Variables x and y are such that y = Ax^b, where A and b are constants. When lgy is plotted against lgx, a straight line graph passing through the points (0.61, 0.57) and (5.36, 4.37) is obtained.

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

1. [1] B1 lg y = b lg x + lg A May be implied by subsequent work
2. [1] M1 For at least one correct equation
3. [1] A1 b = 0.8
4. [1] M1 Dep for substitution to obtain lg A = k and hence A
5. [1] A1 A = 1.21
6. [1] (B1) lg y = b lg x + lg A May be implied by subsequent work
7. [1] (M1) Gradient = (4.37-0.57)/(5.36-0.61)
8. [1] (A1) b = 0.8
9. [1] (M1) Dep for substitution into a correct equation to obtain lg A = k and hence A
10. [1] (A1) A = 1.21
11. [1] (B1) 10^4.37 = A×10^5.36b or 10^0.57 = A×10^0.61b
12. [1] (M1) For eliminating A correctly
13. [1] (A1) b = 0.8
14. [1] (M1) For a correct attempt to find A. Must have B1
15. [1] (A1) A = 1.21
16. [1] B1 FT for substitution into their equation
17. [1] B1 y = awrt 2.9
18. [1] B1 FT for substitution into their equation
19. [1] B1 x = awrt 3.1