21M.1.SL.TZ1.1

pestleMathematicsAISLPaper 121M· sl-1-6-approximating-and-estimatingsource ↗

Katya approximates $π$ , correct to four decimal places, by using the following expression.

$3 + \frac{1}{6 + \frac{13}{16}}$

Calculate Katya’s approximation of $π$ , correct to four decimal places.

[2]

Calculate the percentage error in using Katya’s four decimal place approximation of $π$ , compared to the exact value of $π$ in your calculator.

[2]

Markscheme / solution

$π \approx 3 + \frac{1}{6 + \frac{13}{16}}$

$= 3.14678 \dots (\frac{343}{109}, 3 \frac{16}{109})$ (A1)

$= 3.1468$ A1

Note: Award A1 for correct rounding to 4 decimal places. Follow through within this part.

[2 marks]

$|\frac{3.1468 - π}{π}| \times 100$ (M1)

Note: Award M1 for substitution of their final answer in part (a) into the percentage error formula. Candidates should use the exact value of $π$ from their GDC.

$= 0.166 (%) (0.165754 \dots)$ A1

[2 marks]

Examiners’ report

[N/A]