O-LevelAdditional MathematicsLogarithmic and exponential functions4037/21 · May/June 2021 · Q24 Marks
Variables x and y are such that, when lny is plotted against lnx, a straight line graph passing through the points (6, 5) and (8, 9) is obtained. Show that y = ePxq where p and q are integers.
- Variables x and y are such that, when lny is plotted against lnx, a straight line graph passing through the points (6, 5) and (8, 9) is obtained. Show that y = ePxq where p and q are integers.[4]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [M1] m = (9-5)/(8-6) oe
- [M1] 9 = their 2(8) + c oe or 5 = their 2(6) + c
- [A1] lny = 2lnx - 7
- [A1] Correct completion to answer: y = elnx²-7 = e-7x² nfww
- [B1] (Alternative) lny = p + qlnx soi
- [M1] (Alternative) m = (9-5)/(8-6) oe
- [M1] (Alternative) 9 = their 2(8) + c oe or 5 = their 2(6) + c
- [A1] (Alternative) y = e-7x²
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