Mathematics · May / June 2024 · Paper 41 · Question 8

Correct sketch with roots indicated at x = –9 and x = 2 and y intercept = –18 Minimum should be in 3rd quadrant [4]

B1 for U shaped parabola

B2 for roots at –9 and 2 on diagram

or M1 for (x + 9) (x – 2) [= 0]

B1 for y – intercept at –18 on diagram Maximum 3 marks if sketch not fully correct

2x – 3 [2]

B1 for 2x + k or kx[p] – 3

(1.5, –30.25) oe [3]

B2 for x = 1.5

or M1 for their (b)(i) = 0 or for (x – 1.5)2

x2 – x – 33 [ = 0] seen ( ) ()( ) −− ± − 2 − − [ ]1 [ ]1 4 1 33 oe × 2 1 –5.27 or –5.267 to –5.266 and 6.27 or 6.266 to 6.267 (–5.27, 15.53 or 15.54) and (6.27, –7.53 or −7.54) [9]

B1 B2FT FT their quadratic dep on no factors

B1 for ( ) ()( ) − 2 − − [ ]1 4 1 33 or better −− + −− −

or B1 for [ ]1 q oe or [ ]1 q 2(1) 2(1) oe

B2 B1 for each If 0 scored,

SC1 for –6.27 and 5.27 B1