0580.E2.2.05 — ax3 + bx2 + cx.: past paper questions

Real questions on 0580.e2.2.05 — ax3 + bx2 + cx.

The newest 5 of 5 written questions. Open one to see it on the real paper.

1. 0980/41 · October/November 2023 · Q9e[3]
   9 \quad f(x) = (3x+1)(x+5)(x-4) \quad g(x) = 2x-3 \quad h(x) = 4^{2x-1} (e) \quad f(x) = (3x+1)(x+5)(x-4) This can be written in the form $f(x)=a{x}^3+b{x}^2+cx+d$. Find the value of each of $a,b,c$ and $d$.See it on the paper →
2. 0980/21 · October/November 2021 · Q16a[2]
   16 Find the $n$th term of each sequence. (a) 8, 15, 34, 71, 132, ....See it on the paper →
3. 0980/42 · May/June 2021 · Q9a(i)[2]
   (a) (i) The equation $y=x^3-4x^2+4x$ can be written as $y=x(x-a{)}^2$. Find the value of $a$. $a=$See it on the paper →
4. 0980/42 · May/June 2021 · Q9a(ii)[4]

   4-mark question — its maths and diagrams are best seen on the paper.

   See it on the paper →
5. 0980/42 · May/June 2021 · Q9b[7]
   (b) Find the equation of the tangent to the graph of $y=x^3-4x^2+4x$ at $x=4$. Give your answer in the form $y=mx+c$.See it on the paper →

What examiners said

Of those candidates who attempted this part, the ones who were most successful were those who set out their working clearly and began by expanding one pair of brackets then, after simplifying, set out clearly the multiplication of this quadratic and the third bracket to form the cubic expression. Inconsistent use of brackets, e.g., not surrounding their answer to the expansion of the first two bra...

— Examiner report, October/November 2023, 0980/41 Q9(e) (Cambridge)

This part proved challenging for many. Candidates that were successful generally used one of two methods, either showing that the expression factorised to x( x − 2)2 leading to the answer of 2 when comparing it to x( x − a)2 or alternatively x( x − a)2 expands to x 3 − 2ax 2 + a 2 x also leading to the answer of 2 when comparing to x 3 − 4 x 2 + 4 x .

— Examiner report, May/June 2021, 0980/42 Q9(a)(i) (Cambridge)

Curve sketching is new to the syllabus and the sketching of the curve for the equation in part (a)(i) proved to be very challenging. Candidates are expected to have knowledge of cubic graphs and also when a curve passes through the origin. Sketching a correctly shaped positive cubic passing through the origin was awarded two of the available marks. A significant number of candidates did not draw...

— Examiner report, May/June 2021, 0980/42 Q9(a)(ii) (Cambridge)