O-LevelAdditional MathematicsLogarithmic and exponential functions4037/12 · May/June 2016 · Q88 Marks
Variables x and y are such that when lgy is plotted against x², the straight line graph shown above is obtained.
- (i)Given that y = Ab^(x²), find the value of A and of b.[4]
- (ii)Find the value of y when x = 1.5.[2]
- (iii)Find the positive value of x when y = 2.[2]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.
- [1] B1 for lgb = ±0.21 may be implied
- [1] B1 b = 0.617 allow 0.62, 10^(-0.21)
- [1] B1 lgA = 0.94 allow 0.93 to 0.95
- [1] B1 A = 8.71 allow awrt 8.5 to 8.9
- [1] M1 for correct use of graph y = theirA × theirb^(1.5²) or lg y = lg theirA + (1.5² lg theirb)
- [1] A1
- [1] M1 for correct use of graph to read off x²
- [1] A1
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