O-LevelAdditional MathematicsLogarithmic and exponential functions4037/22 · May/June 2022 · Q55 Marks

Solve the equation 625^((x³-1)/2) / 125^(x³) = 5.

(a)Solve the equation 625^((x³-1)/2) / 125^(x³) = 5.[3]
(b)On the axes, sketch the graph of y = 4e^x +3 showing the values of any intercepts with the coordinate axes.[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

[B1] converts the terms given to powers of 5 or 25 or separates the power in the numerator correctly or applies a correct log law
[M1] FT their exponential equation in the same base or their logarithmic equation with any consistent base, providing their exponential or logarithmic equation has at most one sign or arithmetic error
[A1] [x =]-3 oe or -1.442249... rot to 3 or more figs. mark final answer; not from wrong working
[B2] B1 for correct shape; tending to y = 3
[B1] for shape with correct curvature and correct intercept of 7 marked or (0, 7) indicated

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