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Date	November Example question	Marks available	2	Reference code	EXN.1.SL.TZ0.5
Level	Standard Level	Paper	Paper 1	Time zone	Time zone 0
Command term	Find	Question number	5	Adapted from	N/A

Question

The $p H$ of a solution is given by the formula $p H = - \log_{10} C$ where $C$ is the hydrogen ion concentration in a solution, measured in moles per litre ( ${Ml}^{- 1}$ ).

Find the $p H$ value for a solution in which the hydrogen ion concentration is $5.2 \times 10^{- 8}$ .

[2]

a.

Write an expression for $C$ in terms of $p H$ .

[2]

b.i.

Find the hydrogen ion concentration in a solution with $p H 4.2$ . Give your answer in the form $a \times 10 k$ where $1 \leq a < 10$ and $k$ is an integer.

[2]

b.ii.

Markscheme

* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.

$p H = - \log_{10} (5.2 \times 10^{- 8}) = 7.29 (7.28399 \dots)$ (M1)A1

[2 marks]

a.

$C = 10^{- p H}$ (M1)A1

Note: Award M1 for an exponential equation with $10$ as the base.

[2 marks]

b.i.

$C = 10^{- 4.2} = 6.30957 \dots \times 10^{- 5}$ (M1)

$6.31 \times 10^{- 5}$ A1

[2 marks]

b.ii.

Examiners report

[N/A]

a.

[N/A]

b.i.

[N/A]

b.ii.

Syllabus sections

Topic 1—Number and algebra » SL 1.1—Using standard form

22M.2.SL.TZ1.2d:
Find the total area of the tiles in Eddie’s path. Give your answer in the form $a \times 10^{k}$ where $1 \leq a < 10$ and $k$ is an integer.
EXN.1.SL.TZ0.5b.i:
Write an expression for $C$ in terms of $p H$ .
22M.1.SL.TZ2.4a:
Calculate the pH of the coffee.
20N.1.SL.TZ0.T_1c:
The actual volume of the asteroid is found to be $6.074 \times 10^{6} {km}^{3}$ .

Find the percentage error in James’s estimate of the volume.
20N.1.SL.TZ0.T_1b:
Calculate James’s estimate of its volume, in ${km}^{3}$ .
17N.1.SL.TZ0.T_3a:
Calculate the time, in minutes, it takes for light from the Sun to reach the Earth.
20N.1.SL.TZ0.T_1a:
Write down the value of the iron in the form $a \times 10^{k}$ where $1 \leq a < 10, k \in ℤ$ .
EXN.1.SL.TZ0.5b.ii:
Find the hydrogen ion concentration in a solution with $p H 4.2$ . Give your answer in the form $a \times 10 k$ where $1 \leq a < 10$ and $k$ is an integer.
16N.1.SL.TZ0.T_1c:
Write your answer to part (b)(ii) in the form $a \times {10^k}$ , where $1 \leqslant a < 10,{\text{ }}k \in \mathbb{Z}$ .

Topic 1—Number and algebra » SL 1.5—Intro to logs

Topic 1—Number and algebra