A1 3 1 (0.3,1.9) M1 for substitution or for rearrangement A1A1 one mark each coordinate 2 ( M1 for substitution or for rearrangement A1A1 one mark each coordinate Note: award B2 if roiunded to 1dp or worse 3 ( or (-1,-2) or answer given as M1 substituting linear into non-linear x=, y= M1 forming quadratic in x A1A1 one mark for each set of solutions 4 1(i) 7 M1 9-2 A1 1(ii) + M1 multiplying top and bottom by 3 + M1 if one (or none) error only A1 2(i) M1 for = or = 30√2 √8 2√2 √50 5√2 A1 2(ii) + M1 multiplying top and bottom by 6 + M1 denominator = 11 (or 33) A1 5 1(i) 1 B1 1(ii) a8 B1 1(iii) B1 3b B1 a3 B1 inverse 2(i) ±5 M1 for or seen A1 2(ii) 8x10y13z4 (or 23x10y13z4) B3 B2 for 3 elements correct B1 for 2 elements correct 6 1(i) Grad AB = 1 M1 Grad BC = -1 M1 product of gradients = -1 hence C1 perp 1(ii) 10 M1 Use of pythagoras A1 2 y = -4x + 19 cao M1 calculating m M1 using (y -7) = m(x-3) A1 Midpoint (4,3) B1 verifying on line x + 2y = 10 C1 7 1 Cubic the correct way up G1 -1, 2 and 5 indicated on x-axis G1 10 indicated on y-axis G1
A1 3 1 (0.3,1.9) M1 A1A1 for substitution or for rearrangement one mark each coordinate 2 ( M1 A1A1 for substitution or for rearrangement one mark each coordinate Note: award B2 if roiunded to 1dp or worse 3 ( or (-1,-2) or answer given as x=, y= M1 M1 A1A1 substituting linear into non-linear forming quadratic in x one mark for each set of solutions 4 1(i) 7 M1 A1 9-2 1(ii) + M1 M1 A1 multiplying top and bottom by 3 + if one (or none) error only 2(i) 30√2 M1 A1 for √8 = 2√2 or √50 = 5√2 2(ii) + M1 M1 A1 multiplying top and bottom by 6 + denominator = 11 (or 33) 5 1(i) 1 B1 1(ii) a8 B1 1(iii) B1 B1 B1 3b a3 inverse 2(i) ±5 M1 A1 for or seen 2(ii) 8x10y13z4 (or 23x10y13z4) B3 B2 for 3 elements correct B1 for 2 elements correct 6 1(i) Grad AB = 1 Grad BC = -1 product of gradients = -1 hence perp M1 M1 C1 1(ii) 10 M1 A1 Use of pythagoras 2 y = -4x + 19 cao Midpoint (4,3) verifying on line x + 2y = 10 M1 M1 A1 B1 C1 calculating m using (y -7) = m(x-3) 7 1 Cubic the correct way up -1, 2 and 5 indicated on x-axis 10 indicated on y-axis G1 G1 G1