Edexcel IAL P1 June 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 · 7 marks

   Let $f(x)=5-4x-2x^2$.
   
   (a) Express $f(x)$ in the form $A-B(x+C{)}^2$, where $A$, $B$, and $C$ are integers.
   (b) State the maximum value of $f(x)$ and the value of $x$ at which it occurs.
   (c) Solve $f(x)=0$, giving your answers in exact form.

   Worked solution

   (a) M1 Factors out $-2$ from the $x$ terms: $5-2(x^2+2x)$.

   1. M1 Completes the square inside the bracket: $5-2((x+1{)}^2-1)$.
   2. A1 Expands and simplifies to obtain $7-2(x+1{)}^2$.

   (b) B1 States the maximum value is $7$.

   1. B1 States this occurs at $x=-1$.

   (c) M1 Sets $7-2(x+1{)}^2=0$ and rearranges to $(x+1{)}^2=\frac{7}{2}$.

   1. A1 Solves for $x$ by square rooting, yielding $x=-1\pm \sqrt{\frac{7}{2}}$ (or equivalent exact surd).

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. Graphs and Transformations · 4 marks

   Show that the line $y=2x-7$ does not intersect the curve $y=x^2-3x+5$.

   Worked solution

   1. M1 for equating the line and the curve: $x^2-3x+5=2x-7$.
   2. M1 for rearranging into a quadratic equation: $x^2-5x+12=0$.
   3. M1 for calculating the discriminant: $b^2-4ac=(-5{)}^2-4(1)(12)=25-48=-23$.
   4. A1 for concluding that since the discriminant is less than zero, there are no real roots, and thus no points of intersection.

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

What's on this paper

What this paper is like

• Shape: 10 questions, 75 marks in 1 h 30 min (about 1.2 minutes a mark); questions from 4 to 10 marks.
• Biggest question: Q5, 10 marks: garden plan: arcs and areas.
• Marks by main topic: Algebra 23, Trigonometry 19, Differentiation 17, Coordinate Geometry 16.
• More Trigonometry in other sittings: October 2023 Q5 (7 marks), January 2023 Q6 (10 marks), January 2024 Q8 (9 marks).
• Against the other 17 sittings we mapped: more marks on Coordinate Geometry (16 marks here, 7 on average) and Differentiation (17 marks here, 10 on average); fewer on Integration (0 marks here, 15 on average) and Graphs and Transformations (0 marks here, 11 on average).
• Not on this paper: Integration, Graphs and Transformations.
• 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. Q1Quadratic inequality (4 marks) · P1 Algebra
2. Q2Inequalities for a sports pitch (6 marks) · P1 Algebra
3. Q3Completing the square and a sketch (6 marks) · P1 Algebra
4. Q4Writing in index form, then differentiating (7 marks) · P1 Differentiation
5. Q5Garden plan: arcs and areas (10 marks) · P1 Trigonometry
6. Q6Expanding brackets with surds (7 marks) · P1 Algebra
7. Q7Regions defined by lines and inequalities (6 marks) · P1 Coordinate Geometry, P1 Algebra
8. Q8Tangent to a curve and where it meets an axis (10 marks) · P1 Differentiation
9. Q9Identifying a trig graph and its transformation (9 marks) · P1 Trigonometry
10. Q10Quadratic curve and two lines (10 marks) · P1 Coordinate Geometry

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