Mathematics · May / June 2020 · Paper 42 · Question 9

x + 2 − ( 4) 25 [2]

B1 for + 2 −− 2 + 2 − ( x k ) 9 ( theirk ) ( x 4) h or or k = 4

x + 4 = [ ± ] 5 –9 and 1 [2]

M1 FT their (a)(i) A1

[b =] 7 [c =] –3 [3]

B1 for [b = ] 7

M1 for b2 – 4c = 61

Correct sketch 8 8 8 8 6 6 6 6 4 4 4 4 2 2 2 2 0 0 0 0 -2 -2 -2 -2 0 0 0 0 2 2 2 2 4 4 4 4 [2]

B2 for correct quadratic curve with min touching x-axis

or B1 for parabola vertex downwards Correct sketch 6 6 6 6 5 5 5 5 4 4 4 4 3 3 3 3 2 2 2 2 1 1 1 1 4 4 4 4 -3 -3 -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 0 0 0 0 0 0 0 0 1 1 1 1 2 2 2 2 -1 -1 -1 -1 [2]

B2 for correct straight line intersecting curve on y-axis

or B1 for straight line with positive gradient and positive y-intercept

2.8[0] or 2.795... [7]

5 2 − =

B3 for x x 0 oe 2 1 − 2 = +

or M1 for ( x 1) x 1 2

B1 for [(x – 1)2 =] x2 – x – x + 1 AND

B2 for (0, 1) and 5 9 , oe 2 4 or B1 [x =] 0 and 5 2 oe AND

M1 for (difference in x )2 + (difference in y)2