O-LevelMathematicsAlgebra and graphs4024/22 · Oct/Nov 2019 · Q413 Marks

Complete the table for y = 3+2x - (x^3)/5. x -4 -3 -2 -1 0 1 2 3 4 y 7.8 2.4 0.6 1.2 3 4.8 5.4 3.6

(a)Complete the table for y = 3+2x - (x^3)/5. x -4 -3 -2 -1 0 1 2 3 4 y 7.8 2.4 0.6 1.2 3 4.8 5.4 3.6[1]
(b)Draw the graph of y = 3+2x - (x^3)/5 for -4 ≤ x ≤ 4.[3]
(c)By drawing a tangent, estimate the gradient of the graph of y = 3+2x - (x^3)/5 at (1, 4.8).[2]
(d)(i)On the grid, draw the line 2y+x = 8.[2]
(d)(ii)Write down the x-coordinates of the points where the line intersects the graph of y = 3+2x - (x^3)/5.[2]
(d)(iii)These x-coordinates are the solutions of the equation 2x³ +Ax+B = 0. Find the value of A and the value of B.[3]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[1] -1.8
[3] Correct smooth curve
[3] B2FT for 8 or 9 points correctly plotted or B1FT for 6 or 7 points correctly plotted
[2] Tangent drawn at (1, 4.8)
[2] 1.2 to 1.6
[2] B1 Dep on curve drawn between (0, 3) and (2, 5.4)
[2] B1 Dep on close attempt at tangent
[2] Ruled line through (–2, 5) to (2, 3) crossing curve three times
[2] B1 for short or unruled line or for two correct coordinates soi
[2] -3.8 to -3.7
[2] 0.4 to 0.5
[2] 3.3 to 3.4
[2] FT intersection of their line with their 'curve'
[2] B1FT for two correct
[3] A = -25
[3] B = 10
[3] B2 for one correct
[3] or M1 for (8-x)/2 = 3+2x - x^3/5 oe

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