A-LevelMathematicsLogarithmic and exponential functions9709/22 · May/June 2017 · Q56 Marks
The variables x and y satisfy the equation y = K/a²ˣ, where K and a are constants. The graph of ln y against x is a straight line passing through the points (0.6, 1.81) and (1.4, 1.39), as shown in the diagram. Find the values of K and a correct to 2 significant figures. [Figure 5.1]
- N/AThe variables x and y satisfy the equation y = K/a²ˣ, where K and a are constants. The graph of ln y against x is a straight line passing through the points (0.6, 1.81) and (1.4, 1.39), as shown in the diagram. Find the values of K and a correct to 2 significant figures.[6]
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 2017). The mark or mark type is shown in brackets.
- B1 State or imply ln y = ln K – 2xln a
- (M1 Obtain -0.525 as gradient of line
- M1 Equate their -2lna to their gradient and solve for a
- A1 Obtain a = 1.3
- M1 Substitute to find value of K
- A1) Obtain K = 8.4
- (M1 Obtain two equations using coordinates correctly
- M1 Solve these equations to obtain 2lna or equivalent
- A1 Obtain a = 1.3
- M1 Substitute to find value of K
- A1) Obtain K = 8.4
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