| Date | November 2011 | Marks available | 1 | Reference code | 11N.1.sl.TZ0.1 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Write down | Question number | 1 | Adapted from | N/A |
Question
Given that \(z = \frac{{12\cos (A)}}{{4q + r}}\) and that \(A = {60^ \circ }\), \(q = 8\) and \(r = 32\);
Find the exact value of \(z\).
Write your answer to part (a) correct to 2 decimal places.
Write your answer to part (a) correct to three significant figures.
Write your answer to part (a) in the form \(a \times {10^k}\), where 1 ≤ a < 10, \(k \in {\mathbb{Z}}\) .
Markscheme
\(z = \frac{{12\cos ({{60}^ \circ })}}{{(4(8) + 32)}}\) (M1)
Note: Award (M1) for correct substituted formula seen.
\( = 0.09375\left( {\frac{3}{{32}}} \right)\) (A1)(C2)
[2 marks]
\(0.09\) (A1)(ft) (C1)
[1 mark]
\(0.0938\) (A1)(ft) (C1)
[1 mark]
\(9.375 \times {10^{ - 2}}\) (\(9.38 \times {10^{ - 2}}\)) (A1)(ft)(A1)(ft) (C2)
Note: Award (A1)(ft) for \(9.375\), (A1)(ft) for \( \times {10^{ - 2}}\). Follow through from their part (a).
[2 marks]
Examiners report
Although the use of radians leading to an incorrect answer of \( - 0.1785774388\) was seen on a minority of scripts, many candidates produced correct answers for parts (a) and (b)(i). The requirement for an answer to 3 significant figures led many to count the first zero after the decimal point and as a consequence gave an incorrect answer of \(0.094\). Despite any previous incorrect working, it was pleasing to see that most candidates were able to express their answer to part (a) in standard form.
Although the use of radians leading to an incorrect answer of \( - 0.1785774388\) was seen on a minority of scripts, many candidates produced correct answers for parts (a) and (b)(i). The requirement for an answer to 3 significant figures led many to count the first zero after the decimal point and as a consequence gave an incorrect answer of \(0.094\). Despite any previous incorrect working, it was pleasing to see that most candidates were able to express their answer to part (a) in standard form
Although the use of radians leading to an incorrect answer of \( - 0.1785774388\) was seen on a minority of scripts, many candidates produced correct answers for parts (a) and (b)(i). The requirement for an answer to 3 significant figures led many to count the first zero after the decimal point and as a consequence gave an incorrect answer of \(0.094\). Despite any previous incorrect working, it was pleasing to see that most candidates were able to express their answer to part (a) in standard form.
Although the use of radians leading to an incorrect answer of \( - 0.1785774388\) was seen on a minority of scripts, many candidates produced correct answers for parts (a) and (b)(i). The requirement for an answer to 3 significant figures led many to count the first zero after the decimal point and as a consequence gave an incorrect answer of \(0.094\). Despite any previous incorrect working, it was pleasing to see that most candidates were able to express their answer to part (a) in standard form.
