Edexcel IAL P1 June 2022 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. Differentiation · 6 marks

   The normal to the curve $y=\sqrt{x}$ at the point where $x=4$ cuts the x-axis at $A$ and the y-axis at $B$. Calculate the exact area of the triangle $AOB$, where $O$ is the origin.

   Worked solution

   1. M1 for finding the y-coordinate at $x=4$: $y=2$.
   2. M1 for finding $\frac{dy}{dx}=\frac{1}{2}{x}^{-\frac{1}{2}}$ and evaluating at $x=4$ to get gradient $m_t=\frac{1}{4}$.
   3. M1 for finding the normal gradient $m_n=-4$ and its equation: $y-2=-4(x-4)⟹y=-4x+18$.
   4. M1 for finding the axis intercepts of the normal: at $y=0,4x=18⟹x=4.5$ (point $A$) and at $x=0,y=18$ (point $B$).
   5. M1 for using the area of a triangle formula $\frac{1}{2}\times \text{base}\times \text{height}=\frac{1}{2}\times 4.5\times 18$.
   6. A1 for the final area of $40.5$ square units.

2. Integration · 5 marks

   Given that $f^{\prime }(x)=\frac{6x^3+1}{x^2}$ and $f(1)=4$, find an expression for $f(x)$.

   Worked solution

   1. M1 for splitting the fraction: $f^{\prime }(x)=6x+x^{-2}$.
   2. M1 for integrating to find $f(x)$: $3x^2+\frac{x^{-1}}{-1}+c$.
   3. A1 for simplifying to $f(x)=3x^2-x^{-1}+c$.
   4. M1 for substituting $(1,4)$ to find $c$: $4=3(1{)}^2-(1{)}^{-1}+c⟹4=2+c⟹c=2$.
   5. A1 for the final function $f(x)=3x^2-\frac{1}{x}+2$.

3. Graphs and Transformations · 4 marks

   A cubic curve crosses the x-axis at $x=-2$, $x=1$, and $x=4$. It crosses the y-axis at the point $(0,16)$. Find the equation of the curve in the form $y=a{x}^3+b{x}^2+cx+d$.

   Worked solution

   1. M1 for writing the equation in the factored form $y=k(x+2)(x-1)(x-4)$.
   2. M1 for substituting $(0,16)$ to find $k$: $16=k(2)(-1)(-4)⟹16=8k$.
   3. A1 for finding $k=2$.
   4. A1 for expanding to get $y=2(x^3-3x^2-6x+8)=2x^3-6x^2-12x+16$.

More on these topics: Differentiation · Integration · 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 12 marks.
• Biggest question: Q10, 12 marks: tangent to a curve and an enclosed area.
• Marks by main topic: Trigonometry 23, Algebra 21, Integration 13, Differentiation 12, Graphs and Transformations 6.
• More Differentiation in other sittings: October 2022 Q1 (6 marks), January 2023 Q10 (10 marks), October 2021 Q8 (10 marks).
• Against the other 17 sittings we mapped: more marks on Trigonometry (23 marks here, 15 on average) and Algebra (21 marks here, 16 on average); fewer on Coordinate Geometry (0 marks here, 8 on average) and Graphs and Transformations (6 marks here, 11 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. Q1Integrating powers of x (4 marks) · P1 Integration
2. Q2Sine rule with an ambiguous case (5 marks) · P1 Trigonometry
3. Q3Surds: showing a value is an integer (5 marks) · P1 Algebra
4. Q4Curve with an asymptote and a transformation (6 marks) · P1 Graphs and Transformations
5. Q5Quadratic from given conditions (9 marks) · P1 Algebra
6. Q6Simultaneous equations for a shape (7 marks) · P1 Algebra
7. Q7Curve from its gradient function (9 marks) · P1 Integration
8. Q8Ceiling fan design: sectors in radians (10 marks) · P1 Trigonometry
9. Q9Transforming y = sin x (8 marks) · P1 Trigonometry
10. Q10Tangent to a curve and an enclosed area (12 marks) · P1 Differentiation, P1 Integration

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