O-LevelMathematicsAlgebra and graphs4024/21 · Oct/Nov 2016 · Q812 Marks

The table shows some values of x and the corresponding values of y, correct to one decimal place where necessary. y = (3/2) * 2^x x -1.5 -1 0 1 2 2.5 3 3.5 4 y p 0.3 0.6 1.2 2.4 3.4 4.8 6.8 9.6

(a)Calculate p.[1]
(b)On the grid, • using a scale of 2 cm to 1 unit, draw a horizontal x-axis for -2 ≤ x ≤ 4, • using a scale of 1 cm to 1 unit, draw a vertical y-axis for 0 ≤ y ≤ 10, • plot the points from the table and join them with a smooth curve.[3]
(c)By drawing a tangent, estimate the gradient of the curve at the point where x = 2.5.[2]
(d)(i)On the same grid, draw the straight line that passes through (-0.4, 0) and (2, 3.6).[1]
(d)(ii)Find the equation of this line in the form y = mx + c.[2]
(d)(iii)Write down the x-coordinates of the points where the line intersects the curve.[1]
(d)(iv)These x-coordinates satisfy the equation 2ˣ = Ax + B. Find the values of A and B.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2016). The mark or mark type is shown in brackets.

[1] (a) 0.2 or 0.21[2...]
[3] (b) Correct axes B1 Correct shape curve through 9 correct points B2 B1ft for at least 7 correct points plotted
[2] (c) Clear, correct, tangent drawn M1 2.2 to 2.5 A1
[1] (d)(i) Ruled line from (–0.4, 0) to (2, 3.6)
[2] (d)(ii) y = 1.5x + 0.6 or y=(3/2)x+(3/5) B1 for m = 1.5 oe or for c = 0.6 oe or for correct equation in a different form
[1ft] (d)(iii) 0 and 3.1 to 3.2 FT intersections of their ruled line with their curve
[2] (d)(iv) A = 2.4 to 2.6 B1 B = 1 B1

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