Edexcel IAL P1 October 2023 mark scheme and question paper (WMA11/01)

3 P1 questions like these, with worked solutions

Written and checked by us, not taken from the Pearson paper. Try each one, then tap "Worked solution" to see every step and its marks.

1. Algebra · 5 marks

   The quadratic equation $x^2+kx+(k+3)=0$, where $k$ is a constant, has equal roots. Find the possible values of $k$.

   Worked solution

   M1 Uses the condition for equal roots: $b^2-4ac=0$.

   1. A1 Substitutes the coefficients to form an equation in $k$: $k^2-4(1)(k+3)=0$.
   2. M1 Expands to a 3-term quadratic: $k^2-4k-12=0$.
   3. M1 Factorises the quadratic equation: $(k-6)(k+2)=0$.
   4. A1 States the possible values for $k$ are $k=6\text{ or }k=-2$.

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 solution

   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: $y-(-3)=-2(x-1)⟹y=-2x-1$.
   4. M1 for finding the equation of the second tangent: $y-(-3)=2(x-3)⟹y=2x-9$.
   5. M1 for equating the two tangent equations: $-2x-1=2x-9⟹4x=8⟹x=2$.
   6. A1 for finding the corresponding y-coordinate $y=-5$, giving $P(2,-5)$.

3. Integration · 6 marks

   Given that $f^{″}(x)=12x-4$, $f^{\prime }(1)=2$ and $f(-1)=5$, find $f(x)$.

   Worked solution

   1. M1 for integrating $f^{″}(x)$ to find $f^{\prime }(x)=6x^2-4x+c_1$.
   2. M1 for substituting $f^{\prime }(1)=2$ to find $c_1$: $2=6(1{)}^2-4(1)+c_1⟹c_1=0$.
   3. M1 for substituting $c_1=0$ and integrating again to find $f(x)=2x^3-2x^2+c_2$.
   4. M1 for substituting $f(-1)=5$: $5=2(-1{)}^3-2(-1{)}^2+c_2$.
   5. M1 for solving for $c_2$: $5=-2-2+c_2⟹c_2=9$.
   6. A1 for the final correct function $f(x)=2x^3-2x^2+9$.

More on these topics: Algebra · Differentiation · Integration

What's on this paper

What this paper is like

• Shape: 11 questions, 75 marks in 1 h 30 min (about 1.2 minutes a mark); questions from 4 to 10 marks.
• Biggest question: Q7, 10 marks: curve from its gradient function.
• Marks by main topic: Trigonometry 20, Algebra 16, Differentiation 15, Graphs and Transformations 14, Integration 10.
• More Integration in other sittings: January 2024 Q10 (8 marks), June 2024 Q10 (10 marks), January 2023 Q8 (8 marks).
• Against the other 17 sittings we mapped: more marks on Differentiation (15 marks here, 10 on average) and Trigonometry (20 marks here, 16 on average); fewer on Coordinate Geometry (0 marks here, 8 on average) and Integration (10 marks here, 15 on average).
• Not on this paper: Coordinate Geometry.
• Calculator: allowed.

WMA11/01: question by question

Labels and topics are ours, read from the WMA11/01 paper (checked 2026-11-01); marks as printed. Tap a number to practise that topic.

1. Q1First and second derivatives (5 marks) · P1 Differentiation
2. Q2Index laws in the form kx^n (4 marks) · P1 Algebra
3. Q3Rationalising a surd (6 marks) · P1 Algebra
4. Q4Curve with asymptotes (7 marks) · P1 Graphs and Transformations
5. Q5Cosine rule for a frame (7 marks) · P1 Trigonometry
6. Q6Equation with a parameter p: discriminant (6 marks) · P1 Algebra
7. Q7Curve from its gradient function (10 marks) · P1 Integration
8. Q8Two curves meeting (7 marks) · P1 Graphs and Transformations, P1 Algebra
9. Q9Plan view with sectors (7 marks) · P1 Trigonometry
10. Q10Transformed cosine graph (6 marks) · P1 Trigonometry
11. Q11Tangent and an enclosed area (10 marks) · P1 Differentiation, P1 Integration

Practise every P1 topic free →