| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2017 |
| Session | June |
| Marks | 6 |
| Topic | Discriminant and conditions for roots |
| Type | Find k for equal roots |
| Difficulty | Moderate -0.8 This is a straightforward discriminant question requiring only direct application of b²-4ac formula and setting it equal to zero. Part (a) is pure recall/calculation, and part (b) is a standard textbook exercise with no problem-solving insight needed—just substitute into the discriminant formula and solve a simple linear equation for k. |
| Spec | 1.02d Quadratic functions: graphs and discriminant conditions1.02f Solve quadratic equations: including in a function of unknown |
**Question 2: Discriminant and real roots**
**(a)(i)**
- $\Delta = b^2 - 4ac$ **M1** Attempt discriminant
- $= 9 - 20 = -11$ **A1** Obtain $-11$
**(a)(ii)**
- No real roots **B1\*** FT. Correct conclusion, following *their* numerical discriminant – allow BOD if *their* (i) had square root present
- as $-11 < 0$ **B1d\*** FT. Correct reasoning, using discriminant (insufficient to just state that roots are imaginary as the reason)
**(b)**
- $\Delta = 9 - 20k = 0$ **M1** Equate attempt at discriminant to 0. Allow M1 if using an incorrect discriminant formula if this is the same as used in (a)(i)
- $k = \frac{9}{20}$ **A1** Obtain $\frac{9}{20}$ oe. Allow BOD for both M1 and A1 if equating the square root of the discriminant to 0
**Total: 6 marks**2
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Find the value of the discriminant of $x ^ { 2 } + 3 x + 5$.
\item Use your value from part (i) to determine the number of real roots of the equation $x ^ { 2 } + 3 x + 5 = 0$.
\end{enumerate}\item Find the non-zero value of $k$ for which the equation $k x ^ { 2 } + 3 x + 5 = 0$ has only one distinct real root.
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2017 Q2 [6]}}