CAPE Pure Mathematics Unit 1 · May/June 2017 · Paper 2 · Question 2(a)(i)
Given that a² + b² = 14ab, prove that ln((a+b)/4) = (1/2)(ln a + ln b).
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- 2(a)(ii)Solve the equation 2ˣ + 3(2⁻ˣ) = 4. [Your response may be expressed in terms of logarithms.][6 marks]
- 2(b)(i)On the diagram, insert the asymptotes for the function f.[2 marks]
- 2(b)(ii)sketch the graph of f⁻¹, the inverse of f showing the asymptotes for f⁻¹.[4 marks]
- 2(c)Given that α, β and γ are the roots of the equation x³ + 3x + 2 = 0, form an equation whose roots are βγ, αγ and αβ.[8 marks]
More practice: the rest of this paper · more Exponential and Logarithmic Functions questions · all CAPE Pure Mathematics Unit 1 past papers