Q Scheme Marks AOs Pearson Progression Step and Progress descriptor 1a Makes an attempt to rearrangeto make t the subject. For example,is seen. M1 2.2a 5th Convert between parametric equations and cartesian forms using substitution. Correctly states A1 1.1b Makes an attempt to substituteinto For example,is seen. M1 2.2a Simplifies the expression showing all steps. For example, A1 1.1b (4) 1b Interprets the gradient of line being −1 asand finds M1 2.2a 5th Convert between parametric equations and cartesian forms using substitution. Substitutes t = −1 to find x =and y = And substitutes t = 0 to find x = 1 and y = 2 M1 1.1b Makes an attempt to use Pythagoras’ Theorem to find the length of the line: M1 1.1b Correctly finds the length of the line segment,or states A1 1.1b (4) (8 marks) Notes Q Scheme Marks AOs Pearson Progression Step and Progress descriptor 2 Recognises that the identity can be used to find the cartesian equation. M1 2.2a 6th Convert between parametric equations and cartesian using trigonometry. Statesor Also states M1 1.1b Substitutesandinto M1 1.1b Solves to find, accept x < 1 or A1 1.1b (4 marks)
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
Alternative method: use, withand. Award one mark for the attempt and one for the correct answer. Q Scheme Marks AOs Pearson Progression Step and Progress descriptor 4a Shows or implies that if y = 0, t = 1 M1 1.1b 7th Solve coordinate geometry problems involving parametric equations. Finds the coordinates of P. A1 1.1b (2) 4b Attempts to find a cartesian equation of the curve. For example, t = x − 2 is substituted into M1 2.2a 7th coordinate geometry problems involving parametric equations. Correctly the cartesian equation of the curveAccept any equivalent answer. For example, A1 1.1b (2) 4c M1 2.2a 7th Solve coordinate geometry problems involving parametric equations. Substitutes t = −1 to find x = 1 and M1 1.1b Finds the gradient of the normal M1 1.1b Substitutes t = −1 to find x = 1 and y = −2 A1 1.1b an attempt to find the equation of the normal. For example, is seen. M1 1.1b States fully correct answer A1 1.1b (6) 4d Substitutesandintoobtaining M1 ft 2.2a Manipulates and simplifies this equation to obtain M1 ft 1.1b Factorises and solves to find t = −1 or t = −11 M1 ft 1.1b
involving parametric equations. Substitutes t = −11 to find x = −9 and , i.e. A1 ft 1.1b (4) (14 marks) Notes 4c Award ft marks for correct answer using incorrect values from part b. Q Scheme Marks AOs Pearson Progression Step and Progress descriptor 5a Interprets the stone hitting the ground as when M1 3.4 8th Use parametric equations in modelling in a variety of contexts. Makes an attempt to use the quadratic formula to find t. For example,is seen. M1 2.2a Finds M1 1.1b Deducesm. Accept awrt 24.6 A1 3.2a (4) 5b Finds M1 2.2a 8th Use parametric equations in modelling in a variety of contexts. Demonstrates an understanding that the greatest height will occur when. For example, M1 3.1a Solves to find M1 1.1b Makes an attempt to find the greatest height by substituting into For example, M1 ft 3.2a Finds y ==13.265… m. Accept awrt 13.3 m. A1 ft 1.1b (5) (9 marks) Notes 5b can also be found using. This is an acceptable method. 5b Award ft marks for correct sketch using incorrect values from earlier in part b.
Q Scheme Marks AOs Pearson Progression Step and Progress descriptor 6a Rearrangesto obtain M1 1.1b 8th Use parametric equations in modelling in a variety of contexts. Substitutesinto For example,is seen. M1 1.1b A1 1.1b (3) 6b Deduces that the width of the arch can be found by substituting into M1 3.4 8th Use parametric equations in modelling in a variety of contexts. Finds x = 0 and x = 160 and deduces the width of the arch is 160 m. A1 3.2a (2) 6c Deduces that the greatest height occurs when M1 3.4 8th Use parametric equations in modelling in a variety of contexts. Deduces that the height is 100 m. A1 3.2a (2) (7 marks) Notes