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IB Maths AI SL 1.6 Approximation and Error

IB Maths AI SL 1.6 Approximation and Error
IB Mathematics: applications and interpretation guide, first assessment 2021

Practise rounding to appropriate precision, calculating absolute or percentage error and using upper and lower bounds to decide what can be concluded from measured data.

How this is tested

  • derive lower and upper bounds from the stated rounding unit before substituting into a formula
  • calculate absolute or percentage error against the exact or accepted value
  • use the bound that maximises or minimises a derived result to justify whether a claim is certain

Question 2

[Maximum number: 10]

A digital caliper is used to measure the diameter of a spherical ball.

Figure for Question 2 — IB Maths AI SL

The digital caliper displays the diameter of the ball as 8.4 cm , and is accurate to one decimal place.

Question 2(a)(i)

(a)

Write down the smallest possible diameter of the ball.

[ 4 ]

Question 2(a)(ii)

(b)

Hence, calculate the smallest possible volume of the ball.

The exact diameter of the ball is 8.38 cm .

[ 4 ]

Question 2(b)

(c)

Calculate the percentage error in the measurement of 8.4 cm , as shown on the digital caliper.

[ 2 ]