A-LevelMathematicsAlgebra9709/23 · Oct/Nov 2017 · Q37 Marks

It is given that the variable x is such that 1.3²ˣ < 80 and |3x-1| > |3x – 10. Find the set of possible values of x, giving your answer in the form a < x < b where the constants a and b are correct to 3 significant figures.

It is given that the variable x is such that 1.3²ˣ < 80 and |3x-1| > |3x – 10. Find the set of possible values of x, giving your answer in the form a < x < b where the constants a and b are correct to 3 significant figures.[7]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

M1 Take logarithms of both sides and apply power law
A1 Obtain 2x < ln 80 / ln 1.3 or equivalent using log₁₀
A1 Obtain x = 8.35...
B1 State or imply non-modulus inequality (3x-1)² > (3x-10)² or corresponding equation or linear equation 3x-1=-(3x-10)
M1 Attempt solution of inequality or equation (obtaining 3 terms when squaring each bracket or solving linear equation with signs of 3x different)
A1 Obtain x = 9/2 or x=1.83...
A1 Conclude 1.83 < x < 8.35

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