When eʸ is plotted against 1/x, a straight line graph passing through the points (2, 20) and (4, 8) is obtained.

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

1. [B1] eʸ = m/x + c May be implied by subsequent work
2. [M1] Either 20 = 2m + c 8 = 4m + c For at least 1 correct equation
3. [M1] Dep For attempt to solve their 2 equations simultaneously to obtain at least one unknown
4. [A1] leading to m=-6, c=32 For both
5. [A1] y = ln (32 - 6/x) Must have correct brackets Mark the final answer given
6. [M1] Or: Gradient = m = (-6) For attempt to find gradient and equate it to m
7. [M1] 20 = 2m + c or 8 = 4m + c or eʸ-8=m(1/x - 4) or eʸ-20=m(1/x - 2) For at least 1 correct equation, may be using their m
8. [A1] leading to c = 32 and m = -6 For both m=-6, c=32
9. [A1] y = ln (32 - 6/x)
10. [B1] x > 3/16 oe
11. [B1] y = ln 30 isw
12. [M1] 2 = ln(32 - 6/x) For a correct substitution and attempt to re-arrange using 2, their 32 and their – 6, keeping exactness to obtain x =
13. [A1] x = 6/(32-e²) oe Must be exact