Analysis of Edexcel C3 Mathematics June 2013
I show here that those students who prepared for the C3 June 2013 maths exam using the
previous nine C3 past papers would not have found adequate rehearsal of question types. I
analyse all eight questions, pointing out the papers where a similar type of question
appeared, and showing those questions where the previous nine past papers would have
provided no assistance.
My conclusion is that question Nos 1, 2, 3(a), and 5 had extra levels of difficult over the
previous nine papers measured against similar types of question. Also the provision of
unnecessary information for No. 8 made it seem more difficult than it was.
While Edexcel might correctly argue that all elements of this paper were on the syllabus, the
difficulty of a paper depends on the way these elements are coordinated. My analysis shows
that some of this coordination was more complex than in the previous nine papers. So I
conclude that compared with the previous nine C3 papers, the Edexcel C3 mathematics
paper June 2013 was far more difficult and that the grade boundaries should therefore be
lower than all of these.
Barry R. Clarke
Mathematics tutor and puzzle author
http://barryispuzzled.com
Usually done with a long division and the banana skin is that a 0x term is required in the x2 – 4. Could
be done by multiplying through by x2 – 4 and comparing coefficients each side of x4, x3, etc.
Verdict. I think many students would have been expecting a cancelling algebraic fractions question
as occurred in the previous nine papers. (Jan 2013 No. 7, June 2012 No. 1, Jan 2012 No. 7, June 2011
No. 7, Jan 2011 No. 2, June 2010 No. 8, Jan 2010 No. 1, June 2009 No. 7, Jan 2009 No. 2). At the top
end of algebraic long division difficulty and outside past paper preparation.
(7)
This has two levels: knowing the ln x graph, and performing transformations on it. The previous nine
papers had only the transformations element and the function was already drawn (Jan 2013 No. 3,
June 2012 No.4, Jan 2012 No. 2, June 2011 No. 3, Jan 2011 No. 6, June 2010 No. 6, Jan 2010 No. 6,
June 2009 No. 5, Jan 2009 No. 3)
Verdict. With the added requirement of knowing the ln x graph it’s at the top end of difficulty for
this question type and lies outside past paper preparation.
Part 3(a) required knowledge that sin(x) = cos (90 – x). Previous papers have tested double angle
formulae (Jan 2013 No. 6, June 2012 No. 5, June 2011 No. 6, Jan 2011 No. 3, June 2010 No. 1), the
sin(A+B) and cos(A+B) identities (Jan 2012 No. 8, Jan 2009 No. 6), the 1 + cot2x = cosec2x and 1 +
tan2x = sec2x identities (Jan 2010 No.8, June 2009 No. 2). Part (b) makes use of part (a).
Verdict. None of the last nine papers have tested sin(x) = cos (90 – x). Even if the student knew this
there is considerable work to do to extract the solution. Much more difficult than previous papers.
Part (a) is a product and chain rule differentiation. Previous papers have involved the natural
logarithm function (Jan 2013 No. 5, June 2012 No. 7, Jan 2011 No. 1, June 2011 No. 1, Jan 2010 No.
4, June 2009 No. 4, Jan 2009 No. 5). There are precedents for the exponential function in a product
rule (e.g. June 2012 No. 3, June 2010 No. 5, Jan 2010 No. 7). Parts (c) and (d) are standard iteration.
Verdict. Most students would have expected a natural logarithm differentiation but an exponential
function in a product rule could have been prepared for using past papers.
This is a question about converting dx/dy into dy/dx with x eventually built into it. In Jan 2013 (No. 5)
it was cot(y), June 2012 (No. 7) it was 3tan(2y), Jan 2012 (No. 4) it was 2tan(y+(π/12)), June 2011 it
didn’t occur, Jan 2011 (No. 8) it was sec(2y), June 2010 it didn’t occur, Jan 2010 (No. 4) it was tan(y),
June 2009 it didn’t occur, and Jan 2009 (No. 4) it was cos(2y+ π). What makes June 2013 more
difficult than the previous papers cited here is that it’s a triple chain rule not a double as with the
others. It has an added square function with sec2(3y).
Verdict. The triple chain rule makes it more difficult than the previous nine papers. None of these
papers asked for a second derivative d2y/dx2 in any question never mind one as challenging as this!
Part (a) is a C2 question. June 2010 (No. 8) has a similar question so there is a precedent. Part (b)
involves taking logarithms of both sides.
Verdict. A reasonable question that had a precedent so could have been prepared for.
Part (a) is reasonable, part (b) requires using eqn straight line to get y from x=0 then use this y value
in another straight line eqn as x to estimate y again. Jan 2013 (No. 3) and Jan 2011 (no. 6) were
similar though neither uses the eqn of a straight line. Part (c) is finding an inverse by setting g equal
to y and making x the subject (e.g. June 2012 No. 6, Jan 2012 No. 7).
Verdict. Preparation using past papers was possible for this question but it’s definitely one of the
more difficult examples of this type of question taken over the past nine papers.
The V function can be derived from the information in the diagram but the question does not
require a derivation so it is not necessary to give the 3 ms-1 and 24m information. All the student
needs is the V function and the triangle. Parts (a) and (b) are similar to Jan 2013 No. 4, but the
theory also occurs in June 2012 No. 8, and June 2011 No. 8. Part (c) needs a calculation of the angle
θ then trigonometry yields distance AB. Part (d) uses the function V to find the angle θ.
Verdict. No mechanics required but by giving the 3 ms-1 and 24m information it was made to seem
more difficult than it was.
Conclusion
I think students have a right to feel that this paper was more difficult than previous ones.