CAIE P1 2002 June — Question 1 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2002
SessionJune
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 a linear expression into a reciprocal curve equation, leading to a quadratic. The algebraic manipulation is routine and the question is a standard textbook exercise with no conceptual challenges beyond basic technique.
Spec1.02c Simultaneous equations: two variables by elimination and substitution1.02q Use intersection points: of graphs to solve equations

1 The line \(x + 2 y = 9\) intersects the curve \(x y + 18 = 0\) at the points \(A\) and \(B\). Find the coordinates of \(A\) and \(B\).

AnswerMarks Guidance
\(x = 12, y = -1.5\) and \(x = -3, y = 6\)M1, A1, DM1, A1 Complete elimination of \(x\) or \(y\); Correct 3-term equation (not = 0); Correct method of solving quadratic = 0; Everything ok. Condone simple algebraic errors in first M1. Guesswork B2 B2
$x = 12, y = -1.5$ and $x = -3, y = 6$ | M1, A1, DM1, A1 | Complete elimination of $x$ or $y$; Correct 3-term equation (not = 0); Correct method of solving quadratic = 0; Everything ok. Condone simple algebraic errors in first M1. Guesswork B2 B2
1 The line $x + 2 y = 9$ intersects the curve $x y + 18 = 0$ at the points $A$ and $B$. Find the coordinates of $A$ and $B$.

\hfill \mbox{\textit{CAIE P1 2002 Q1 [4]}}