O-LevelMathematicsAlgebra and graphs4024/22 · May/June 2018 · Q612 Marks

Complete the table for y = x²/2 - 3x + 2. x | -1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 y | 2 | | -0.5 | -2 | -2.5 | -2 | -0.5 | | 2

(a)Complete the table for y = x²/2 - 3x + 2. x | -1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 y | 2 | | -0.5 | -2 | -2.5 | -2 | -0.5 | | 2[1]
(b)Draw the graph of y = x²/2 - 3x + 2 for -1 ≤ x ≤ 7. [Figure: grid with x-axis from -1 to 7 and y-axis from -4 to 6][3]
(c)By drawing a tangent, estimate the gradient of the curve at x = 1.5.[2]
(d)Complete these inequalities to describe the range of values of x where y ≥ 0. Answer x ≤ ............, x ≥ ...........[2]
(e)(i)On the same grid, draw the line 4y + 3x = 12 .[2]
(e)(ii)The x-coordinates of the points of intersection of this line and the curve are the solutions of the equation 2x² + Ax + B = 0 . Find the value of A and the value of B.[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

[1] Both correct
[3] B2FT for 8 or 9 points correctly plotted or B1FT for 6 or 7 points correctly plotted
B1 Dependent on a curve drawn between x = 1 and x = 2
B1
[2] B1 for one correct or SC1 for answers reversed
[2] B1 for short or unruled line or for two correct points plotted
[2] B1 for either correct or 2x² –9x – 4 [=0] or M1 for (x^2/2 -3x + 2) = (12-3x)/4 oe
After 0, SC1 for A = -9.2 to -8.8 and B = -4.2 to -3.8

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