O-LevelMathematicsAlgebra and graphs4024/21 · Oct/Nov 2014 · Q312 Marks

Complete the table and hence draw the graph of y = x² - 2x – 8 . x: -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6 y: 7, 0, -5, -8, -9, -8, -5, 0, 7

(a)(i)Complete the table and hence draw the graph of y = x² - 2x – 8 . x: -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6 y: 7, 0, -5, -8, -9, -8, -5, 0, 7[3]
(a)(ii)Use your graph to solve x² - 2x − 8 = 2 .[2]
(a)(iii)By drawing a tangent, estimate the gradient of the curve at (3, -5).[2]
(b)Solve algebraically x²+x-9 = 0, giving your answers correct to 2 decimal place[3]
(c)The x-coordinates of the intersection of the line L and the curve y = x² - 2x - 8 are the solutions of the equation x² + x - 9 = 0 . Find the equation of the line L.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2014). The mark or mark type is shown in brackets.

[3] Correct quadratic graph through 11 points
[3] B2 for curve through at least 8 ft points or for 11 ft points or B1 for 16 in the table twice or for 6 ft points
[2ft] - 2.35 to 2.25 and 4.25 to 4.4
[2ft] B1 for one correct solution or M1 for y = 2 drawn
[2] 3.25 to 4.75
[2] B1 for tangent drawn at x = 3 or for a gradient in range
[3] 2.54, -3.54
[3] Working seen and www
[3] B1 for √12-4×1×(-9) soi
[3] and B1 for -1±√their37 / 2×1
[3] After B1 or BO so far, M1 for both real values of their p±√a / r
[2] (y =) -3x+1
[2] B1 for (y =) – 3x + c or (y =)mx+1 or M1 for (i) theoretical or (ii) practical

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