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Hello and Welcome to AS and Advanced GCE Mathematics: Feedback on June 2015 (Unit FP1) Live Online
Event. Here are the Aims and Objectives for the session.
In this training session, you will: Receive feedback on national performance of
candidates in Unit FP1 of the June 2015 examination series.
Consider the variation of candidates performance on different questions and possible reasons
why. Discuss the Examiners' reports.
Address common issues and FAQs.
Here's the outline that we will be following during this training session:
Introductions, delegate polls and Agenda. Introduction to the FP1 Qualification and
Feedback on the FP1 June 2015 examination. Common issues, further training, any questions.
Finish.
Now we're going to start with the Introduction to FP1.
Here's a screenshot of the Specification. Please download it from the website if you
think it's necessary. The paper was found to be accessible to a
wide range of candidates. The mean score was 61 out of 75.
Questions 1,2,3,4 and 5 were familiar and provided all candidates with a good source
of marks. The work was generally well set out.
Questions 6, 7 and 8 proved more demanding. Timing did not seem to be a problem as most
candidates seemed to finish the paper. All steps need to be shown in questions involving
proof. This question tested finding the roots of
a cubic equation Almost all candidates recognised that (x 5)
was a factor. The majority successfully found the correct
quadratic factor, usually by performing algebraic long division.
Most candidates were confident at solving the resulting quadratic with complex roots.
Candidates appeared to be aware that solutions appeared as a complex conjugate pair.
Very few candidates ended with only real solutions. Candidates who did well, found the quadratic
factor by long division or inspection. And then quoted and used the quadratic formula
correctly to find the complex roots. Candidates who did less well could find the
quadratic factor but found real roots incorrectly. This question tested interval bisection in
part (a) and linear interpolation in part (b).
Interval bisection in part (a) was generally well understood, with most candidates arriving
at the correct answer. A few only bisected the interval once, while
several continued until the function values (rather than input values) had an interval
of less than 0.25. The method of linear interpolation in part
(b) was generally well attempted although some candidates used negative lengths.
Some candidates attempted to find the equation of the line between two points but with less
success. Some errors were made where candidates used
the interval found in part (a) to interpolate instead of the interval given in the question.
In part (a), candidates who did well, sometimes set their work out in a table.
In part (b), candidates who did well, used similar triangles.
In part (b), candidates who did less well, used similar triangles but with a negative
length. This question tested finding the sum of a
series using standard formulae in part (a) and then to using this result to find a particular
sum in part (b). Most candidates used the general formulae
successfully in part (a). Many candidates multiplied out all the brackets and only removed
a factor at the end of their working. This was usually a successful approach.
Of those removing a factor of n/3 or n/2 at the start, the biggest problem was carelessness
in their working, leading to unnecessary slips. Most candidates were fully successful in part
(b), although those who had been unable to complete part (a), often did not attempt part
(b). Common errors included inaccurate multiplying
out of brackets, not using the formula shown in part (a), or calculating f(n + 1) f(n)
or other incorrect combinations. In part (a), candidates who did well, substituted
the correct formulae and often left any factorising after multiplying out.
In part (a), candidates who did less well, often started correctly but sometimes made
careless errors. This question tested knowledge of complex
numbers. Almost all candidates made a confident attempt
at part (a). In part (b), a significant number of candidates
neglected to calculate the modulus. This suggested that they did not read the question properly.
Almost all candidates recognised the use of the tan function to calculate the argument.
However, many candidates did not make use of an argand diagram or their knowledge of
complex numbers to use the correct sign for the argument, leaving their answer as ?/3.
The Argand diagram in part(c) was frequently completed successfully, although not all candidates
could place z2 in the correct quadrant. In part (a), candidates who did well, followed
a correct method and set their work out so it was easy to follow.
In part (b), candidates who did well found the modulus correctly and located the argument
in the correct quadrant. In part (b) some candidates did not consider
the appropriate quadrant when calculating the argument.
This was a coordinate geometry question involving the rectangular hyperbola.
Most candidates found part (a) accessible, using a variety of different approaches and
the given equation was generally reached successfully without errors.
Most candidates successfully obtained an equation in one variable in part (b) and worked their
solution through to find the correct coordinates. Errors appeared to be mostly careless, rather
than brought about by poor understanding of the question.
In part (a) most candidates could establish the required result without errors.
In part (b) this candidate did well by obtaining an equation in x and then used the quadratic
formula to solve the equation. In part (b) this candidate did less well as
they made a mistake in calculating the value of y.
This was a question on proof by induction. Generally, most candidates were able to demonstrate
their understanding of the concept of proof by induction and a large number of candidates
produced clear, well-structured solutions, with correct conclusions.
In part (i), matrix multiplication was generally well executed, although many candidates struggled
to rearrange their answer to resemble what they were trying to prove. Some missed out
an intermediate stage altogether. In part (ii), candidates who took (2k + 1)
out as a factor at the beginning were generally successful. More candidates, however, multiplied
everything out and then took (k + 1) out as a factor. Some candidates arrived at the expression
with 3 linear factors and then struggled to complete the proof.
In part (i), candidates who did well, started by showing clearly that the result was true
for n = 1. In part (i), candidates who did well, then
showed clearly that the result was true for k + 1 if it is true for k.
And then gave a complete conclusion. This question tested matrices and transformations.
Part (i) was usually completely correct and most candidates also successfully found the
inverse in part (ii)(a). Where marks were lost, it was usually because the elements
of the matrix were not changed according to the correct rules.
Those candidates who post multiplied their inverse by a 2 ? 3 matrix in part (ii)(b)
were generally successful, although a few forgot the factor of 1/45.
Some candidates attempted to pre-multiply their inverse by a matrix and some candidates
used simultaneous equations, with varying degrees of success.
Candidates who had completed part (b) successfully often completed part (ii)(c) successfully
too. Many candidates did not attempt this part because they had struggled with earlier
parts of the question. Some candidates could not successfully calculate the area of T,
some did not use the area of T ? and some did not divide it by 45.
In part (i) Many candidates found the values of k correctly.
Many candidates knew what to do in (c) but sometimes there were careless errors.
This was the second coordinate geometry question but this time involving the parabola.
Most candidates completed part (a) successfully, although many had trouble dealing with polynomial
expressions underneath a square root. Many errors were made by candidates incorrectly
using the length formula (i.e. 6p2 instead of 36p2). Those candidates using the directrix
were seldom explicit enough in their proof. Most candidates made a good attempt at part
(b) and reached correct equations for the two tangents. Problems included incorrect
differentiation and incorrect substitution. Many candidates also struggled to eliminate
one of the variables, but of those who did, usually completed correctly.
Many successfully attempted to calculate SR2. Several candidates tried to calculate SQ (and
sometimes SP) from scratch, usually without success. Some candidates did manage to prove
the equality, but many gave up. Often, marks were lost when the candidate failed to write
a concluding statement.
Candidates should make sure that they read the questions carefully.
Candidates should be very careful in their use/omission of brackets.
Candidates should be prepared to include all steps in a 'show that' or proof question.
Make sure that your candidates can recognise how to link up the parts in a question. Key
words like 'hence' could be highlighted.