Edexcel IAL S1 June 2025 question paper and mark scheme (WST01/01)

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1. Probability · 3 marks

   Three independent events $A$, $B$, and $C$ have probabilities $P(A) = 0.5$, $P(B) = 0.4$, and $P(C) = 0.3$. Find the probability that exactly one of these events occurs.

   Worked answer

   1. M1 for identifying the three scenarios: $(A \cap B' \cap C')$, $(A' \cap B \cap C')$, and $(A' \cap B' \cap C)$.
   2. M1 for calculating the probabilities of these scenarios: $(0.5\times0.6\times0.7) + (0.5\times0.4\times0.7) + (0.5\times0.6\times0.3)$.
   3. A1 for evaluating and summing: $0.21 + 0.14 + 0.09 = 0.44$.

2. Discrete Random Variables · 4 marks

   The discrete random variable $X$ takes the values $1, 2,$ and $3$ with probabilities $a, b,$ and $0.3$ respectively. Given that $E(X) = 1.9$, find the values of $a$ and $b$.

   Worked answer

   1. M1 for forming the sum of probabilities equation: $a + b + 0.3 = 1 \implies a + b = 0.7$.
   2. M1 for forming the expected value equation: $1(a) + 2(b) + 3(0.3) = 1.9 \implies a + 2b = 1.0$.
   3. M1 for solving the simultaneous equations (e.g., subtracting the first from the second: $b = 1.0 - 0.7$).
   4. A1 for concluding $b = 0.3$ and $a = 0.4$.

3. Measures of Location and Spread · 4 marks

   A dataset $x$ has mean $\bar{x} = 5$ and standard deviation $\sigma_x = 2$. A new dataset $y$ is formed using the linear transformation $y = ax + b$, where $a > 0$. The new dataset has mean $\bar{y} = 15$ and standard deviation $\sigma_y = 6$. Find the values of $a$ and $b$.

   Worked answer

   1. M1 for linking the standard deviations: $\sigma_y = a \sigma_x$.
   2. A1 for solving for $a$: $6 = a(2) \implies a = 3$.
   3. M1 for linking the means: $\bar{y} = a\bar{x} + b$.
   4. A1 for substituting $a=3$ to find $b$: $15 = 3(5) + b \implies b = 0$.

More on these topics: Probability · Discrete Random Variables · Measures of Location and Spread

S1 topics this paper can test

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• Data and Summary Statistics
• Representation of Data
• Probability
• Correlation and Regression
• Discrete Random Variables
• Normal Distribution
• Measures of Location and Spread

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What the examiners said about this paper

Summarised in our own words from the board's examiner report (Examiner Insights).

• WST01/01: Standardisation not shown when the question requires it (Q6); Outliers (Q5); Comparisons without figures or context (Q5(e)). Official examiner report ↗

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Formula booklet

Mathematical Formulae and Statistical Tables (International AS/A Level Mathematics) · Pearson Edexcel · For the 2018 IAL specification (current)