CAIE P1 2003 November — Question 1 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2003
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicSimultaneous equations
TypeLine intersecting reciprocal curve
DifficultyModerate -0.8 This is a straightforward simultaneous equations problem requiring substitution of y = 11 - 2x into xy = 12, leading to a simple quadratic. It's more routine than average A-level questions since it involves only basic algebraic manipulation with no conceptual challenges or multi-step reasoning.
Spec1.02c Simultaneous equations: two variables by elimination and substitution

1 Find the coordinates of the points of intersection of the line \(y + 2 x = 11\) and the curve \(x y = 12\).

\(x(11-2x) = 12\)
\(2x^2-11x+12=0\)
AnswerMarks Guidance
Solution of quadratic \(\rightarrow (1\frac{1}{2},8)\) and \((4,3)\)M1, A1, DM1, A1 Complete elimination of \(x\), or of \(y\). Correct quadratic. Correct method of solution \(\rightarrow\) 2 values. All correct (guesswork or TI B1 for one pair of values, full marks for both).
$x(11-2x) = 12$
$2x^2-11x+12=0$
Solution of quadratic $\rightarrow (1\frac{1}{2},8)$ and $(4,3)$ | M1, A1, DM1, A1 | Complete elimination of $x$, or of $y$. Correct quadratic. Correct method of solution $\rightarrow$ 2 values. All correct (guesswork or TI B1 for one pair of values, full marks for both).
1 Find the coordinates of the points of intersection of the line $y + 2 x = 11$ and the curve $x y = 12$.

\hfill \mbox{\textit{CAIE P1 2003 Q1 [4]}}