2023 HCI H2 PH Prelim P4 MS

1 © Hwa Chong Institution 2023 2023 Prelim Practical Exam Mark Scheme and Examiners Comments Question 1 [10 marks] Part Marking Point Mark (a) Value of b in the range 11.8 to 12.2 cm Value of c in the range 15.8 to 16.2 cm [1] (b) Value of y in measured to nearest 1 mm Value of y in the range 4.6 to 5.0 cm [1] [1] (c)(i) Value of c in the range 9.8 to 10.2 cm [1] (c)(ii) Value of y in the range 4.9 to 5.3 cm [1] (d)(i) Value of y is calculated correctly with units and expressed to 2 or 3 s.f. [1] (d)(ii) Correct identification of graph to be plotted. (Gradient and y-intercept expressions should not include y and/or c) [1] (d)(iii) Correct expression stated for the gradient. Correct expression stated for the y-intercept. (Gradient and y-intercept expressions should not include y and/or c) [1] [1] (e) Reasonable explanation why value of y is equal to 6 cm. (E.g. when y is zero, the card becomes a square or rectangle, hence the centre of gravity is at the midpoint/middle/centre of the card. [1]

2 © Hwa Chong Institution 2023 Question 2 [11 marks] Part Marking Point Mark (a) Value of I2 in the range 50.0 to 80.0 mA I2 > I1 [1] (b) 6 sets of raw data + appropriate Ry range (accept 0 or 1 d.p precision) + correct trend of I1 / I2 ratio Column headings: Each column heading must contain a quantity, a unit and a separating mark where appropriate. The presentation of quantity and unit must conform to accepted scientific convention Correct precision for raw data and s.f for calculated data. Correct calculation. [1] [1] [1] (c) Linearization: Graph of I1/I2 vs RY graph plotted. If wrong linearization, penalize Rx. Axes: Sensible scales must be used, no awkward scales (e.g. 3:10). Scales must be chosen so that the plotted points occupy at least half the graph grid in both x and y directions. Scale markings should be no more than three large squares apart Plotting of points: All observations in the table must be plotted on the grid. Points must be plotted to an accuracy of half a small square. Line of best fit or BFL: Judge by balance of all points on the grid about the candidate’s line (at least 5 points). There must be an even distribution of points either side of the line along the full length. If there are 6 or more points, allow one anomalous point only if clearly indicated by the candidate. Gradient: The hypotenuse of the triangle used must be greater than half the length of the drawn line. The method of calculation must be correct. Do not allow Δx / Δy. Both read-offs must be accurate to half a small square in both the x and y directions. RX calculated correctly with units from gradient (e.g. = 1/2RX ), appropriate range from 10 to 40 Ω. Penalise Rx if 1 s.f. [0] [1] [1] [1] [1] [1] (d) As RY = RX, RX can be determined from the graph by identifying the RY value when I1 / I2 = 1. [1] (e) Line W must have a gentler gradient and will always be lower than the original graph at all points except for the y-intercept. (if graph of I1/I2 vs RY plotted) Accept equivalent answer for graph of RY vs I1/I2 plotted. [1]

3 © Hwa Chong Institution 2023 Question 3 [21 marks] Part Marking Point Mark (a)(i) Value of x in the range 3.0 to 3.5 cm Require repeated measurements for x Value of h in the range 12.5 to 13.5 cm Correct units for x and h [1] (a)(ii) Value of Δx in the range 0.2 to 0.5 cm Correct calculation [1] (b)(i) Value of θ in the range 45° to 60° Require repeated measurement for θ Precision of θ should be 1° Correct unit for θ [1] Value of y in the range 8.5 to 12.0 cm Require repeated measurements for y Precision of y should be 1 mm Correct unit for y [1] (b)(ii) Correct calculation, using the measured value of θ from part (b)(i) [1] (c)(ii) Value of x in the range 2.5 to 3.0 cm Value of h in the range 10.5 to 11.5 cm Correct units Correct calculation of tan θ, using the measured value of θ [1] The value of θ should be larger than the one recorded in (b)(i) [1] (d)(i) Both values of k are correctly calculated Values of k given to an appropriate number of s.f. (least s.f. or 1 more) [1] (d)(ii) Percentage difference between two values for k correctly calculated Percentage difference between k values compared with the percentage uncertainty found in (a)(ii) Appropriate conclusion drawn [1] (e)(i) Reasonable, significant sources of error, while mentioning which measurement is affected Possible answers: • It is very difficult to keep the cone in place after the ping-pong ball has dropped, affecting measurements of y and θ. • The cone is not a perfect shape, as the tip of the cone gets crumpled when we place the cone on the workbench, affecting measurement of h and y. • It is difficult to determine the exact instance or orientation of the cone when the ping-pong ball tips over, affecting the measurement of y and θ. • It is difficult to tilt the cone in a steady manner, affecting the measurement of y and θ. Not accepted: • Diameter not fixed due to pressing the cone (human error) The base of the cone may not be a perfect circle [2]

4 © Hwa Chong Institution 2023 (e)(ii) Reasonable means of improvement, that addresses one of the identified errors Possible answers: • Clamp a ruler (vertically) behind the setup, so that y can immediately be read off when the ball drops. • Attach a small lump of Blu Tack with a depression in the centre to the tabletop, to pivot the cone. • Rest the cone at a slight inclination against a book or block of suitable size. Not accepted: • Use cones made out of a harder material such as wood or plastic Clamping the cone [1] (f)(i) All points plotted accurately to a precision of half a small square Appropriate best-fit line drawn [1] (f)(ii) Gradient correctly calculated 0 out of 2 marks are awarded if the gradient is incorrect Vertical intercept correctly calculated [1] [1] (f)(iii) • Answer of (f)(ii) compared to the precision of cos θ in the graph (0.005) Appropriate conclusion drawn Alternatively, also accept: • Statement that the graph must pass through the origin Conclusion drawn based on the answer of (f)(ii) [1] (g) Create at least 10 cones of varying height and constant diameter Take a cone, place a tennis ball in it, tilt the cone until the tennis ball drops Record all data in a table: h/cm, y/cm (optional), θ/° Plot a graph of θ against h Fit a line or curve through the points and read off the value of h for θ = 60° [1] [1] [1] [1] [1] (e)(i) Reasonable, significant sources of error, while mentioning which measurement is affected Possible answers: • It is very difficult to keep the cone in place after the ping-pong ball has dropped, affecting measurements of y and θ. • The cone is not a perfect shape, as the tip of the cone gets crumpled when we place the cone on the workbench, affecting measurement of h and y. • It is difficult to determine the exact instance or orientation of the cone when the ping-pong ball tips over, affecting the measurement of y and θ. • It is difficult to tilt the cone in a steady manner, affecting the measurement of y and θ. Not accepted: • Diameter not fixed due to pressing the cone (human error) • The base of the cone may not be a perfect circle [2] (e)(ii) Reasonable means of improvement, that addresses one of the identified errors Possible answers: • Clamp a ruler (vertically) behind the setup, so that y can immediately be read off when the ball drops. • Attach a small lump of Blu Tack with a depression in the centre to the tabletop, to pivot the cone. • Rest the cone at a slight inclination against a book or block of suitable size. [1]

5 © Hwa Chong Institution 2023 Not accepted: • U