10   5. The height, h metres, of a tree, t years after being planted, is modelled by the equation h 2 = at + b        0  t < 25 where a and b are constants. Given that • the height of the tree was 2.60 m, exactly 2 years after being planted • the height of the tree was 5.10 m, exactly 10 years after being planted (a) find a complete equation for the model, giving the values of a and b to 3 significant figures. (4) Given that the height of the tree was 7 m, exactly 20 years after being planted (b) evaluate the model, giving reasons for your answer. 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_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over 11   Question 5 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 5 is 6 marks) 12   6. (2, 8) C x 6 O y Figure 1 Figure 1 shows a sketch of a curve C with equation y = f (x) where f (x) is a cubic expression in x. The curve • passes through the origin • has a maximum turning point at (2, 8) • has a minimum turning point at (6, 0) (a) Write down the set of values of x for which f ʹ(x) < 0 (1) The line with equation y = k, where k is a constant, intersects C at only one point. (b) Find the set of values of k, giving your answer in set notation. (2) (c) Find the equation of C. You may leave your answer in factorised form. (3) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over 13   Question 6 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 6 is 6 marks)