O-LevelMathematicsAlgebra and graphs4024/12 · Oct/Nov 2025 · Q1510 Marks

Complete the table for y = x³ - 4x² + 12. [Table with x values -2 to 4, and y values -12, 7, 12, 9, 4, 3 filled in, missing y for x=0, x=1, x=2, x=3, x=4]

(a)Complete the table for y = x³ - 4x² + 12. [Table with x values -2 to 4, and y values -12, 7, 12, 9, 4, 3 filled in, missing y for x=0, x=1, x=2, x=3, x=4][1]
(b)Draw the graph of y = x³ - 4x² + 12 for -2 ≤ x ≤ 4. [Figure: empty Cartesian grid][4]
(c)Use your graph to solve the equation x³ - 4x² + 12 = 0.[1]
(d)By drawing a suitable line on the grid, find the roots of the equation x³ - 4x² + x + 4 = 0.[4]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

[1] (a) 12
[4] (b) Correct smooth curve
[4] (b) B3FT for 6 points correctly plotted
[4] (b) B2FT for 4 points correctly plotted
[4] (b) B1FT for 2 points correctly plotted
[1] (c) -1.7 to -1.3
[4] (d) Ruled line y = 8 - x
[4] (d) M2 M1 for short or unruled line y = 8 – x or for y = 8 – x soi or for y = k − x drawn or y = 8 – kx drawn, but not y = 8
[4] (d) A2 A1 for two correct solutions
[4] (d) If M1 scored, SC1 for three correct solutions
[4] (d) (Roots: -0.9 to -0.7, 1.4 to 1.6, 3.2 to 3.5)

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