O-LevelMathematicsAlgebra and graphs4024/21 · May/June 2021 · Q710 Marks

y = 2x+1 y = 2x-1 y=-2x+1 y=-2x-1 The diagrams below show sketches of two of these lines. Write the correct equation below each diagram. [Figure 7.1]

(a)y = 2x+1 y = 2x-1 y=-2x+1 y=-2x-1 The diagrams below show sketches of two of these lines. Write the correct equation below each diagram. [Figure 7.1][2]
(b)This diagram shows a sketch of the graph of y = x² + ax+b. Find the value of a and the value of b. [Figure 7.2][2]
(c)(i)The grid shows the graph of y = x³ - 2x² – 5x+6. x³-2x²-5x+6 = k has exactly 2 solutions. Use the graph to find the possible values of k. [Figure 7.3][2]
(c)(ii)By drawing a suitable line on the grid, find the solutions of x³ - 2x² −7x+5 = 0.[4]

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Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

[2] [y =] 2x – 1 [y =] −2x + 1
[2] B1 for one correct
[2] a = 1 b = -6
[2] B1 for one correct or (x + 3)(x - 2) or better seen or 0 = 4 + 2a + b oe and 0 = 9 - 3a + b oe
[2] 8 to 8.5, - 4.3 to - 3.8
[2] B1 for one correct
[4] Ruled line y = 2x + 1
[4] Reading the three x values of intersections between their non-horizontal ruled line and given curve
[4] M2 M1 for short or unruled line or 2x + 1 seen
[4] B2 B1 for reading two correct
[4] After B0 scored, SC1 for 3 correct with no/incorrect line

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