Practice IB Mathematics Applications & Interpretation (AI) Topic SL 1.6—approximating and Estimating with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 1.6—approximating and Estimating and mirrors Paper 1, 2, 3 style where relevant.
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Aisha travels from Johannesburg to New York. She converts 8200 South African Rand (ZAR) into US Dollars (USD). The exchange rate is 1 ZAR = 0.0512 USD. The exchange bureau deducts a 2.5% commission from the USD amount obtained. Before returning home, Aisha has 75 USD remaining and converts this amount back into ZAR. The exchange rate is 1 ZAR = 0.0480 USD, and the bureau takes a commission of % of the ZAR amount obtained. The commission fee for this exchange is 31.25 ZAR.
Calculate the final amount of US Dollars Aisha obtains. Provide your answer rounded to two decimal places.
Determine the value of .
The speed (in ) of a skydiver seconds after a parachute opens is modelled by , .
Calculate using Euler's method with a step size .
Solve the differential equation analytically to find the exact solution for .
Determine the percentage error in your Euler approximation.
State the limiting speed as .
Let , where .
Find the value of , giving your answer as a fraction.
Let . Find the value of , giving your answer as a fraction.
John estimates the value of to be 0.3. Calculate the percentage error in John's estimate.
Noah traveled from Switzerland to the United Kingdom and converted 1250 Swiss francs (CHF) into pounds sterling (GBP). The conversion rate was 1 CHF = 0.88 GBP. Returning home, Noah had 420 GBP left to convert back into CHF. A service fee of 6% was applied to this conversion.
Determine the total amount of GBP Noah obtained
Calculate the value of the service fee, in GBP, that Noah was charged
The exchange rate for this transaction was 1 CHF = 0.84 GBP. Calculate the amount of CHF Noah received back. Write your answer correct to two decimal places
Daniel exchanged 760 euros (EUR) into Swiss francs (CHF) for a trip to Switzerland. The exchange rate was 1 EUR = 0.96 CHF. When he returned home, Daniel exchanged his remaining 420 CHF back into euros. The bank charged a 3 % commission on this transaction.
Determine the total amount in CHF that Daniel obtained.
Work out the commission fee, in CHF, that Daniel was charged.
The exchange rate used for the return conversion was 1 EUR = 1.05 CHF. Calculate the final amount of EUR Daniel received after the commission was deducted. Give your answer rounded to two decimal places.