Mark Scheme
(a) Calculate the percentage error in Aisha’s approximation. [2]
- Percentage error formula:
\[
\text{Percentage error} = \frac{\text{Actual value} – \text{Approximation}}{\text{Actual value}} \times 100
\]
Substitution: \[ \frac{30,150 – 28,500}{30,150} \times 100 \]
Simplification: \[ \frac{1650}{30,150} \times 100 \approx 5.47\% \] - Final answer: \( 5.47\% \) (correct to two decimal places). [1 mark]
- Correct working shown and accurate use of formula. [1 mark]
(b) (i) Determine the weight of the materials needed for three sculptures, rounded to three significant figures. [2]
- Calculation: \[ 3 \times 30,150 = 90,450 \, \text{kg} \]
- Rounded to three significant figures: \( 9.05 \times 10^4 \, \text{kg} \). [1 mark]
- Accurate calculation and correct rounding. [1 mark]
(b) (ii) Express your answer to part (b)(i) in the form \( a \times 10^k \), where \( 1 \leq a < 10 \), \( k \in \mathbb{Z} \). [1]
- Answer in scientific notation: \( 9.05 \times 10^4 \). [1 mark]