SPM.1.AHL.TZ0.18

pestleMathematicsAIHLPaper 1SPM· sl-1-8-use-of-technology-to-solve-systems-of-linear-equations-and-polynomial-equationssource ↗

The rate, $A$ , of a chemical reaction at a fixed temperature is related to the concentration of two compounds, $B$ and $C$ , by the equation

$A = k{B^x}{C^y}$ , where $x$ , $y$ , $k \in \mathbb{R}$ .

A scientist measures the three variables three times during the reaction and obtains the following values.

Find $x$ , $y$ and $k$ .

Markscheme / solution

${\text{log}}\,A = x\,{\text{log}}\,B + y\,{\text{log}}\,C + {\text{log}}\,k$ (M1)

${\text{log}}\,5.74 = x\,{\text{log}}\,2.1 + y\,{\text{log}}\,3.4 + {\text{log}}\,k$

${\text{log}}\,2.88 = x\,{\text{log}}\,1.5 + y\,{\text{log}}\,2.4 + {\text{log}}\,k$

${\text{log}}\,0.980 = x\,{\text{log}}\,0.8 + y\,{\text{log}}\,1.9 + {\text{log}}\,k$ M1A1

Note: Allow any consistent base, allow numerical equivalents.

attempting to solve their system of equations (M1)

$x$ = 1.53, $y$ = 0.505 A1

$k$ = 0.997 A1

[6 marks]

Examiners’ report

[N/A]