Mathematics — Numbers, Operations, Geometry & Measurement — Practice

Question 1

Write in Roman numerals: (a) 49 (b) 94 (c) 450.

Accepted Answer

Step 1 — Break each number into Roman numeral components.

(a) 49 = 40 + 9 = XL + IX = XLIX
(b) 94 = 90 + 4 = XC + IV = XCIV
(c) 450 = 400 + 50 = CD + L = CDL

✦ Answer: (a) XLIX (b) XCIV (c) CDL.

Question 2

List all prime numbers between 20 and 40.

Accepted Answer

Step 1 — Test each number from 21 to 39.
  21 = 3 × 7 (composite). 22 = 2 × 11 (composite). 23 = factors: 1, 23 only → PRIME.
  24, 25, 26, 27, 28, 29, 30: 29 = factors: 1, 29 only → PRIME.
  31 = factors: 1, 31 only → PRIME.
  32, 33, 34, 35, 36, 37: 37 = factors: 1, 37 only → PRIME.
  38, 39 = composite.

✦ Answer: 23, 29, 31, 37.

Question 3

Find all factors of 48.

Accepted Answer

Step 1 — List factor pairs (both numbers that multiply to 48):
  1 × 48, 2 × 24, 3 × 16, 4 × 12, 6 × 8. Next would be 8 × 6 — already seen, stop.

Step 2 — Collect all unique factors in order:
  1, 2, 3, 4, 6, 8, 12, 16, 24, 48. (10 factors total.)

✦ Answer: Factors of 48 = {1, 2, 3, 4, 6, 8, 12, 16, 24, 48}.

Question 4

Round each number: (a) 4,532 to nearest 100. (b) 7,865 to nearest 1,000.

Accepted Answer

(a) Nearest 100: look at tens digit of 4,532 → 3. Since 3 < 5 → round DOWN → 4,500.
(b) Nearest 1,000: look at hundreds digit of 7,865 → 8. Since 8 ≥ 5 → round UP → 8,000.

✦ Answer: (a) 4,500. (b) 8,000.

Question 5

A strip of cloth is 7/9 m long. A piece of 2/9 m is cut off. What length remains? Then find 4/11 + 5/11.

Accepted Answer

Strip remaining: 7/9 − 2/9 = (7−2)/9 = 5/9 m.
(Like fractions: subtract numerators, keep denominator 9.)

4/11 + 5/11 = (4+5)/11 = 9/11.
(Like fractions: add numerators, keep denominator 11.)

✦ Answer: Remaining cloth = 5/9 m. 4/11 + 5/11 = 9/11.

Question 6

Draw and name a shape with (a) exactly 2 lines of symmetry, (b) 0 lines of symmetry. Also: name the angle type for 45°, 90°, 130°.

Accepted Answer

(a) 2 lines of symmetry: RECTANGLE (horizontal and vertical midlines are lines of symmetry; diagonals are NOT).
(b) 0 lines of symmetry: SCALENE TRIANGLE (all sides different, no fold creates matching halves).

Angle types:
  45° → ACUTE (less than 90°, sharp angle)
  90° → RIGHT (exactly 90°, like a corner of a square)
  130° → OBTUSE (more than 90° but less than 180°, 'wide' angle)

✦ Answer: Rectangle (2), Scalene triangle (0). Angles: 45°=acute, 90°=right, 130°=obtuse.

Question 7

Find the next two terms: (a) 4, 8, 16, 32, ___, ___. (b) 100, 91, 82, 73, ___, ___.

Accepted Answer

(a) Each term is DOUBLED (multiplied by 2).
  32 × 2 = 64. 64 × 2 = 128.
  Pattern: 4, 8, 16, 32, 64, 128.

(b) Each term DECREASES by 9 (arithmetic pattern, common difference = −9).
  73 − 9 = 64. 64 − 9 = 55.
  Pattern: 100, 91, 82, 73, 64, 55.

✦ Answer: (a) 64, 128. (b) 64, 55.

Question 8

A school buys 1,248 notebooks to distribute equally among 6 classes. Each class then shares the notebooks equally among 8 students. How many notebooks does each student get? How many are left over, if any?

Accepted Answer

Step 1 — Divide 1,248 by 6 (one per class).
  1,248 ÷ 6:
  12 ÷ 6 = 2. 04 ÷ 6 = 0 remainder 4. 48 ÷ 6 = 8.
  So 1,248 ÷ 6 = 208 notebooks per class. Remainder = 0.

Step 2 — Divide 208 by 8 (per student).
  208 ÷ 8:
  20 ÷ 8 = 2 remainder 4. 48 ÷ 8 = 6.
  So 208 ÷ 8 = 26 notebooks per student. Remainder = 0.

Verify: 26 × 8 × 6 = 26 × 48 = 1,248 ✓

✦ Answer: Each student gets 26 notebooks. No notebooks are left over.

Question 9

Is every odd number prime? Justify your answer with examples and a counter-example. Also: between 50 and 60, find all prime numbers.

Accepted Answer

CLAIM: 'Every odd number is prime.' This is FALSE.

Counter-examples of odd COMPOSITE numbers:
  9 = 3 × 3 (factors: 1, 3, 9 — three factors, so composite)
  15 = 3 × 5 (factors: 1, 3, 5, 15 — four factors, so composite)
  21 = 3 × 7 (factors: 1, 3, 7, 21 — four factors, so composite)
  25 = 5 × 5 (factors: 1, 5, 25 — three factors, so composite)

Conclusion: Some odd numbers are prime (3, 5, 7, 11, 13…) but many are NOT.
Note: 2 is even and prime — the ONLY even prime.

PRIMES between 50 and 60:
  51 = 3 × 17 (composite). 52, 54, 56, 58, 60 (all even). 53: test ÷2, ÷3, ÷5, ÷7 — none divide evenly → PRIME. 55 = 5 × 11 (composite). 57 = 3 × 19 (composite). 59: test ÷2, ÷3, ÷5, ÷7 — none divide evenly → PRIME.

✦ Answer: NOT all odd numbers are prime (e.g. 9, 15, 25 are odd composites). Primes between 50 and 60: 53 and 59.

Practice — Mathematics — Numbers, Operations, Geometry & Measurement

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