Edexcel IAL P1 January 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 · 5 marks

   Find the equation of the normal to the curve $y=x^3-2x$ at the point where $x=2$.

   Worked solution

   1. M1 for finding the y-coordinate at $x=2$: $y=2^3-2(2)=4$. Point is $(2,4)$.
   2. M1 for differentiating to find $\frac{dy}{dx}=3x^2-2$.
   3. M1 for finding the tangent gradient $m_t=3(4)-2=10$, and hence the normal gradient $m_n=-\frac{1}{10}$.
   4. M1 for setting up the normal equation: $y-4=-\frac{1}{10}(x-2)$.
   5. A1 for the correct equation, e.g. $10y+x=42$ or $y=-0.1x+4.2$.

2. 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 $f(x)=2x^3-2x^2+9$.

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 11 marks.
• Biggest question: Q6, 11 marks: curve from its gradient function.
• Marks by main topic: Integration 22, Graphs and Transformations 20, Algebra 13, Trigonometry 11, Coordinate Geometry 9.
• More Integration in other sittings: October 2021 Q6 (10 marks), June 2022 Q7 (9 marks), June 2021 Q6 (8 marks).
• Against the other 17 sittings we mapped: more marks on Graphs and Transformations (20 marks here, 10 on average) and Integration (22 marks here, 14 on average); fewer on Differentiation (0 marks here, 11 on average) and Trigonometry (11 marks here, 16 on average).
• Not on this paper: Differentiation.
• 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. Q2Completing the square and a maximum (6 marks) · P1 Algebra
3. Q3Simplifying surds (7 marks) · P1 Algebra
4. Q4Region between a curve and a line (7 marks) · P1 Integration
5. Q5Semicircular garden: arcs and angles (7 marks) · P1 Trigonometry
6. Q6Curve from its gradient function (11 marks) · P1 Integration
7. Q7Sketching a cubic and its tangent (11 marks) · P1 Graphs and Transformations, P1 Differentiation
8. Q8Perpendicular lines and a triangle (9 marks) · P1 Coordinate Geometry
9. Q9Cosine curve with a constant A (4 marks) · P1 Trigonometry
10. Q10Sketching y = -9/x^2 and a translation (9 marks) · P1 Graphs and Transformations

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