Edexcel IAL P1 October 2020 question paper and mark scheme (WMA11/01)

Try 3 P1 questions like these

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1. Algebra · 7 marks

   Solve the simultaneous equations $x - y = 2$ and $x^2 - xy + y^2 = 7$.

   Worked answer

   M1 Rearranges the linear equation to make $y$ the subject: $y = x - 2$.

   1. M1 Substitutes this expression into the quadratic equation: $x^2 - x(x - 2) + (x - 2)^2 = 7$.
   2. M1 Expands the brackets correctly: $x^2 - x^2 + 2x + (x^2 - 4x + 4) = 7$.
   3. A1 Simplifies to a 3-term quadratic equation: $x^2 - 2x - 3 = 0$.
   4. M1 Factorises the quadratic: $(x - 3)(x + 1) = 0$.
   5. A1 Finds the $x$-values: $x = 3$ and $x = -1$.
   6. A1 Substitutes back into the linear equation to find the corresponding $y$-values, giving the final solution pairs $x = 3, y = 1$ and $x = -1, y = -3$.

2. 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 $y = \frac{8}{3}x^{\frac{3}{2}} - x - 43$.

3. Graphs and Transformations · 4 marks

   Find the x-coordinates of all the points of intersection between the curves $y = x(x+3)$ and $y = x^3(x+3)$.

   Worked answer

   1. M1 for equating the functions: $x^3(x+3) = x(x+3)$.
   2. M1 for bringing all terms to one side and factorising: $x(x+3)(x^2 - 1) = 0$.
   3. M1 for further factorising $x^2-1$ to $(x-1)(x+1)$.
   4. A1 for listing all four correct x-coordinates: $x = 0, -3, 1, -1$.

More on these topics: Algebra · Integration · Graphs and Transformations

P1 topics this paper can test

Every P1 paper can test any of the 6 P1 topics in the specification.

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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)