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Subjects · Leaving Cert Applied Maths

Leaving Cert Applied Maths: Work, energy & conservation

How often Work, energy & conservation comes up on the Applied Maths papers, every year it was asked, and questions to try.

HL Asked on 1 of the last 3 Higher Level papers, most recently in 2025.

OL Asked on 2 of the last 3 Ordinary Level papers, most recently in 2024. most years

Work, energy & conservation, Higher Level(8 marks)

Quick ones on Work, energy & conservation.

(a)When is total mechanical energy (KE + PE) conserved?
  1. When the body moves at constant speed (no acceleration)
  2. When only gravity does work (no friction or drag)
  3. Whenever the total momentum is conserved
(b)Work done lifting a 5 kg mass vertically through 3 m at steady speed (g = 9.8)?
  1. 49 J
  2. 15 J
  3. 147 J
(c)Kinetic energy of a 1500 kg car travelling at 20 m/s?
  1. 300 kJ
  2. 600 kJ
  3. 30 kJ
Show the answers

(a) When only gravity does work (no friction or drag)

(b) 147 J

(c) 300 kJ

Your turn: Higher Level questions on Work, energy & conservation.

Higher Level

Asked on 1 of the last 3 Higher Level papers, most recently in 2025.

Every paper, year by year

YearWhere it came up
2025Q4, Q9
2024Not asked
2023Not asked

Links open the State Examinations Commission’s paper for that year.

More Work, energy & conservation questions

Work, energy & conservation, 2 marks

How much work does the normal reaction do on a block sliding along a surface?

  1. mg × distance moved along the surface
  2. μR × distance moved along the surface
  3. None, it is perpendicular to the motion
Show the answer

None, it is perpendicular to the motion

Work = force component along the motion × distance. R is at 90° to the motion and cos 90° = 0. μR × distance is the work done against friction.

Work, energy & conservation, 3 marks

A block slides down a rough slope. The PE it loses equals…?

  1. The work done against friction only
  2. Its KE gain + work done against friction
  3. Its KE gain only
Show the answer

Its KE gain + work done against friction

Energy is conserved overall: some of the PE becomes KE and the rest does work against friction (lost as heat). KE gain alone would only be right on a smooth slope.

Work, energy & conservation, 3 marks

A 1000 kg car speeds up from 10 m/s to 20 m/s. Work done by the resultant force?

  1. 150 kJ
  2. 50 kJ
  3. 200 kJ
Show the answer

150 kJ

Work = change in KE = ½(1000)(20² − 10²) = 500 × 300 = 150 000 J = 150 kJ. Squaring the change in speed (10) would wrongly give 50 kJ.

Ordinary Level

Asked on 2 of the last 3 Ordinary Level papers, most recently in 2024. most years

Every paper, year by year

YearWhere it came up
2025Not asked
2024Q7
2023Q7

Links open the State Examinations Commission’s paper for that year.

More Work, energy & conservation questions

Work, energy & conservation, 3 marks

A child slides from rest down a smooth slide 10 m high. Speed at the bottom? (g = 9.8 m s⁻²)

  1. 196 m s⁻¹
  2. 7 m s⁻¹
  3. 14 m s⁻¹
Show the answer

14 m s⁻¹

PE lost = KE gained: mgh = ½mv², so v² = 2 × 9.8 × 10 = 196 and v = 14 m s⁻¹. The mass cancels. 196 is v², not v.

Work, energy & conservation, 2 marks

Work done by a 15 N force moving an object 4 m in the force's direction?

  1. 19 J
  2. 60 J
  3. 3.75 J
Show the answer

60 J

Work = force × distance moved in its direction = 15 × 4 = 60 J. One joule is one newton acting through one metre.

Work, energy & conservation, 3 marks

Kinetic energy of a 2 kg mass moving at 5 m s⁻¹?

  1. 25 J
  2. 10 J
  3. 50 J
Show the answer

25 J

KE = ½mv² = ½ × 2 × 5² = 25 J. 10 J is the momentum value (mv); 50 J forgets the ½.

Other Applied Maths topics

All of Leaving Cert Applied Maths