| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2008 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Basic factored form sketching |
| Difficulty | Moderate -0.8 This is a straightforward C1 question requiring basic polynomial expansion and sketching a cubic from factored form. Students only need to identify x-intercepts from factors, find the y-intercept by substituting x=0, and sketch a standard cubic shape—all routine procedures with no problem-solving required. |
| Spec | 1.02j Manipulate polynomials: expanding, factorising, division, factor theorem1.02n Sketch curves: simple equations including polynomials |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \((x-5)(x+2)(x+5)\) | B1 | \(x^2 - 3x - 10\) or \(x^2 + 7x + 10\) or \(x^2 - 25\) seen |
| \(= (x^2 - 3x - 10)(x+5)\) | M1 | Attempt to multiply a quadratic by a linear factor |
| \(= x^3 + 2x^2 - 25x - 50\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Positive cubic with 3 roots (not 3 line segments) | B1 | |
| \((0, -50)\) labelled or indicated on \(y\)-axis | B1\(\checkmark\) | |
| \((-5, 0)\), \((-2, 0)\), \((5, 0)\) labelled or indicated on \(x\)-axis and no other \(x\)-intercepts | B1 |
## Question 6(i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $(x-5)(x+2)(x+5)$ | B1 | $x^2 - 3x - 10$ or $x^2 + 7x + 10$ or $x^2 - 25$ seen |
| $= (x^2 - 3x - 10)(x+5)$ | M1 | Attempt to multiply a quadratic by a linear factor |
| $= x^3 + 2x^2 - 25x - 50$ | A1 | |
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## Question 6(ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Positive cubic with 3 roots (not 3 line segments) | B1 | |
| $(0, -50)$ labelled or indicated on $y$-axis | B1$\checkmark$ | |
| $(-5, 0)$, $(-2, 0)$, $(5, 0)$ labelled or indicated on $x$-axis and no other $x$-intercepts | B1 | |
---6 (i) Expand and simplify $( x - 5 ) ( x + 2 ) ( x + 5 )$.\\
(ii) Sketch the curve $y = ( x - 5 ) ( x + 2 ) ( x + 5 )$, giving the coordinates of the points where the curve crosses the axes.
\hfill \mbox{\textit{OCR C1 2008 Q6 [6]}}