O-LevelMathematicsAlgebra and graphs4024/22 · Oct/Nov 2024 · Q610 Marks

Complete the table for y = x/4 (2x²-x-10).

(a)Complete the table for y = x/4 (2x²-x-10).[1]
(b)Draw the graph of y = x/4 (2x²-x-10) for -3 ≤ x ≤ 3. [Figure showing an empty grid with x-axis from -3 to 3 and y-axis from -10 to 6.][3]
(c)The equation x/4 (2x²-x-10) = k has exactly two solutions. Use your graph to find the possible values of k.[2]
(d)By drawing a suitable line on the grid, find the solutions of 2x³-x² - 10x = 2x-4.[4]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

[1] -8.25
[3] Correct smooth curve
[B2FT] for 6 or 7 points correctly plotted
[B1FT] for 4 or 5 points correctly plotted
[2] k = -2.6 to -2.3 or k = 0.2 to 0.4 or k = 2.3 to 2.7
[M2] Line y = x/2 - 1 drawn
[M1] for y = x/2 + k drawn or y = px - 1 drawn (p ≠ 0) or for [y =] x/2 - 1 oe soi
[A2] A2 dep on M2 for two correct dep on at least M1 earned
[SC1] After M0, for all 3 correct
[4] x = -1.6 to -1.4 , x = 0.5 to 0.7 , x = 2.8 to 3.0
[M1] for elimination of fraction
[M1] for isolation of terms in x, FT their first step
[M1] for factorising and completing to x =, FT their second step
[Max 2 marks] if final answer not correct

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