O-LevelMathematicsAlgebra and graphs4024/22 · Oct/Nov 2014 · Q1012 Marks

[Table 10.1] The table below is for y = x² - 4x − 1. x | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 y | | 4 | -1| -4| -5| -4| -1| 4 |

(a)Complete the table.[1]
(b)Using a scale of 2cm to 1 unit, draw a horizontal x-axis for -2 ≤ x ≤ 6. Using a scale of 2 cm to 5 units, draw a vertical y-axis for -10 ≤ y ≤ 15. Plot the points from the table and join them with a smooth curve.[3]
(c)By drawing a tangent, estimate the gradient of the curve at x = 3.[2]
(d)(i)Find the least value of y.[1]
(d)(ii)y ≤ 4 for a ≤ x ≤ b. Find the least possible value of a and the greatest possible value of b.[2]
(e)Use your graph to solve the equation x² - 4x + 2 = 0. Show your working to explain how you used your graph.[3]

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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.

[1] 11 11
[3] correct scales, plots (ft) and curve
[3] P2 correct scales and at least 7 plots (ft) All plots correct ft or P1 for at least 7 plots (ft) or Correct scales drawn
[2] 2 (±0.5)
[2] Dependent on tangent drawn at x = 3 M1 for tangent at x = 3
[1] -5 cao
[2] (a) -1 (b) 5
[2] B1 for either
[3] (0.6) (3.4)
[3] B1 for x² - 4x - 1 = -3 soi and B1 for the line y = -3 or M1 for x² - 4x - 1 = k and A1 for the line y = k SC3 for 0 for new curve drawn

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