O-LevelMathematicsAlgebra and graphs4024/22 · Oct/Nov 2020 · Q313 Marks

(a) Complete the table for y = x/4 + 2/x . The values of y are given correct to 2 decimal places where appropriate. x | 0.5 | 1 | 1.5 | 2 | 3 | 4 | 5 | 6 | 7 --|-----|---|-----|---|---|---|---|---|--- y | 4.13| 2.25| 1.71| 1.5 | 1.42| 1.5 | 1.65| 1.83|

(a)Complete the table for y = x/4 + 2/x . The values of y are given correct to 2 decimal places where appropriate. [Table as given above][1]
(b)On the grid, draw the graph of y = x/4 + 2/x for 0.5 ≤ x ≤ 7. [Grid with x and y axes][3]
(c)By drawing a tangent, estimate the gradient of y = x/4 + 2/x when x = 1.[2]
(d)(i)On the grid, draw the graph of 2y+x = 6.[2]
(d)(ii)Write down the x-coordinates of the points of intersection of the graphs of 2y+x = 6 and y = x/4 + 2/x . x = .......... and x = ..........[2]
(d)(iii)These x-coordinates are the solutions of the equation 3x² + Ax + B = 0. Use 2y+x = 6 and y = x/4 + 2/x to find the value of A and the value of B. A = .......... B = ..........[3]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[1] 2.04 or 2.035 to 2.036 (for x=7).
[3] B2FT for 8 or 9 points correctly plotted; or B1FT for 6 or 7 points correctly plotted; Correct smooth curve drawn.
[2] B1 for Tangent drawn at (1, 2.25); B1 Dependent on close attempt at tangent for gradient -2 to -1.1.
[2] B1 for short or unruled line or for two correct points soi or line with negative gradient passing through (0, 3); Ruled line through (0, 3) and (6, 0) drawn.
[2] Strict FT intersections of their line with their curve; B1FT for each x-coordinate.
[3] M1 for forming an equation in x from 2y+x=6 and y=x/4+2/x; B2 for 6x²- 24x + 16 [= 0] or 3x² - 12x + k [= 0] or 3x² – kx + 8 [= 0], k ≠ 0; Final answer A=-12, B=8.

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