| Date | May 2018 | Marks available | 5 | Reference code | 18M.1.hl.TZ0.3 |
| Level | HL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 3 | Adapted from | N/A |
Question
A number written in base 5 is 4303. Find this as a number written in base 10.
[2]
a.
1000 is a number written in base 10. Find this as a number written in base 7.
[5]
b.
Markscheme
43035 = 4 × 53 + 3 × 52 + 0 × 51 + 3 × 50 (M1)
= 500 + 75 + 3
= 578 A1
[2 marks]
a.
METHOD 1
\(1000 = {a_0} + 7{a_1} + 49{a_2} + 343{a_3}\) (M1)
(since \(343{a_3} < 1000\))\( \Rightarrow {a_3} = 2\) (A1)
\(1000 = {a_0} + 7{a_1} + 49{a_2} + 686\)
\({a_0} + 7{a_1} + 49{a_2} = 314 \Rightarrow {a_2} = 6\) (A1)
\({a_0} + 7{a_1} = 20 \Rightarrow {a_1} = 2,\,\,{a_0} = 6\) (A1)
\( \Rightarrow {1000_{10}} = {2626_7}\) A1
METHOD 2
1000 = 7 × 142 + 6 (M1)
142 = 7 × 20 + 2 (A1)
20 = 7 × 2 + 6 (A1)
2 = 7 × 0 + 2 (A1)
⇒ (1000)10 = 26267 A1
[5 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
