9 a h B1 3 B1 for clear explanation Need to find both times when = 0. M1 h M1 for setting = 0 u Substitute = 16 m/s into the equation. 16t 5t2 = 0 – t(16 5t) = 0 – t so = 0 or (16 5t) = 0 – 3.2 s A1 t A1 for 0 and 3.2 = 0 or 5t = 16 A1 A1 for 3.2 seconds t = 3.2 b B1 M1 for substituting t = 1.6 B1 B1 for 12.8 m Maximum height = 16 × 1.6 5 × 1.62 – = 25.6 12.8 – = 12.8 m c B1 B1 cao 7 h ut = + 5t2 + 1 10 a s ut gt2. Parabola/quadratic equation B1 3 B1 for either of these B Use = – g u θ Assuming = 10, given = 8 sin b and assuming suitable value for θ, for B1 EC for stating suitable assumptions for the starting point example, 30° sin 30° = 0.5 s So = + 4t –5t2 Complete the square to give: = 0 M1 M1 for a suitable method for finding greatest height, could also be sketch graph y x2. Comparing this to the equation of = Then the horse will reach its maximum at t = 0.4. M1 M1 for suitable comparison Substitute this into s = + 4t –5t2 s to give = 0.8 m. s A1 A1 for ft from the initial assumption = 0.8 m c A1 A1 cao Suitable justification, e.g. Yes it does, the horse is in the air for 0.8 s and jumps 0.8 m into the air. 6
9 a b c Need to find both times when h = 0. Substitute u = 16 m/s into the equation. 16t – 5t2 = 0 t(16 – 5t) = 0 so t = 0 or (16 – 5t) = 0 t = 0 or 5t = 16 t = 3.2 Maximum height = 16 × 1.6 – 5 × 1.62 = 25.6 – 12.8 = 12.8 m h = ut + 5t2 + 1 3.2 s B1 M1 A1 A1 B1 B1 B1 3 B1 for clear explanation M1 for setting h = 0 A1 for 0 and 3.2 A1 for 3.2 seconds M1 for substituting t = 1.6 B1 for 12.8 m B1 cao 7 10 a b c Use s = ut – gt2. Assuming g = 10, given u = 8 sin θ and assuming suitable value for θ, for example, 30° sin 30° = 0.5 So s = –5t2 + 4t Complete the square to give: = 0 Comparing this to the equation of y = x2. Then the horse will reach its maximum at t = 0.4. Substitute this into s = –5t2 + 4t to give s = 0.8 m. Parabola/quadratic equation s = 0.8 m Suitable justification, e.g. Yes it does, the horse is in the air for 0.8 s and jumps 0.8 m into the air. B1 B1 M1 M1 A1 A1 3 B1 for either of these EC for stating suitable assumptions for the starting point M1 for a suitable method for finding greatest height, could also be sketch graph M1 for suitable comparison A1 for ft from the initial assumption A1 cao B 6
Higher_Skills_Algebra_MarkScheme_AQA.docx