Notes Pearson Progression Step Q Scheme Marks AOs and Progress descriptor Statesand 3a M1 1.1b 6th Convert between Recognises that the identitycan be used to find the cartesian M1 2.2a parametric equation. equations and Makes the substitution to find cartesian forms A1 1.1b using trigonometry. (3) States or implies that the curve is a circle with centre (−4, 3) 2.2a 6th 3b M1 ft and radius 7 Sketch graphs of Substitutesto find = and = 3 (−11, 3) parametric x −11 y M1 ft 1.1b functions. Substitutes to find 2.06 and = 6.5 (2.06, 6.5) x y ≈ Could also substitute = 0 to find = and = 10 (−4, 10) t x y −4 Figure 1 Draws fully A1 ft 1.1b correct curve. (3) Makes an attempt to find the length of the curve by recognising 3c M1 ft 1.1b 6th that the length is part of the circumference. Must at least Sketch graphs of attempt to find the circumference to award method mark. parametric functions. Uses the fact that the arc isof the circumference to write A1 ft 1.1b arc length = (2) (8 marks) Notes 3b Award ft marks for correct sketch using incorrect values from part a. 3c Award ft marks for correct answer using incorrect values from part a. 3c
Notes Q Scheme Marks AOs Pearson Progression Step and Progress descriptor 3a Statesand M1 1.1b 6th Convert between parametric equations and cartesian forms using trigonometry. Recognises that the identitycan be used to find the cartesian equation. M1 2.2a Makes the substitution to find A1 1.1b (3) 3b States or implies that the curve is a circle with centre (−4, 3) and radius 7 M1 ft 2.2a 6th Sketch graphs of parametric functions. Substitutesto find x = −11 and y = 3 (−11, 3) Substitutes to find x ≈ 2.06 and y = 6.5 (2.06, 6.5) Could also substitute t = 0 to find x = −4 and y = 10 (−4, 10) M1 ft 1.1b Figure 1 Draws fully correct curve. A1 ft 1.1b (3) 3c Makes an attempt to find the length of the curve by recognising that the length is part of the circumference. Must at least attempt to find the circumference to award method mark. M1 ft 1.1b 6th Sketch graphs of parametric functions. Uses the fact that the arc isof the circumference to write arc length = A1 ft 1.1b (2) (8 marks) Notes 3b Award ft marks for correct sketch using incorrect values from part a. 3c Award ft marks for correct answer using incorrect values from part a. 3c
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