Edexcel IAL P1 January 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. Trigonometry · 4 marks

   In triangle $XYZ$, $XY=14$ cm, $YZ=9$ cm and $\mathrm{\angle }X={30}^{\circ }$. Find the two possible values of $\mathrm{\angle }Z$ to 1 decimal place.

   Worked solution

   1. M1 for using the sine rule: $\frac{\sin Z}{14}=\frac{\sin {30}^{\circ }}{9}$.
   2. M1 for calculating $\sin Z=\frac{14\times 0.5}{9}=\frac{7}{9}$.
   3. A1 for the principal acute angle $Z={51.1}^{\circ }$.
   4. A1 for the alternative obtuse angle $Z={180}^{\circ }-{51.1}^{\circ }={128.9}^{\circ }$.

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

   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: Trigonometry · Differentiation · Graphs and Transformations

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: Q6, 10 marks: stage design with sectors.
• Marks by main topic: Integration 21, Differentiation 15, Trigonometry 14, Algebra 10, Graphs and Transformations 10, Coordinate Geometry 5.
• More Trigonometry in other sittings: October 2022 Q8 (14 marks), June 2023 Q5 (10 marks), June 2022 Q8 (10 marks).
• Against the other 17 sittings we mapped: more marks on Integration (21 marks here, 14 on average) and Differentiation (15 marks here, 10 on average); fewer on Algebra (10 marks here, 17 on average).
• Coverage: every topic on the list came up.
• 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. Q1Gradient of a curve with powers of x (5 marks) · P1 Differentiation
2. Q2Right angle in a triangle of points (5 marks) · P1 Coordinate Geometry
3. Q3Integrating a fraction with powers of x (5 marks) · P1 Integration
4. Q4Discriminant: no real roots (4 marks) · P1 Algebra
5. Q5Equation solved with the substitution p = 3x (6 marks) · P1 Algebra
6. Q6Stage design with sectors (10 marks) · P1 Trigonometry
7. Q7Transforming a reciprocal curve (10 marks) · P1 Graphs and Transformations
8. Q8Area between a line and a curve (8 marks) · P1 Integration
9. Q9Graph of tan x and a line (4 marks) · P1 Trigonometry
10. Q10Tangent and normal to a curve (10 marks) · P1 Differentiation
11. Q11Curve from its second derivative (8 marks) · P1 Integration

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