Edexcel A Level Maths November 2021 Paper 1: question paper and mark scheme (9MA0/01)

3 A Level questions like these, with worked solutions

Written and checked by us, not taken from the Pearson Edexcel paper. Try each one, then tap "Worked solution" to see every step and its marks.

1. Algebra and functions · 5 marks

   Let $f(x)=x^3+c{x}^2+dx-4$. Given $f(x)$ has a factor $(x+2)$ and leaves a remainder of $-10$ when divided by $(x-3)$, find the values of $c$ and $d$.

   Worked solution

   1. M1 for applying the Factor Theorem for $(x+2)$: $f(-2)=0⟹-8+4c-2d-4=0⟹4c-2d=12$.
   2. M1 for applying the Remainder Theorem for $(x-3)$: $f(3)=-10⟹27+9c+3d-4=-10⟹9c+3d=-33$.
   3. M1 for simplifying both equations (e.g., $2c-d=6$ and $3c+d=-11$).
   4. M1 for solving the simultaneous equations (e.g., adding them gives $5c=-5$).
   5. A1 for finding the correct values $c=-1$ and $d=-8$.

2. 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

3. Sequences and series · 4 marks

   The first three terms of the expansion $(a+bx{)}^6$ are $64-192x+c{x}^2$. Find the values of the constants $a$, $b$, and $c$.

   Worked solution

   1. M1 for equating the first term: $a^6=64⟹a=2$.
   2. M1 for equating the $x$ coefficient to find $b$: $(\genfrac{}{}{0ex}{}{6}{1})a^{5}b=-192⟹6(32)b=-192⟹192b=-192$.
   3. A1 for obtaining $b=-1$.
   4. A1 for finding the $x^2$ coefficient: $c=(\genfrac{}{}{0ex}{}{6}{2})a^4{b}^2=15(16)(-1{)}^2=240$.

More on these topics: Algebra and functions · Coordinate geometry · Sequences and series

What this paper covers

What this paper is like

• Shape: 15 questions, 100 marks in 2 h (about 1.2 minutes a mark); questions from 3 to 11 marks.
• Biggest question: Q9, 11 marks: partial fractions, then a binomial expansion.
• Marks by main topic: Differentiation 22, Algebra and functions 18, Sequences and series 12, Coordinate geometry 12, Exponentials and logarithms 9, Trigonometry 8, Integration 8, Proof 6, Vectors 5.
• More Algebra and functions in other sittings: June 2022 Q5 (6 marks), October 2020 Q4 (5 marks), June 2023 Q7 (8 marks).
• Against the other 7 sittings we mapped: more marks on Coordinate geometry (12 marks here, 7 on average) and Differentiation (22 marks here, 17 on average); fewer on Integration (8 marks here, 16 on average) and Trigonometry (8 marks here, 16 on average).
• Not on this paper: Numerical methods.
• Calculator: allowed.

9MA0/01: question by question

Labels and topics are ours, read from the 9MA0/01 paper (checked 2026-11-01); marks as printed. Tap a number to practise that topic.

1. Q1Factor theorem to find a constant (3 marks) · Algebra and functions
2. Q2Completing the square and a transformation (4 marks) · Algebra and functions
3. Q3Recurrence relation with an integer k (6 marks) · Sequences and series
4. Q4Turning point with ln and an iteration (9 marks) · Differentiation, Numerical methods
5. Q5Profit growth as a geometric series (6 marks) · Sequences and series
6. Q6Vectors in a triangle and an angle (5 marks) · Vectors
7. Q7Circle centre, radius and tangents (9 marks) · Coordinate geometry
8. Q8Two bacteria population models (9 marks) · Exponentials and logarithms
9. Q9Partial fractions, then a binomial expansion (11 marks) · Algebra and functions, Sequences and series
10. Q10Trig identity and a trig equation (8 marks) · Trigonometry
11. Q11Area under y = (ln x)^2 by parts (8 marks) · Integration
12. Q12Quadratic model of a golf ball's path (9 marks) · Differentiation, Algebra and functions
13. Q13Parametric curve to Cartesian (a circle) (3 marks) · Coordinate geometry
14. Q14Differentiating a quotient with surds (4 marks) · Differentiation
15. Q15Proof by exhaustion and proof by contradiction (6 marks) · Proof