Date | November 2020 | Marks available | 2 | Reference code | 20N.1.SL.TZ0.T_1 |
Level | Standard Level | Paper | Paper 1 | Time zone | Time zone 0 |
Command term | Find | Question number | T_1 | Adapted from | N/A |
Question
Iron in the asteroid 16 Psyche is said to be valued at 8973 quadrillion euros (EUR), where one quadrillion =1015.
James believes the asteroid is approximately spherical with radius 113 km. He uses this information to estimate its volume.
Write down the value of the iron in the form a×10k where 1≤a<10 , k∈ℤ.
Calculate James’s estimate of its volume, in km3.
The actual volume of the asteroid is found to be 6.074×106 km3.
Find the percentage error in James’s estimate of the volume.
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
8.97×1018 (EUR) (8.973×1018) (A1)(A1) (C2)
Note: Award (A1) for 8.97 (8.973), (A1) for ×1018. Award (A1)(A0) for 8.97E18.
Award (A0)(A0) for answers of the type 8973×1015.
[2 marks]
4×π×11333 (M1)
Note: Award (M1) for correct substitution in volume of sphere formula.
6 040 000 (km3) (6.04×106, 5771588π3, 6 043 992.82) (A1) (C2)
[2 marks]
|6 043 992.82-6.074×1066.074×106|×100 (M1)
Note: Award (M1) for their correct substitution into the percentage error formula (accept a consistent absence of “×106” from all terms).
0.494 (%) (0.494026…(%)) (A1)(ft) (C2)
Note: Follow through from their answer to part (b). If the final answer is negative, award at most (M1)(A0).
[2 marks]