Mathematics · Oct / Nov 2020 · Paper 41 · Question 5

2.7 to 2.8 [1]

tangent ruled at x = –2 6 to 10 [3]

B1 2 dep on B1 or a close attempt at tangent at x = –2

or M1 for rise/run for their tangent, or close attempt, at any point Must see correct or implied calculation from a drawn tangent After M0,

SC1 for gradient of tangent (or close attempt) in range embedded in y = mx + c

y = 2x – 2 ruled and x = –2.9 to –2.8 cao [3]

B2 for correct ruled line

or B1 for short line or for freehand line or broken line or ruled line with gradient 2 or with y-intercept at –2 (but not y = –2)

A (4, 17) B (–1.5, 0.5) [5]

B4 for (–1.5, 0.5) and (4, 17), or for x = 4 and x = –1.5 OR

B3 for A(4, 17) or B(–1.5, 0.5) OR

M1 for 2x2 –2x – 7 = 3x + 5 oe AND either

M2 for (2x + 3)(x – 4)

or M1 for 2x(x – 4) + 3(x – 4) or x(2x + 3) – 4(2x + 3) or (2x +c)(x + d) where cd = –12 or c + 2d = –5 [c and d are integers] OR

M2 for 2 − their b ± ( theirb ) − 4( their a their c )( ) 2( their a ) 2

or M1 for ( or their b ) − 4( their a their c )( ) ௣ ା √௤ ௣ ି √௤ or for p = –their b, r = 2(their a) if in the ௥ ௥ form