Edexcel A Level Maths June 2019 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 · 7 marks

   Let $f(x)=5-4x-2x^2$.
   
   (a) Express $f(x)$ in the form $A-B(x+C{)}^2$, where $A$, $B$, and $C$ are integers.
   (b) State the maximum value of $f(x)$ and the value of $x$ at which it occurs.
   (c) Solve $f(x)=0$, giving your answers in exact form.

   Worked solution

   (a) M1 Factors out $-2$ from the $x$ terms: $5-2(x^2+2x)$.

   1. M1 Completes the square inside the bracket: $5-2((x+1{)}^2-1)$.
   2. A1 Expands and simplifies to obtain $7-2(x+1{)}^2$.

   (b) B1 States the maximum value is $7$.

   1. B1 States this occurs at $x=-1$.

   (c) M1 Sets $7-2(x+1{)}^2=0$ and rearranges to $(x+1{)}^2=\frac{7}{2}$.

   1. A1 Solves for $x$ by square rooting, yielding $x=-1\pm \sqrt{\frac{7}{2}}$ (or equivalent exact surd).

2. Trigonometry · 5 marks

   Triangle $ABC$ has sides $AB=4$ cm and $BC=5$ cm, with angle $ABC={60}^{\circ }$. Triangle $ACD$ shares side $AC$ and has a right angle at $C$. If $CD=7$ cm, find the exact length of $AD$.

   Worked solution

   1. M1 for using the cosine rule in triangle ABC to find $A{C}^2$: $A{C}^2=4^2+5^2-2(4)(5)\cos {60}^{\circ }$.
   2. M1 for evaluating to get $A{C}^2=16+25-40(0.5)=21$.
   3. M1 for recognising that triangle $ACD$ is right-angled at $C$, so Pythagoras' theorem applies: $A{D}^2=A{C}^2+C{D}^2$.
   4. M1 for substituting the known values: $A{D}^2=21+7^2=21+49=70$.
   5. A1 for finding $AD=\sqrt{70}$ cm.

3. Differentiation · 5 marks

   A curve has parametric equations $x=\ln t$ and $y=t^2$, $t>0$. Find the equation of the normal to the curve at the point where $t=1$. Give your answer in the form $ax+by+c=0$.

   Worked solution

   1. M1 for finding the coordinates at $t=1$: $x=0$, $y=1$.
   2. M1 for calculating $\frac{dx}{dt}=\frac{1}{t}$ and $\frac{dy}{dt}=2t$, giving $\frac{dy}{dx}=2t^2$.
   3. M1 for evaluating the tangent gradient at $t=1$ to get $m_t=2$.
   4. M1 for determining the normal gradient $m_n=-\frac{1}{2}$ and using $(0,1)$ to form the equation $y-1=-\frac{1}{2}(x-0)$.
   5. A1 for rearranging to the required integer format: $x+2y-2=0$.

More on these topics: Algebra and functions · Trigonometry · Differentiation

What this paper covers

What this paper is like

• Shape: 14 questions, 100 marks in 2 h (about 1.2 minutes a mark); questions from 3 to 11 marks.
• Biggest question: Q13, 11 marks: rational function with vertical asymptotes.
• Marks by main topic: Algebra and functions 24, Differentiation 22, Trigonometry 13, Sequences and series 13, Exponentials and logarithms 12, Integration 10, Proof 6.
• More Algebra and functions in other sittings: October 2020 Q4 (5 marks), November 2021 Q9 (11 marks), June 2022 Q5 (6 marks).
• Against the other 7 sittings we mapped: more marks on Algebra and functions (24 marks here, 16 on average) and Differentiation (22 marks here, 17 on average); fewer on Coordinate geometry (0 marks here, 8 on average) and Integration (10 marks here, 16 on average).
• Not on this paper: Coordinate geometry, Numerical methods, Vectors.
• 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. Q2Graph of cos x and the number of roots (5 marks) · Trigonometry, Numerical methods
3. Q3Quotient rule and where a curve decreases (5 marks) · Differentiation
4. Q4Binomial expansion and an approximation (6 marks) · Sequences and series
5. Q5Completing the square and graph transformations (10 marks) · Algebra and functions
6. Q6Trig equation with sin 2x and tan x (8 marks) · Trigonometry
7. Q7Comparing exponential and linear depreciation (7 marks) · Exponentials and logarithms
8. Q8Areas of two regions under a cubic (10 marks) · Integration
9. Q9Log equation and a restriction on its values (5 marks) · Exponentials and logarithms
10. Q10Proof by exhaustion and a counter-example (6 marks) · Proof
11. Q11Race times as a geometric series (7 marks) · Sequences and series
12. Q12Turning points of e^(-x) sin x and an iteration (10 marks) · Differentiation, Numerical methods
13. Q13Rational function with vertical asymptotes (11 marks) · Algebra and functions
14. Q14Parametric curve, tangent at the origin, small angles (7 marks) · Differentiation, Trigonometry