme
71May / June 2017 · Paper 13 · Q2Show mark scheme →
A10.0 N at an angle of 37° downwards from the direction of X
B10.0 N at an angle of 37° upwards from the direction of X
C14.0 N at an angle of 53° downwards from the direction of X
D14.0 N at an angle of 53° upwards from the direction of X
Mark scheme
72Feb / March 2017 · Paper 12 · Q18Show mark scheme →
A12.9 m s⁻¹
B20.7 m s⁻¹
C25.1 m s⁻¹
D33.1 m s⁻¹
Mark scheme
73Oct / Nov 2016 · Paper 11 · Q3Show mark scheme →
Avector diagram A
Bvector diagram B
Cvector diagram C
Dvector diagram D
Mark scheme
74Oct / Nov 2016 · Paper 12 · Q3Show mark scheme →
Ascalar, scalar
Bscalar, vector
Cvector, scalar
Dvector, vector
Mark scheme
75Oct / Nov 2016 · Paper 13 · Q3Show mark scheme →
Avector diagram A
Bvector diagram B
Cvector diagram C
Dvector diagram D
Mark scheme
76May / June 2016 · Paper 11 · Q1Show mark scheme →
AR
BR
CR
DR
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77May / June 2016 · Paper 12 · Q3Show mark scheme →
Adiagram A
Bdiagram B
Cdiagram C
Ddiagram D
Mark scheme
78May / June 2016 · Paper 13 · Q3Show mark scheme →
A
B
C
D
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79May / June 2016 · Paper 13 · Q8Show mark scheme →
A2.0 m
B2.0 m due south
C3.1 m
D3.1 m due south
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