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Numerical and quantitative thinking

Numerical reasoning

Arithmetic, fractions, percentages, ratios, rates, estimation, word problems, and number relationships.

Lesson

Start with the shared skill lesson — objectives, worked examples, and glossary.

Open skill lesson

Diagnostic practice

100 questions published across 10 sections. Every question is written for this skill specifically — no universal or borrowed bank is substituted. Answers are checked on this device only, and the result is an educational practice band for that exercise, never a clinical, diagnostic, or IQ-style score.

Choose a section

This bank has 10 themed sections and 100 questions in total, ordered so the earlier sections are the gentler ones. Sit a single section, or work through the whole bank in one go. Nothing here is timed — the minutes are only a guide.

  1. 1. Everyday arithmetic10 questions · about 9 min, untimed
  2. 2. Fractions and decimals10 questions · about 9 min, untimed
  3. 3. Percentages10 questions · about 9 min, untimed
  4. 4. Ratios and proportion10 questions · about 9 min, untimed
  5. 5. Rates, time, and conversions10 questions · about 9 min, untimed
  6. 6. Money and financial arithmetic10 questions · about 9 min, untimed
  7. 7. Averages and simple data10 questions · about 9 min, untimed
  8. 8. Number sequences and relationships10 questions · about 9 min, untimed
  9. 9. Multi-step word problems10 questions · about 9 min, untimed
  10. 10. Compound change and combined rates10 questions · about 9 min, untimed

Section 1: Everyday arithmetic

Warm up with whole-number addition, subtraction, multiplication, and division.

1. One shelf holds 24 books and a second shelf holds 38 books. How many books are there altogether?
2. A box of 96 pencils is shared equally among 8 pupils. How many pencils does each pupil receive?
3. Cinema tickets cost £9 each. What is the total cost of 7 tickets?
4. A tank holds 500 litres of water. If 137 litres are drained out, how many litres remain?
5. What is the value of 18 − 12 ÷ 3?
6. A train has 6 carriages and each carriage seats 72 passengers. How many seats does the train have in total?
7. A crate contains 12 boxes, and each box holds 15 apples. How many apples are in the crate?
8. 75 chairs are arranged into complete rows of 9, with any spare chairs left at the side. How many chairs are left over?
9. What is the value of 7 × 8 − 6?
10. A shop opens at 9:00 am and closes at 5:30 pm. For how many hours is it open?

0 of 10 answered

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