Edexcel IAL P1 January 2021 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. Coordinate Geometry · 8 marks

   The line $L_1$ has equation $y=x+2$ and the line $L_2$ has equation $y=-2x+14$. The lines intersect at point $A$.

   1. Find the coordinates of $A$.

   2. Point $B$ lies on $L_1$ such that its $x$-coordinate is less than the $x$-coordinate of $A$. The distance $AB$ is exactly $\sqrt{18}$ units. Find the coordinates of $B$.

   3. The line $L_3$ passes through point $B$ and is perpendicular to $L_1$. Find the equation of $L_3$ and determine where it intersects $L_2$.

   Worked solution

   1. Solve simultaneously: $x+2=-2x+14⟹3x=12⟹x=4$. M1
      $y=4+2=6$. $A(4,6)$. A1

   2. Let $B$ be $(x,x+2)$. Distance $AB=\sqrt{18}$.
      $(x-4{)}^2+(x+2-6{)}^2=18⟹(x-4{)}^2+(x-4{)}^2=18$. M1
      $2(x-4{)}^2=18⟹(x-4{)}^2=9$. A1
      $x-4=\pm 3⟹x=7$ or $x=1$. A1
      Since $x$ for $B$ is less than $x$ for $A$ (which is $4$), $x=1$.
      $y=1+2=3$. $B(1,3)$. A1

   3. $L_3$ is perpendicular to $L_1$ ($m=1$), so $m_3=-1$. M1
      Passes through $B(1,3)$: $y-3=-1(x-1)⟹y=-x+4$.
      Intersection with $L_2$ ($y=-2x+14$):
      $-x+4=-2x+14⟹x=10$. $y=-10+4=-6$.
      Intersection point is $(10,-6)$. A1

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

   Find the x-coordinates of all the points of intersection between the curves $y=x(x+3)$ and $y=x^3(x+3)$.

   Worked solution

   1. M1 for equating the functions: $x^3(x+3)=x(x+3)$.
   2. M1 for bringing all terms to one side and factorising: $x(x+3)(x^2-1)=0$.
   3. M1 for further factorising $x^2-1$ to $(x-1)(x+1)$.
   4. A1 for listing all four correct x-coordinates: $x=0,-3,1,-1$.

More on these topics: Coordinate Geometry · Integration · Graphs and Transformations

What's on this paper

What this paper is like

• Shape: 9 questions, 75 marks in 1 h 30 min (about 1.2 minutes a mark); questions from 5 to 11 marks.
• Biggest question: Q9, 11 marks: integrating, then finding a curve through a point.
• Marks by main topic: Integration 19, Differentiation 17, Trigonometry 14, Graphs and Transformations 10, Algebra 9, Coordinate Geometry 6.
• More Integration in other sittings: October 2020 Q9 (6 marks), June 2021 Q6 (8 marks), October 2021 Q6 (10 marks).
• Against the other 17 sittings we mapped: more marks on Differentiation (17 marks here, 10 on average) and Integration (19 marks here, 14 on average); fewer on Algebra (9 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. Q1Differentiating powers of x and a tangent (8 marks) · P1 Differentiation
2. Q2Linear model for a tree's height (6 marks) · P1 Coordinate Geometry
3. Q3Graph of 4 cos x and a transformation (5 marks) · P1 Trigonometry
4. Q4Area between a curve and a line (8 marks) · P1 Integration
5. Q5Viewing platform: sector and triangle (9 marks) · P1 Trigonometry
6. Q6Reciprocal curves and intersections (10 marks) · P1 Graphs and Transformations
7. Q7Equation in root x solved as a quadratic (9 marks) · P1 Algebra
8. Q8Tangent and normal to a curve (9 marks) · P1 Differentiation
9. Q9Integrating, then finding a curve through a point (11 marks) · P1 Integration

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