Home / iGCSE Mathematics (0580) : C1.10 Give appropriate upper and lower bounds for data given to a specified accuracy. iGCSE Style Questions Paper 1

iGCSE Mathematics (0580) : C1.10 Give appropriate upper and lower bounds for data given to a specified accuracy. iGCSE Style Questions Paper 1

IGCSE Mathematics(0580) Practice Questions Paper 1 - All Chapters
Question

(a) Tanvi rounds the number 4896. She writes down 4900. Rahul says Tanvi rounded 4896 correct to the nearest 100. Explain why Rahul cannot be certain that Tanvi rounded 4896 correct to the nearest 100.

(b) Calculate \(\frac{6.4\times 4^{2}}{17.9-6.1}\). Give your answer correct to 3 decimal places.

▶️ Answer/Explanation
Answer:

(a) 4900 could result from rounding to different place values (e.g., nearest 10 or 100). Since 4896 rounds to 4900 in both cases, Rahul can’t be certain which method Tanvi used.

(b) Solution steps:

  1. Calculate numerator: 6.4 × 4² = 6.4 × 16 = 102.4
  2. Calculate denominator: 17.9 – 6.1 = 11.8
  3. Divide: 102.4 ÷ 11.8 ≈ 8.678 (to 3 decimal places)

Final answer: 8.678

Question

(a) The mass, $m$ kilograms, of object $A$ is $350$ kg, correct to the nearest 10 kg.
Complete this statement about the value of $m.$

(b) The mass of object $B$ is $348$ kg, correct to the nearest kilogram.
Show that the mass of object $B$ may be more than the mass of object $A.$

▶️ Answer/Explanation
Solution

(a) Ans: $345 \leq m < 355$

When rounding to the nearest 10 kg, the maximum error is $\pm 5$ kg. Thus, the mass $m$ of object $A$ lies in the range $350 \pm 5$ kg, which gives $345 \leq m < 355$.

(b)

Object $B$’s mass is $348 \pm 0.5$ kg, so $347.5 \leq m_B < 348.5$ kg. Object $A$’s minimum mass is $345$ kg, but its maximum is just under $355$ kg. However, if $m_A = 345$ kg (minimum) and $m_B = 348.4$ kg (within its range), then $m_B > m_A$, proving the statement.

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