O-LevelMathematicsAlgebra and graphs4024/21 · Oct/Nov 2017 · Q712 Marks

The points (4, -3) and (0, 5) lie on the line L. Find the equation of line L.

(a)(i)The points (4, -3) and (0, 5) lie on the line L. Find the equation of line L.[2]
(a)(ii)The line M is parallel to line L and passes through the point (-2, 3). Find the equation of line M.[2]
(b)(i)Complete the table.[1]
(b)(ii)Using a scale of 2cm to 1 unit on both axes, draw a horizontal x-axis for 0 ≤ x ≤ 7 and a vertical y-axis for 0 ≤ y ≤ 4. Draw the graph of y = x + 3/x - 3 for 0.5 ≤ x ≤ 6.[3]
(b)(iii)By drawing a tangent, estimate the gradient of the curve at (1, 1).[2]
(b)(iv)Use your graph to solve the equation x + 3/x = 5.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

[2] B1 for y = −2x + c oe or for y = mx + 5 oe
[2] or M1 for gradient = (5+3) / (0-4) oe
[2] y = -2x + 5 oe
[2] B1 for answer y = their (−2)x + k, where k ≠ their 5
[2] or M1 for 3 = their (−2) × −2 + k_oe
[2] y = -2x - 1 oе FT their gradient from (a)(i)
[1] 3.5
[3] B2FT for 7 or 8 points correctly plotted or B1FT for 5 or 6 points correctly plotted
[3] Correct smooth curve through 8 correct points
[2] M1 Clear correct tangent drawn at (1, 1)
[2] A1 -2.4 to -1.6
[2] FT reading from their graph at y = 2
[2] B1 for one correct
[2] or for y = 2 soi
[2] 0.6 to 0.8 and 4.2 to 4.4

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