Moderate -0.8 This is a straightforward integration question requiring recognition of the standard form (x-a)^(-2), direct integration to get -4/(x-3), and using the given point to find the constant. It's simpler than average A-level questions as it involves only one standard technique with no algebraic manipulation or problem-solving insight required.
The equation of a curve is such that \(\frac{dy}{dx} = \frac{4}{(x-3)^2}\) for \(x > 3\). The curve passes through the point \((4, 5)\).
Find the equation of the curve. [3]
Correct use of (4,5) to find c in an integrated expression
(defined by the correct power and no extra x’s or terms).
2
y 7 or y2x32 7
Answer
Marks
Guidance
x32
A1
4
OE must be simplified to –2. Condone c = 7 as their
2
final line as long as either y or f(x) = is seen elsewhere.
Do not ISW if the result is of the form y = mx+c.
3
Answer
Marks
Guidance
Question
Answer
Marks
Question 1:
1 | 4 4
y x331 or c
2 2x32 | B1 | 4
OE Allow and 31 for the power.
31
4 4
5 432 c or 5 c leading to c
2 2432 | M1 | Correct use of (4,5) to find c in an integrated expression
(defined by the correct power and no extra x’s or terms).
2
y 7 or y2x32 7
x32 | A1 | 4
OE must be simplified to –2. Condone c = 7 as their
2
final line as long as either y or f(x) = is seen elsewhere.
Do not ISW if the result is of the form y = mx+c.
3
Question | Answer | Marks | Guidance
The equation of a curve is such that $\frac{dy}{dx} = \frac{4}{(x-3)^2}$ for $x > 3$. The curve passes through the point $(4, 5)$.
Find the equation of the curve. [3]
\hfill \mbox{\textit{CAIE P1 2023 Q1 [3]}}