Edexcel IAL P2 October 2023 mark scheme and question paper (WMA12/01)

3 P2 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. Sequences and Series · 5 marks

   The second term of a geometric series is 12 and its sum to infinity is 64. Find the two possible values of the common ratio, $r$, and the corresponding values of the first term, $a$.

   Worked solution

   1. M1 for setting up the two equations: $ar=12$ and $\frac{a}{1-r}=64$.
   2. M1 for substituting $a=\frac{12}{r}$ to get $\frac{12/r}{1-r}=64⟹12=64r(1-r)$.
   3. M1 for forming the quadratic $16r^2-16r+3=0$.
   4. A1 for finding $r=0.25$ and $r=0.75$.
   5. A1 for finding the corresponding first terms: $a=48$ and $a=16$.

2. Logarithms and Exponentials · 4 marks

   Given that ${\log }_{2}x=p$ and ${\log }_{2}y=q$, express ${\log }_2(8x^2{y}^3)$ in terms of $p$ and $q$.

   Worked solution

   1. M1 for splitting the logarithm into a sum: ${\log }_{2}8+{\log }_2{x}^2+{\log }_2{y}^3$.
   2. B1 for evaluating ${\log }_{2}8=3$.
   3. M1 for applying the power law: $2{\log }_{2}x+3{\log }_{2}y$.
   4. A1 for the final expression $3+2p+3q$.

3. The Binomial Expansion · 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: Sequences and Series · Logarithms and Exponentials · The Binomial Expansion

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 3 to 12 marks.
• Biggest question: Q9, 12 marks: tangent to a curve and an enclosed area.
• Marks by main topic: Sequences and Series 13, Differentiation (stationary points) 12, The Binomial Expansion 12, Algebraic Methods 9, Further Trigonometry 7, Circles 7, Logarithms and Exponentials 6, Integration (definite integrals and area) 6, Proof 3.
• More Differentiation (stationary points) in other sittings: January 2024 Q10 (9 marks), June 2023 Q10 (10 marks), June 2024 Q9 (8 marks).
• Against the other 16 sittings we mapped: more marks on The Binomial Expansion (12 marks here, 6 on average); fewer on Logarithms and Exponentials (6 marks here, 11 on average).
• Coverage: every topic on the list came up.
• Calculator: allowed.

WMA12/01: question by question

Labels and topics are ours, read from the WMA12/01 paper (checked 2026-11-01); marks as printed. Tap a number to practise that topic.

1. Q1Proof by exhaustion with three integers (3 marks) · P2 Proof
2. Q2Periodic sequence and a sum (5 marks) · P2 Sequences and Series
3. Q3Trig equations in degrees (7 marks) · P2 Further Trigonometry
4. Q4Factor theorem with two constants (9 marks) · P2 Algebraic Methods
5. Q5Exponential and log equations (6 marks) · P2 Logarithms and Exponentials
6. Q6Trapezium rule for a river's cross-section (6 marks) · P2 Integration (definite integrals and area)
7. Q7Theatre seating as an arithmetic series (8 marks) · P2 Sequences and Series
8. Q8Circle and a tangent through a point (7 marks) · P2 Circles
9. Q9Tangent to a curve and an enclosed area (12 marks) · P2 Differentiation (stationary points), P2 Integration (definite integrals and area)
10. Q10Binomial expansion with chosen terms (12 marks) · P2 The Binomial Expansion

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