Periodic Test-2 — Practice Papers
Chapters 1–6 · five full papers of 40 marks each, plus worked solutions to the school's revision worksheet.
Suggested order
Revise the concepts
All six chapters, topic by topic: key ideas, rules, worked examples, common mistakes and a self-check list for each chapter.
0 · School worksheet
All 16 "Do as directed" questions from the school's PT-2 revision worksheet, solved step by step, with the 22 definitions in one table.
Paper 1
Factors, factor tree, divisibility of 4,356, shoe-size tally, odd-number squares, tiling a hall, sports bar graph, clock angles.
Paper 2
Co-primes, 5 points on a line, tree pictograph, Kaprekar 495, factorising 2520, Koch snowflake, garden path, library bar graph.
Paper 3
Rays and angles, L-shape perimeter, missing digits for 3/8/11, powers of 2 and 3, ice-cream pictograph, Jumpy & Grumpy, compass turns.
Paper 4
Diagonals via complete graphs, triangle in a rectangle, parity, "divisible by 4 & 6 ⇒ 24?", Akshi & Toshi, museum bar graph, Idli-Vada.
Paper 5 — the toughest
Remainder puzzle, reflex-angle drawing, supercells, greatest 4-digit number divisible by 2–10, clock at 2:30, Sieve of Eratosthenes.
Paper pattern
| Section | Type | Questions | Marks |
|---|---|---|---|
| A | Multiple choice (6) + Assertion–Reason (2) | 8 × 1 | 8 |
| B | Do as directed — short working, a drawing or a definition | 6 × 2 | 12 |
| C | Short answer — multi-step | 4 × 3 | 12 |
| D | Long answer — graph drawing and case studies | 2 × 4 | 8 |
| Total | 20 questions · 1½ hours | 40 |
Each paper covers all six chapters. Chapter 5 (Prime Time) and Chapter 4 (Data Handling) carry the most marks, because the school worksheet leans heavily on them. Open "Blueprint" at the top of any paper to see that paper's chapter-wise marks. ★ marks the challenging questions.
Facts most worth remembering
Numbers
- 25 primes up to 100; 2 is the only even prime; 1 is neither prime nor composite.
- Co-prime = only common factor is 1 (they need not be prime).
- Divisibility by 4 → last 2 digits; by 8 → last 3 digits; by 3 or 9 → digit sum; by 11 → alternate sums.
- Divisible by co-prime a and b ⇒ divisible by a × b (3 and 8 ⇒ 24, but 4 and 6 ⇏ 24).
- 1 + 3 + 5 + … (n odd numbers) = n × n; Kaprekar: 6174 (4 digits), 495 (3 digits).
Shapes & data
- Clock: 30° per hour mark; minute hand 6° per minute; hour hand moves too (2:30 → 105°).
- Reflex angle = 360° − smaller angle; draw it by drawing the smaller one first.
- Rectangle P = 2(l + b), A = l × b; a right triangle in a rectangle is half its area.
- Cutting a corner notch: area drops, perimeter stays the same.
- Bar graph: equal widths, equal gaps, a scale starting at 0, a title — and always state the scale.