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Subjects · Leaving Certificate

Leaving Cert Maths

What has come up on the Maths papers (2016–2026), topic by topic, with step-by-step practice at Higher Level, Ordinary Level and Foundation Level.

Higher Level Ordinary Level Foundation Level

Maths, Higher Level(6 marks)

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

(a)Solve: 3x − 7 = 11
  1. x = 4/3
  2. x = 6
  3. x = 18
(b)i² = ?
  1. i
  2. 1
  3. −1
(c)Centre of (x − 2)² + (y + 5)² = 16?
  1. (2, −5)
  2. (2, 5)
  3. (−2, 5)
Show the answers

(a) x = 6

(b) −1

(c) (2, −5)

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 10 Maths Higher Level papers asked each topic.

TopicAskedLast seenHow often
Differentiation banker10 of 102026
Trigonometry banker10 of 102026
Probability banker10 of 102026
Algebra banker10 of 102026
Functions banker10 of 102026
Sequences & series banker10 of 102026
Integration banker10 of 102026
Statistics banker10 of 102026
Indices & logs banker10 of 102026
Length, area & volume banker10 of 102026
Coordinate geometry: circle banker10 of 102026
Geometry banker10 of 102026
Coordinate geometry: line banker10 of 102026
Complex numbers banker10 of 102026

More topics: Financial maths, Proof by induction, Number.

Try three

Complex numbers, 2 marks

(1 + 2i)² = ?

  1. 5 + 4i
  2. 1 + 4i
  3. −3 + 4i
Show the answer

−3 + 4i

(1 + 2i)² = 1 + 4i + 4i² = 1 + 4i − 4 = −3 + 4i.

Algebra, 2 marks

(x + 1) is a factor of x³ + k. What is k?

  1. 0
  2. 1
  3. −1
Show the answer

1

Factor theorem: f(−1) = 0, so (−1)³ + k = 0, giving −1 + k = 0 and k = 1.

Indices & logs, 2 marks

√(x³) as a power of x?

  1. x^(3/2)
  2. x^(2/3)
  3. x⁶
Show the answer

x^(3/2)

A square root is the power ½, so √(x³) = (x³)^(1/2) = x^(3/2).

Practise 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 10 Maths Ordinary Level papers asked each topic.

TopicAskedLast seenHow often
Algebra banker10 of 102026
Functions banker10 of 102026
Length, area & volume banker10 of 102026
Financial maths banker10 of 102026
Statistics banker10 of 102026
Probability banker10 of 102026
Trigonometry banker10 of 102026
Differentiation banker10 of 102026
Geometry banker10 of 102026
Coordinate geometry: line banker10 of 102026
Complex numbers banker10 of 102026
Coordinate geometry: circle banker10 of 102026
Number banker9 of 102026
Sequences & series banker9 of 102026

More topics: Indices.

Try three

Financial maths, 3 marks

€1,000 is invested at 5% compound interest for 2 years. What is it worth?

  1. €1,100
  2. €1,050
  3. €1,102.50
Show the answer

€1,102.50

F = 1000(1.05)² = 1000 × 1.1025 = €1,102.50. Year two earns interest on year one's interest too.

Coordinate geometry: circle, 3 marks

A circle has centre (−1, 2) and passes through (5, 10). Find its equation.

  1. (x + 1)² + (y − 2)² = 10
  2. (x + 1)² + (y − 2)² = 100
  3. (x − 1)² + (y + 2)² = 100
Show the answer

(x + 1)² + (y − 2)² = 100

r² = (5 + 1)² + (10 − 2)² = 36 + 64 = 100. Centre (−1, 2) gives (x + 1)² + (y − 2)², so the equation is (x + 1)² + (y − 2)² = 100.

Differentiation, 3 marks

A cost is C = 50 + 2x² euro. Find the rate of change dC/dx when x = 10.

  1. 40
  2. 250
  3. 20
Show the answer

40

dC/dx = 4x (50 gives 0). At x = 10: 4 × 10 = 40 euro per unit. 250 is the cost C at x = 10, not its rate of change.

Practise Maths OL free

Foundation Level

150 flash cards and 90 step-by-step drill questions at Foundation Level.

What comes up

How many of the last 7 Maths Foundation Level papers asked each topic.

TopicAskedLast seenHow often
Number banker7 of 72026
Financial maths banker7 of 72026
Length, area & volume banker7 of 72026
Geometry banker7 of 72026
Statistics banker7 of 72026
Probability banker7 of 72026
Functions banker7 of 72026
Trigonometry most years5 of 72026
Algebra 4 of 72025
Coordinate geometry: line 3 of 72025
Sequences & series 3 of 72026

Try three

Financial maths, 2 marks

€1,000 is saved at 3% compound interest per year. What is it worth after 1 year?

  1. €1,300
  2. €1,003
  3. €1,030
Show the answer

€1,030

3% of €1,000 = €30. Add it on: €1,000 + €30 = €1,030.

Length, area & volume, 2 marks

1 litre = 1000 cm³. How many cm³ are in 2.5 litres?

  1. 25 cm³
  2. 2,500 cm³
  3. 250 cm³
Show the answer

2,500 cm³

Multiply by 1000: 2.5 × 1000 = 2,500 cm³.

Statistics, 2 marks

10 out of 40 students walk to school. What percentage walk?

  1. 25%
  2. 10%
  3. 40%
Show the answer

25%

10/40 = 1/4, and 1/4 as a percentage is 25%.

Practise Maths FL free

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