IB Maths AA HL AA 1.2 Exponents and logarithms questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

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Question 1

Paper 1, no calculatorEasy5 marks

The concentration CC in mg L−1\text{mg L}^{-1} of a dye in a tank tt hours after treatment begins is modelled by

C(t)=32(14)t.C(t)=32\left(\frac14\right)^t.
(a)

Find the concentration after 32\frac32 hours.

[2]
(b)

Determine the time at which the concentration reaches 3 mg L−13\text{ mg L}^{-1} Use logarithms and give your answer exactly in terms of ln⁡\ln including units.

[3]

Question 2

Paper 2, calculatorEasy6 marks

A laboratory measures the mass of two layers in a material sample as 6.40×10−8 kg6.40\times10^{-8}\,\text{kg} and 3.60×10−9 kg3.60\times10^{-9}\,\text{kg}

(a)

Determine the combined mass of the two layers. Give your answer in scientific notation.

[2]
(b)

A batch contains five identical samples, each with the combined mass found in part (a).

Determine the total mass of the batch. Give your answer in scientific notation.

[2]
(c)

The storage limit for the batch is 5.00×10−7 kg5.00\times10^{-7}\,\text{kg}

Using your answer to part (b), determine the mass by which the batch is below this limit. Give your answer in scientific notation.

[2]

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