Edexcel IAL P1 January 2024 question paper and mark scheme (WMA11/01)

Try 3 P1 questions like these

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1. Trigonometry · 5 marks

   Triangle $ABC$ has sides $AB = 4$ cm and $BC = 5$ cm, with angle $ABC = 60^\circ$. Triangle $ACD$ shares side $AC$ and has a right angle at $C$. If $CD = 7$ cm, find the exact length of $AD$.

   Worked answer

   1. M1 for using the cosine rule in triangle ABC to find $AC^2$: $AC^2 = 4^2 + 5^2 - 2(4)(5)\cos 60^\circ$.
   2. M1 for evaluating to get $AC^2 = 16 + 25 - 40(0.5) = 21$.
   3. M1 for recognising that triangle $ACD$ is right-angled at $C$, so Pythagoras' theorem applies: $AD^2 = AC^2 + CD^2$.
   4. M1 for substituting the known values: $AD^2 = 21 + 7^2 = 21 + 49 = 70$.
   5. A1 for finding $AD = \sqrt{70}$ cm.

2. Differentiation · 6 marks

   The tangents to the curve $y = x^2 - 4x$ at the points where $x = 1$ and $x = 3$ intersect at a point $P$. Find the coordinates of $P$.

   Worked answer

   1. M1 for finding the y-coordinates: at $x=1, y=-3$ and at $x=3, y=-3$.
   2. M1 for differentiating $\frac{dy}{dx} = 2x - 4$ to find the gradients: $m_1 = -2$ (at $x=1$) and $m_3 = 2$ (at $x=3$).
   3. M1 for finding the equation of the first tangent: $y - (-3) = -2(x - 1) \implies y = -2x - 1$.
   4. M1 for finding the equation of the second tangent: $y - (-3) = 2(x - 3) \implies y = 2x - 9$.
   5. M1 for equating the two tangent equations: $-2x - 1 = 2x - 9 \implies 4x = 8 \implies x = 2$.
   6. A1 for finding the corresponding y-coordinate $y = -5$, giving $P(2, -5)$.

3. Integration · 5 marks

   The gradient of a curve is given by $\frac{dy}{dx} = 4\sqrt{x} - 1$. The curve passes through the point $(9, 20)$. Find the equation of the curve.

   Worked answer

   1. M1 for rewriting as $4x^{\frac{1}{2}} - 1$ and integrating: $y = \frac{4x^{\frac{3}{2}}}{\frac{3}{2}} - x + c$.
   2. A1 for simplifying the integral to $y = \frac{8}{3}x^{\frac{3}{2}} - x + c$.
   3. M1 for substituting the point $(9, 20)$: $20 = \frac{8}{3}(9)^{\frac{3}{2}} - 9 + c$.
   4. M1 for evaluating $9^{\frac{3}{2}} = 27$ to solve for $c$: $20 = 72 - 9 + c \implies c = -43$.
   5. A1 for the final equation $y = \frac{8}{3}x^{\frac{3}{2}} - x - 43$.

More on these topics: Trigonometry · Differentiation · Integration

P1 topics this paper can test

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• Algebra
• Coordinate Geometry
• Trigonometry
• Differentiation
• Integration
• Graphs and Transformations

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Formula booklet

Mathematical Formulae and Statistical Tables (International AS/A Level Mathematics) · Pearson Edexcel · For the 2018 IAL specification (current)