= A1 x (Total 3 marks) Question 15. The equation of a curve is = f(x) where f(x) = 8x + 21. y x2– Write down the coordinates of the minimum point of this curve. f(x) = 8x + 21 x2– f(x) = (x 4)2 16 + 21 P1 – – f(x) = (x 4)2 + 5 P1 – Substitute = 4, f(x) = (4 4)2 + 5 x – = 5 M1 y (4,5) A1 (Total 4 marks) Question 16. Expand (3x + 1) (2x 2) (3x + 4) – (3x + 1) (2x 2) (3x + 4) – (6x2 4x 2) (3x + 4) M1 – – 18x3 + 24x2 - 12x2 16x 6x 8 – – –
x = A1 (Total 3 marks) Question 15. The equation of a curve is y = f(x) where f(x) = x2– 8x + 21. Write down the coordinates of the minimum point of this curve. f(x) = x2– 8x + 21 f(x) = (x – 4)2 – 16 + 21 P1 f(x) = (x – 4)2 + 5 P1 Substitute x = 4, f(x) = (4 – 4)2 + 5 y = 5 M1 (4,5) A1 (Total 4 marks) Question 16. Expand (3x + 1) (2x – 2) (3x + 4) (3x + 1) (2x – 2) (3x + 4) (6x2 – 4x – 2) (3x + 4) M1 18x3 + 24x2 - 12x2 – 16x – 6x – 8
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