This is a cut-down version of the FP1 “Silver” paper.

More practice questions, taken from Edexcel Bronze papers

**Comments after marking the test**

Q.3 – a few of you made a slip in the multiplication to find A^{2}. You should have been warned about this by part (b).

Edexcel only ever asks you to identify, geometrically, reflections, rotations, and enlargements (scalings by same scale factor in every direction). Never shearings, or scalings by different scale factors in different directions.

Why? I don’t know, but it’s a fact, and it gives you a check on questions like that. If your geometrical transformation comes out as a shearing, or a scaling by different scale factors in different directions, you’ve made a slip.

In fact, in Edexcel questions though not in real life, if the transformation has determinant 1, it’s a rotation; if it has determinant -1, it’s a reflection; if it has any other determinant, it’s an enlargement.

Q.4- a couple of you made a slip by converting a multiplication into an addition.

You got x^{2} = −9/4

then said, correctly, x = plus or minus √(−1).√(9/4)

then, when you should have said x = plus or minus (3/2)i

you said x = plus or minus i plus 3/2

Q.5 – there were a few slips in multiplying to find R^{2}, but most of you got that right.

But then some of you interpreted “R^{2} represents an enlargement with scale factor 15″ to mean R^{2} has a determinant of 15.

It’s simpler than that. An enlargement with scale factor 15 is just a matrix like this:

15 0

0 15

Its determinant – the factor by which it increases *areas* – is in fact 225, because it increases the length of every shape by 15 and its width by 15, too.

Remember, if Mr Bannister puts a display with a picture of you twice life-size height and twice life-size width in the atrium to replace Juan’s picture, then the area of the picture will be four times life-size. If it’s three times life-size height and three times life-size width, then the area will be nine times life-size.

Some of you failed to notice that the question says a>0, which means that the value a=-5 is impossible and the answer must be a=3.

Q.6 – everyone used radians rather than degrees! Well done!

Most common mistake was to do interval bisection rather than linear interpolation, which was asked for.

Remember, interval bisection means bisecting, cutting the interval in two halves.

Linear interpolation means drawing a diagram with a line.

A few of you rounded your values of f(1) and f(2) to one decimal place. Silly move, because then your linear interpolation calculation couldn’t be accurate to 2 d.p. In such cases, use values of f(1) and f(2) accurate to at least one d.p. more than the accuracy required for the result.

Some of you did unnecessary work. Once you’ve got your next guess, or approximation, as 1.61, you don’t have to work out f(1.61) unless you’re doing a second round of linear interpolation.

Q.7 – everyone had the basic method right, but a few people made slips. It is fine to leave your answer for inverse of B with the (1/10) factor standing outside the matrix.

Q.8 – unsurprisingly, many of you were in a rush by the time you got to Q.8, and so made some mistakes which looked as if they were due to rushing it.

8(a) is most easily done by going from

4 | 5^{k} + 8k + 3

to

4 | 5^{k} + 4×5^{k} + 8k + 8 + 3

i.e. using the fact that you can add anything divisible by 4 to the right-hand side of the divisibility statement.

It’s only a bit longer to do it by multiplying the right-hand side by 5

4 | 5×5^{k} + 5×8k + 5×3

so

4 | 5^{k+1} + 8k + 32k + 3 + 12

so

4 | 5^{k+1} + 8k + 3 because 32k+12 is divisible by 4 and can be subtracted from the right-hand side

But a few of you wrote

4 | 5×5^{k} + 8k + 3

which is not valid reasoning, since if you multiply some of the right-hand side by 5, you must multiply it all by 5.