WJEC Unit 1 2024 June — Question 16 10 marks

Exam BoardWJEC
ModuleUnit 1 (Unit 1)
Year2024
SessionJune
Marks10
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCompleting the square and sketching
TypeDiscriminant for real roots condition
DifficultyModerate -0.8 This is a straightforward multi-part question testing standard AS-level techniques: discriminant for no real roots (routine application of b²-4ac < 0), solving a quadratic-linear intersection (standard algebraic manipulation), and sketching graphs using found information. All parts are textbook exercises requiring only direct application of well-practiced methods with no problem-solving insight needed.
Spec1.02d Quadratic functions: graphs and discriminant conditions1.02f Solve quadratic equations: including in a function of unknown1.02n Sketch curves: simple equations including polynomials

  1. Find the range of values of \(k\) for which the quadratic equation \(x^2 - kx + 4 = 0\) has no real roots. [4]
  2. Determine the coordinates of the points of intersection of the graphs of \(y = x^2 - 3x + 4\) and \(y = x + 16\). [4]
  3. Using the information obtained in parts (a) and (b), sketch the graphs of \(y = x^2 - 3x + 4\) and \(y = x + 16\) on the same set of axes. [2]

Question 16:
AnswerMarks
1610
Question 16:
16 | 10
\begin{enumerate}[label=(\alph*)]
\item Find the range of values of $k$ for which the quadratic equation $x^2 - kx + 4 = 0$ has no real roots. [4]

\item Determine the coordinates of the points of intersection of the graphs of $y = x^2 - 3x + 4$ and $y = x + 16$. [4]

\item Using the information obtained in parts (a) and (b), sketch the graphs of $y = x^2 - 3x + 4$ and $y = x + 16$ on the same set of axes. [2]
\end{enumerate}

\hfill \mbox{\textit{WJEC Unit 1 2024 Q16 [10]}}