Math Mark Scheme.pdf

Differentiate to obtain 2x - 4/x, obtain 2 for value of first derivative, attempt equation of tangent through (2, 3) using numerical value of first derivative. Obtain 2x - 3y + 5 = 0 or equivalent. Attempt to square both sides, obtain x^2 - 8x + 14 = 0, obtain correct values x = 2 and x = 4 or 3/2 < x < 4. Attempt valid method for solving inequality, obtain 3/2 < x < 4 or equivalent. Evaluate cubic expression at 2 and 3, obtain -11 and 31, conclude by noting change of sign. Obtain correct first iterate using value such that 2 ≤ x ≤ 3, attempt correct process to obtain at least 3 iterates, obtain 2.34 or equivalent. State whether following is true, obtain x = 1 + ln(ln(y))/ln(5), differentiate to obtain single term of form k/y, obtain 5/ln(y) or equivalent. State sin(2θ) = 2 sin(θ) cos(θ), attempt to find exact value of cos(α) using identity or right-angled triangle, obtain 1/4 or equivalent. Obtain f(-3) = -7, show correct process for composition of functions, obtain -47 or equivalent. Attempt correct process for finding inverse, obtain x = ±√(y + 2) or equivalent. Obtain integral of form -x^4 + 4x + k, obtain -x^4/4 + 4x + c or equivalent, substitute limits and attempt evaluation, obtain 21/2 or equivalent. State R = 13, state at least one equation of form R cos(α) = k, obtain 67.4 or equivalent. Refer to translation and stretch, state translation in positive x direction by 67.4, state stretch in y direction by factor 13. Attempt to express x in terms of y, obtain x = 1 + 2 ln(y)/e or equivalent, state or imply volume involves ∫(2x π) dy, attempt to express in terms of y, obtain ∫(y + 2 + k) dy or equivalent.