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Subjects · Leaving Certificate

Leaving Cert Applied Maths

What has come up on the Applied Maths papers (2023–2025), topic by topic, with step-by-step practice at Higher Level and Ordinary Level.

Higher Level Ordinary Level

Applied Maths, Higher Level(6 marks)

Three quick ones from the Applied Maths topics that come up most.

(a)Given v as a function of t, how do you find displacement?
  1. Differentiate v with respect to t
  2. Integrate v with respect to t
  3. Multiply v by t
(b)Why is a string in a pulley problem modelled as light and inextensible?
  1. So the two masses have equal weights and balance
  2. So there is no friction at the pulley or on the table
  3. So tension is uniform and both masses share one acceleration
(c)Convert 72 km/h to m/s.
  1. 20 m/s
  2. 259.2 m/s
  3. 25 m/s
Show the answers

(a) Integrate v with respect to t

(b) So tension is uniform and both masses share one acceleration

(c) 20 m/s

Your turn: pick the answer for each one.

Higher Level

400 flash cards and 240 step-by-step drill questions at Higher Level.

What comes up

How many of the last 3 Applied Maths Higher Level papers asked each topic.

TopicAskedLast seenHow often
Constant acceleration (suvat) banker3 of 32025
Friction & inclined planes banker3 of 32025
Projectile motion banker3 of 32025
Second-order difference equations banker3 of 32025
Separable differential equations banker3 of 32025
Calculus & variable acceleration banker3 of 32025
Connected particles & pulleys banker3 of 32025
Horizontal circular motion banker3 of 32025
Matrices & adjacency banker3 of 32025
Minimum spanning trees banker3 of 32025
Oblique collisions banker3 of 32025
Reducing second-order DEs banker3 of 32025
Resisted motion & drag banker3 of 32025
Vertical circular motion banker3 of 32025

More topics: Momentum & direct collisions, Dijkstra's algorithm, Dimensional analysis, Dynamic programming & Bellman, First-order difference equations, Project scheduling & critical path, Vectors & the dot product, Work, energy & conservation, Displacement & velocity graphs, Forces & Newton's laws, Graphs & network terminology, Greedy vs dynamic algorithms, Hooke's law & elastic energy.

Try three

Resisted motion & drag, 3 marks

∫ v/(g + kv²) dv = ?

  1. (1/k) ln(g + kv²) + c
  2. ln(g + kv²) + c
  3. (1/2k) ln(g + kv²) + c
Show the answer

(1/2k) ln(g + kv²) + c

The derivative of g + kv² is 2kv, so the top is 1/(2k) times that. So the integral is (1/2k) ln(g + kv²) + c. This appears when a ball rises against drag kv².

Vertical circular motion, 3 marks

0.2 kg on a string of radius 0.5 m, speed 5 m/s at the lowest point of a vertical circle (g = 9.8). Tension?

  1. 8.04 N
  2. 11.96 N
  3. 10.00 N
Show the answer

11.96 N

At the bottom T − mg = mv²/r, so T = 1.96 + 0.2 × 25 ÷ 0.5 = 1.96 + 10 = 11.96 N. 8.04 N subtracts the weight, which is the top-of-circle form.

Oblique collisions, 3 marks

A (1 kg, 6i + 3j m/s) hits B (2 kg) at rest; line of centres along i, e = ½. A's velocity after?

  1. 3j m/s
  2. 2i + 3j m/s
  3. −2i + 3j m/s
Show the answer

3j m/s

Along i: PCM v₁ + 2v₂ = 6, NEL v₂ − v₁ = 3. So 3v₁ = 0, v₁ = 0 and v₂ = 3. A keeps its j-part, so it moves off at 3j. 2i + 3j is the e = 0 answer.

Practise Applied Maths HL free

Ordinary Level

300 flash cards and 150 step-by-step drill questions at Ordinary Level.

What comes up

How many of the last 3 Applied Maths Ordinary Level papers asked each topic.

TopicAskedLast seenHow often
First-order difference equations banker3 of 32025
Constant acceleration (suvat) banker3 of 32025
Friction & inclined planes banker3 of 32025
Minimum spanning trees banker3 of 32025
The modelling cycle & assumptions banker3 of 32025
Connected particles & pulleys banker3 of 32025
Dijkstra's algorithm banker3 of 32025
Displacement & velocity graphs banker3 of 32025
Forces & Newton's laws banker3 of 32025
Graphs & network terminology banker3 of 32025
Horizontal circular motion banker3 of 32025
Loans, savings & finance models banker3 of 32025
Matrices & adjacency banker3 of 32025
Momentum & direct collisions banker3 of 32025

More topics: Projectile motion, Recurrence relations & differences, Second-order difference equations, Vectors & the dot product, Dimensional analysis, Project scheduling & critical path, Work, energy & conservation, Dynamic programming & Bellman.

Try three

Loans, savings & finance models, 3 marks

€1000 is saved at 2% per year compound interest. Value after 2 years?

  1. €1040.00
  2. €1020.00
  3. €1040.40
Show the answer

€1040.40

Multiply by 1.02 each year: 1000 × 1.02 = 1020, then 1020 × 1.02 = €1040.40. €1040 is simple interest, which ignores interest on interest.

Friction & inclined planes, 3 marks

2 kg block, rough level floor, μ = 0.4, pushed with 10 N. Does it move? (g = 9.8 m s⁻²)

  1. No, friction is always 10 N
  2. Yes, 10 N is more than 7.84 N
  3. No, 10 N is less than 19.6 N
Show the answer

Yes, 10 N is more than 7.84 N

R = 2 × 9.8 = 19.6 N. Maximum friction = 0.4 × 19.6 = 7.84 N. The push beats the most friction can give, so it moves.

Momentum & direct collisions, 3 marks

2 kg sphere at 6 m s⁻¹ hits a 1 kg sphere at rest, e = ½. Velocity of the 1 kg sphere after?

  1. 6 m s⁻¹
  2. 3 m s⁻¹
  3. 12 m s⁻¹
Show the answer

6 m s⁻¹

PCM: 2v₁ + v₂ = 12. NEL: v₂ − v₁ = ½ × 6 = 3. Solving, v₁ = 3 and v₂ = 6 m s⁻¹.

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