Irish Numerical Reasoning study materials
Irish Numerical Reasoning study resources

Irish Numerical Reasoning study plan

Irish Numerical Reasoning · Give each week a clear focus.

8 weeks · About 7 hours per week

Week 1

Number series and sequences

  • Classify number series by rule type (arithmetic, geometric, alternating, interleaved, difference-of-difference, square/cube-based) and label 30 given series by type

  • Compute next-term and missing-term answers for 40 arithmetic and geometric series without a calculator

  • Derive the rule for 20 difference-of-difference series by writing first and second differences by hand

  • Time yourself solving 15 mixed series in 20 minutes and log accuracy

Your checkpoint

A 50-item handwritten series log with rule type, working, and answer for each, scored for accuracy

Week 2

Number series and sequences & Approximation and estimation

  • Solve 25 interleaved (two-strand) and alternating-operation series, marking which strand each term belongs to

  • Estimate next-term answers for 20 series by rounding to the nearest convenient value and comparing to the exact answer

  • Identify and correct your three most frequent error patterns from week 1

  • Complete a 25-question series set under 30 minutes with at least 80% accuracy

Your checkpoint

A timed 25-question series test with a written error-pattern analysis of every miss

Week 3

Arithmetic word problems

  • Translate 20 word problems into a single equation or short chain of operations before solving

  • Solve 25 multi-step problems involving money, age, mixtures, and sharing, showing each intermediate value

  • Solve 15 problems with unit mismatches (minutes vs hours, grams vs kilograms) and state the conversion used

  • Build a one-page checklist of question phrasings that signal each operation

Your checkpoint

A 25-problem worked set with full multi-step solutions and a completed phrasing checklist

Week 4

Arithmetic word problems & Percentages, ratios and proportions

  • Solve 20 percentage problems covering increase, decrease, reverse percentage, and successive percentage change

  • Set up and solve 15 ratio and proportion problems including part-to-whole, sharing, and scaling

  • Convert 20 fractions, decimals, and percentages fluently in both directions

  • Complete a 30-question mixed arithmetic and percentage set under 40 minutes

Your checkpoint

A 30-question mixed set scored against a target of 85% or higher

Week 5

Percentages, ratios and proportions

  • Solve 20 problems combining ratios with percentages, such as profit share after a percentage change

  • Solve 15 direct and inverse proportion problems and justify which type applies

  • Apply the unitary method to 15 problems and verify each answer by a second method

  • Rank your weakest three sub-skills and redo 10 problems in each

Your checkpoint

A one-page method summary plus 20 solved combined ratio-percentage problems

Week 6

Data interpretation from tables and charts

  • Read 6 self-written data tables and extract totals, averages, and percentage shares accurately

  • Compute percentage change between rows and columns across 20 table-based questions

  • Answer 15 chart-style questions (bar, line, pie) described in text, showing the arithmetic used

  • Practise rounding intermediate values only at the final step across 15 questions

Your checkpoint

A 25-question data interpretation set with a full calculation trail for each answer

Week 7

Speed, distance, time and work-rate problems & Approximation and estimation

  • Solve 20 speed-distance-time problems including average speed over two legs and unit conversion between km/h and m/s

  • Solve 15 work-rate problems including combined workers and pipes filling and emptying

  • Estimate answers to 20 mixed problems within 10% before calculating exactly, then compare

  • Reduce your average solve time on worked problems by at least 15% versus week 4

Your checkpoint

A 20-problem speed and work-rate set with estimated versus exact answers recorded side by side

Week 8

Number series and sequences & Arithmetic word problems & Percentages, ratios and proportions & Data interpretation from tables and charts & Speed, distance, time and work-rate problems & Approximation and estimation

  • Complete two full-length mixed mock tests under strict timing and record per-domain accuracy

  • Re-solve every question missed in both mocks and write the corrected method

  • Drill your two lowest-scoring domains with 15 targeted questions each

  • Finalise a one-page formula and method sheet covering all six domains

Your checkpoint

Two completed timed mocks with per-domain score breakdown and a final one-page formula sheet

Milestones

Week 2: Score 80% or higher on a timed 25-question number series test with no calculator

Week 4: Score 85% or higher on a 30-question mixed arithmetic and percentage set under 40 minutes

Week 6: Answer 20 of 25 data interpretation questions correctly with a written calculation trail for each

Week 8: Achieve 75% or higher overall on both full-length mocks with no domain below 60%