| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2019 |
| Session | Specimen |
| Marks | 7 |
| Topic | Completing the square and sketching |
| Type | Solve quartic as quadratic |
| Difficulty | Moderate -0.3 Part (a) is a routine completing the square exercise with straightforward coefficient extraction and reading off the minimum point. Part (b) is a standard quadratic substitution (let u = x²) leading to factorizable quadratic, then simple square roots. Both parts are textbook-standard techniques with no novel insight required, making this slightly easier than average overall. |
| Spec | 1.02e Complete the square: quadratic polynomials and turning points1.02f Solve quadratic equations: including in a function of unknown |
**(a)**
Compare coefficients — **M1**
Obtain $a = 2$ and $b = \frac{-5}{2}$ — **A1**
Obtain $c = \frac{-31}{2}$ — **A1**
State $\left(\frac{5}{2}, \frac{-31}{2}\right)$ — **A1** [4]
**(b)**
Use quadratic formula in $x^2$ — **M1**
Obtain $x^2 = \frac{9}{4}$ and $x^2 = 1$ — **A1**
Obtain $x = \pm\frac{3}{2}$ and $x = \pm 1$ — **A1** [3]4
\begin{enumerate}[label=(\alph*)]
\item Show that $2 x ^ { 2 } - 10 x - 3$ may be expressed in the form $a ( x + b ) ^ { 2 } + c$ where $a , b$ and $c$ are real numbers to be found. Hence write down the coordinates of the minimum point on the curve.
\item Solve the equation $4 x ^ { 4 } - 13 x ^ { 2 } + 9 = 0$.
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2019 Q4 [7]}}