1a States correct answer: 5.3 (m s 1 ) B1 2.2a 4th Understand the difference between a scalar and a vector. Notes

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1 1a States correct answer: 5.3 (m s 1 ) B1.a 4th Understand the difference between a scalar and a vector. 1b States correct answer: 4.8 (m s 1 ) B1.a 4th Understand the difference between a scalar and a vector. 1c States correct answer: 30 (m) B1.a 4th Understand the difference between a scalar and a vector. (3 marks) Education Ltd 017. Copying permitted for purchasing institution only. This material is not copyright free.

2 ai States that x = 0 needs to be substituted or implies it by writing h Correctly substitutes x = 0 to get h = 1.7 (m) aii b States that x = 7 needs to be substituted or implies it by writing h = (7) 0.01(7) Correctly substitutes x = 7 to get h =.47 (m) Accept awrt.5 (m) Understands that the ball will hit the ground when h = 0 or writes x 0.01x 0 Realises that the quadratic formula is needed to solve the quadratic. For example a = 0.01, b = 0.18, c = 1.7 seen, or makes attempt to use the formula: Simplifies the b Calculates x = 4.84 (m) Accept awrt 4.8 (m) 4ac part to get or shows Does not need to show that (m) States that the ball will be called in, or says, for example, yes as 4.84 < 5. () () B1 3.a (5) Education Ltd 017. Copying permitted for purchasing institution only. This material is not copyright free.

3 c km 1000 m 1min 1min 1km 60 sec Award 1 method mark for multiplication by 1000 and 1 method mark for division by (m s 1 ) or 33.3 (m s 1 ) M 1.1b 3rd (1 marks) ai Award both marks for a correct final answer. aii Award both marks for a correct final answer. b a 0.01, b 0.18, c 1.7 is also acceptable. b Award the third method mark even if this step is not seen, providing the final answer is correct. Education Ltd 017. Copying permitted for purchasing institution only. This material is not copyright free.

4 3a Understands that the pole vaulter will land when h = 0 or writes 1 15 x Correctly factorises to get x x 15 Solves to get (m) 1 Accept awrt 10.4 (m) o.e. 3b States that the greatest height will occur when x = 5.0 (m) Makes an attempt to substitute x = 5.0 into the equation for 1 h. For example, h seen. 60 h = 5.4 (m) Accept awrt 5.4 (m) A1 ft 1.1b 3c States h = 4.9 or states that x Simplifies this to reach 1x 15x 94 0 o.e. Realises that the quadratic formula is needed to solve the quadratic. For example a 1, b 15, c 94 seen, or makes attempt to use the formula: Simplifies the b x = 6.8 (m) Accept awrt 6.8 (m) x = 3.58 (m) Accept awrt 3.6 (m) 4ac part to get 1513 or shows The pole vaulter can leave the ground between 3.6 m and 6.8 m from the bar. B1 3.a (7) Education Ltd 017. Copying permitted for purchasing institution only. This material is not copyright free.

5 3di Allows the person to be treated as a single mass and allows the effects of rotational forces to be ignored. B rd Understand assumptions common in mathematical modelling. 3dii The effects of air resistance can be ignored. B rd 3b Understand assumptions common in mathematical modelling. (15 marks) For the first method mark, accept their answer to part a divided by. Continue to award marks for a correct answer using their initial incorrect value. 3c Accept 3.6 x 6.8 Education Ltd 017. Copying permitted for purchasing institution only. This material is not copyright free.

6 4a Makes an attempt to find the distance from A to B. For example, 8 80 is seen. Makes an attempt to find the distance from B to C. For example, is seen. Demonstrates an understanding that these two values need to be added. For example, is seen (m) Accept anything which rounds to 16 (m) M1 3.1b 4th M1 3.1b 4b States that AC 10i 95j(m) Award one point for each value. States or implies that Finds Accept awrt tan 10 B 3.1b 4th (8 marks) Education Ltd 017. Copying permitted for purchasing institution only. This material is not copyright free.

7 5a Makes an attempt to find the absolute value. For example, 14 is seen. Simplifies to 680 Finds speed = 6.07 (ms 1 ) Accept awrt 6.1 (ms 1 ) M1 3.1b 4th 5b States that tan 14 Finds the value of θ, θ = 57.5 Demonstrates that the angle with the unit j vector is Finds 3.47 ( ) Accept awrt 3.5( ) 4th 5c Ignore the value of friction between the hockey puck and the ice. B rd Understand assumptions common in mathematical modelling. 5d 1.4 g 1kg 100 cm 100 cm 100 cm 1000 g 1m 1m 1m 1cm 3 Award 1 method mark for division by 1000 and 1 method mark for multiplication by 100 only once and the final method mark for multiplication by 100 three times kg m 3 M3 1.1b 4th Know derived quantities and SI units. 5b Award all 4 marks for a correct final answer. Award marks for a student stating making a mistake with the inverse or subtracting that answer from 90. (1 marks) 14 tan, and then either Education Ltd 017. Copying permitted for purchasing institution only. This material is not copyright free.

Finds the value of θ: θ = ( ). Accept awrt θ = 77.5 ( ). A1 ft 1.1b

Finds the value of θ: θ = ( ). Accept awrt θ = 77.5 ( ). A1 ft 1.1b 1a States that a = 4. 6 + a = 0 may be seen. B1 1.1b 4th States that b = 5. 4 + 9 + b = 0 may be seen. B1 1.1b () Understand Newton s first law and the concept of equilibrium. 1b States that R = i 9j (N).