A Level Mathematics Edexcel Paper 2 – Pure Mathematics Predicted Paper 2022

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Question 1 The equation ?3 − ?2 − 4? + 8 = 0 has exactly one real root ? (i) Show that the Newton-Raphson iterative formula for finding this root can be written as: 2??3 − ??2 − 8 ? ?+1 ... = 3??2 − 2?? − 4 …………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………… (3) (ii) Apply the iterative formula with initial value ?1 = −2 to find ?2, ?3, ?4 correct to four significant figures. …………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………… (1)3 (iii) Use a change of sign method to show that ? = −2.284 is correct to four significant figures. …………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………… (3) (Total 7 Marks)4 Question 2 For all real values of ?, the functions ? and ? are defined by ?(?) = ?2 + 6?? + 3?2 and ?(?) = 3? − 2?, where ? is a positive constant, and ? ∈ ℝ. (i) Find ??(?) and determine the range of ??(?) in terms of ?. …………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………………………………… (4) (ii) If ??(3) = 46 find the value of ?. [Show More]

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