Easy -2.5 This is a trivial 1-mark question requiring only reading comprehension to extract a calculation from given text, with no mathematical content or problem-solving involved. It's essentially asking students to explain a figure that was already calculated in the provided material.
In lines 59 and 60, the text says "In that case the proportion suffering such an attack would be 6.4%."
Explain how this figure was obtained. [1]
Multiply up and equating or substituting: \(1 = A(x^2+1) + (Bx+C)(2x+1)\)
\(x = -\frac{1}{2}: 1 = \frac{5}{4}A \Rightarrow A = \frac{4}{5}\)
Coeff of \(x^2\): \(0 = A + 2B \Rightarrow B = -\frac{2}{5}\)
Constants: \(1 = A + C \Rightarrow C = \frac{1}{5}\)
Answer
Marks
M1
correct form of partial fractions
M1
mult up and equating or substituting oe soi www
B1
www
B1
www
B1
www
For omission of \(B\) or \(C\) on numerator, M0, M1, then (x= -1/2, A= 4/5) B1, B0, B0 is possible.
For \(\frac{A+Dx}{2x+1} + \frac{Bx+C}{x^2+1}\), M1,M1 then B1 for both A=4/5 and D=0, B1 is possible.
isw for incorrect assembly of final partial fractions following correct A,B & C.
condone omission of brackets for second M1 only if the brackets are implied by subsequent working.
Total: [5]
**Answer:** $\frac{1}{(2x+1)(x^2+1)} = \frac{A}{2x+1} + \frac{Bx+C}{x^2+1}$
Multiply up and equating or substituting: $1 = A(x^2+1) + (Bx+C)(2x+1)$
$x = -\frac{1}{2}: 1 = \frac{5}{4}A \Rightarrow A = \frac{4}{5}$
Coeff of $x^2$: $0 = A + 2B \Rightarrow B = -\frac{2}{5}$
Constants: $1 = A + C \Rightarrow C = \frac{1}{5}$
| M1 | correct form of partial fractions |
| M1 | mult up and equating or substituting oe soi www |
| B1 | www |
| B1 | www |
| B1 | www |
| | For omission of $B$ or $C$ on numerator, M0, M1, then (x= -1/2, A= 4/5) B1, B0, B0 is possible. |
| | For $\frac{A+Dx}{2x+1} + \frac{Bx+C}{x^2+1}$, M1,M1 then B1 for both A=4/5 and D=0, B1 is possible. |
| | isw for incorrect assembly of final partial fractions following correct A,B & C. |
| | condone omission of brackets for second M1 only if the brackets are implied by subsequent working. |
**Total: [5]**
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In lines 59 and 60, the text says "In that case the proportion suffering such an attack would be 6.4%."
Explain how this figure was obtained. [1]
\hfill \mbox{\textit{OCR MEI C4 2011 Q1 [1]}}