SAJC 2024 J2 H2 Physics Prelim P4 Soln

1 Mark Scheme for 2024 SAJC Prelims P4 Q1 ( A-lev Pract in 2023) No Marking Point Score (a) € Recorded R as labelled, ie 68 Ω (as per question) € Recorded I as shown on display, ie to nearest 0.1 mA € Accuracy: range of I : 110.0– 130.0 mA € Recorded repeat measurements of y to nearest mm ( ie to 1 mm, 0.1 cm or 0.001 m) € Recorded average value of y to same dp as its raw readings ( ie to nearest mm) /1 (b) Tabulation € At least 5 sets of readings of R & repeated y. /1 Column Headings inTable € Each column heading must have a quantity and a unit: eg R /Ω, y/cm, R/y. /1 Precision of Recording For Raw Data: € Recorded all R to nearest Ω (as labelled) € Recorded all y to nearest mm € Recorded all I to nearest 0.1 mA (if recorded) For Calculated Data: ( eg for R/y, IR, 1/R, 1/y)  Correct no. of sf (which takes into account consistency within a given column) /1 (c) Graph: Scale, Size & Axes € Sensible scales, ie no awkward scales (eg 3 units into 10 small squares) € Plotted pts occupy at least ½ the graph grid in both x & y directions € Axes labelled with the quantity & unit € Successive scale markings: not more than 20 small squares apart. /1 Plotting of Points € ALL observations in table must be plotted € Accurate to within half a small square. € Thickness of plots (ie the crosses, ‘x’)  half a small square /1

2 Best fit line & Anomaly € Straight line drawn with approx. equal number of points on either side of line (anomalous point not considered). € Line must not be kinked/disjointed or thicker than half a small square € Anomalous plot clearly indicated (eg by a circle or labelled “anomaly”.) € Maximum number of anomalous plot allowed: 1 /1 Correct Trend: ( Not awarded for Inappropriate graph) Appropriate graph using data where as R increases, y decreases. /1 Determination of Gradient ( Not awarded for Inappropriate graph) € Gradient coordinates clearly indicated on graph and in working (accurately recorded) € Precision of gradient coordinates: either to 3 sf or to ½ a small square € Hypotenuse of triangle > half length of line drawn € No obscurity of the 2 points used for gradient calculation. {Hence triangle must not be drawn too near a data plot.} € Precision of gradient: either to 3 sf, or, same number of sf as the coordinate with the least number of sf, or 1 more. € Value of F: calculated correctly to 3 sf. ( Accept 4 sf ) /1 Units of the unknown constants  F: A Ω, or V ( Accept mA )  Q: Ω m-1 ( Accept  cm-1) /1 Determination of y-intercept ( Not awarded for Inappropriate graph) € y-intercept calculated using a point on the line {not from the table} & value of gradient. € Value of Q: a POSITIVE value, 3 s.f. ( Accept 4 sf ) Or, € Reading off the y-intercept if x-axis starts from zero ( ie no false origin) € Value of Q: a POSITIVE value, precision to ½ small square /1 Linearisation of Equation ( Not awarded for Inappropriate graph) For graph of R/y against R: € Stated explicitly: QI/F = gradient € Stated explicitly: - Q = y-intercept /1

3 (d) € Recorded repeat measurements (using micrometer) of d & its average to nearest 0.01 mm € Accuracy: acceptable range of d : 0.17 – 0.19 mm /1 Determination of p € Determined p correctly with given units. /1 Total /14

4 Mark scheme for 2024 SAJC Prelims P4 Q2 ( A-lev Pract in 2023) No Marking Point Score (a)(i) Measurement and Observation € Recorded θ to the nearest ⁰ € Accuracy of θ: within range 58 to 62⁰ (“ approx. 600 “)  Recorded repeated values of . /1 (a)(ii) Measurement and Observation € Recorded n to the nearest integer. /1 € Repeated measurements of n. € Accuracy: n between 7-11 /1 (b) Determination of k € Determined k correctly ( k = n/tan) {Allow ecf} € Number of sf: either 2 or 3 (since  has 2 sf & n is considered to be error- free) /1 /1 (c) Tabulation of 2 more values of  (including the 1st set), n & k ● Recorded both θ to the nearest ⁰, { No need to repeat for } ● Recorded repeated readings of n to the nearest integer. ● No mark awarded if not tabulated. /1 Range of θ € The 2 θs use should be at least 10⁰ difference with 60⁰ and one above 60⁰ and one below 60⁰. /1 (d) € If θ = 90⁰, both pendulums would have the same length and thus same period. They would then remain in phase indefinitely/would always be in phase/would never go out of phase. /1 Total 8

5 Mark scheme for 2024 SAJC Prelims P4 Q3 ( A-lev Pract in 2023) No Marking Point Score (a)(i) Measurement and Observation € Recorded at least 2 values each of h and L to nearest mm € Recorded average value of h and L to same dp as their raw readings ( ie to nearest mm) € Accuracy: range of h : 72.0 – 77.0 cm  h + L = betw 97.0 – 99 .0cm { NOT = 100 .0 cm } /1 (a)(ii) € Calculated h/L correctly. € Number of sf for h/L: same number or 1 more sf than the raw data (either h or L,) with the smaller number of sf. {Hence, 3 or 4 sf ) /1 (a)(iii)  Estimated percentage uncertainty of h/L correctly by adding percentage uncertainty of h (using h = 3 - 5 mm) and percentage uncertainty of L (using L = 6 - 8 mm).  L must be > h { as former has additional uncertainty due to position of it cg }  Recorded percentage uncertainty to 1 or 2 sf. /1 /1 (b) € Tabulate 5 sets {since only 5 masses provided} of readings, with column headings m, repeated h, repeated L , h/L & correct units. m / g h1 /cm h2 /cm L1 /cm L2 /cm h/L 100 200 300 /1

6 400 500 Precision of Recording: For Raw Data, ie for m, h and L: € Recorded m to nearest 100 g (as labelled), h to nearest mm and L to nearest mm For Calculated Data, ie for h/L  Correct no. of sf (which takes into account consistency within a given column) /1 (c)(i) € Best fit straight line drawn with 5 sets of readings. /1 (c)(ii) € Calculated X correctly (where X = 2/gradient, for graph of h/L vs m /1 (d) € Recorded X to nearest 0.01 g; Accuracy:range betw 80.00 – 130.00 g € Calculated correctly |𝑋1− 𝑋2| 𝑋2 x 100% (X1 from expt in (c), X2 measured in (d)) € ( Used the percentage uncertainty of (a) (iii) as the criterion.) Concluded that value in (a)(iii) does not explain the difference if |𝑋1− 𝑋2| 𝑋2 x 100% > percentage uncertainty of (a)(iii), or, concluded that value in (a)(iii) does explain the difference if |𝑋1− 𝑋2| 𝑋2 x 100% < percentage uncertainty of (a)(iii). /1 (e)(i) Measurement and Observation € Recorded a to nearest mm. ( range: not assessed, 2.5 – 12.0 cm) € Recorded M = 0.100 kg or value read fr mass balance to nearest 0.01 g. € Recorded L to nearest mm. (range: not assessed 12 - 20 cm) € Recorded u to nearest mm (if using metre rule). (range: not assessed, u = 1.2 cm )  Recorded t to nearest 0.01 mm (using micrometer). Accuracy: 0.70 -0.80 mm /1

7 € Repeat measurements of a & L. ( u & t: not necessary) /1 € Calculated Y correctly with the unit GPa (1 GPa = 109 Pa ) /1 € Number of sf for Y: same no. or 1 more sf than the raw data ( among M, L, u, t & g ) with the least number of sf. /1 (e)(ii) Significant/Major Sources of Error (Any one) € In the measurement of a, uncertainty arises as the reference horizontal axis is imaginary/not well-defined, or, € In the measurement of a, uncertainty arises due to the unsteadiness of the hand when holding the rule. /1 (e)(iii) Candidates are required to make the correct deduction by comparing Y for wood ( ie 12 GPa) with the experimental value for the hacksaw blade in (e) (i).) /1

8 (f) g-clamp slott