Edexcel IAL S1 October 2024 question paper and mark scheme (WST01/01)

Try 3 S1 questions like these

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1. Representation of Data · 5 marks

   A histogram is drawn. The class $0 \le x < 20$ has frequency $10$, and the class $20 \le x < 30$ has frequency $30$. If the height of the bar for the first class is $2\text{ cm}$, find the height of the bar for the second class, assuming the width of the bars is proportional to the class width.

   Worked answer

   1. M1 for stating the class widths: $20$ and $10$.
   2. M1 for establishing the width ratio: if class width $20$ has a certain drawn width, class width $10$ has half that drawn width. Let drawn width of first bar be $2w$, then second bar is $w$.
   3. M1 for using Area $\propto$ Frequency for the first bar: Area $= 2w \times 2 = 4w$. So $4w$ represents frequency $10$, meaning $w$ represents frequency $2.5$.
   4. M1 for applying to the second bar: Area $= w \times h$. Frequency $= 30$. So $w \times h$ represents $30$. Since $w$ represents $2.5$, Area must be $12w$.
   5. A1 for solving for height: $w \times h = 12w \implies h = 12\text{ cm}$.

2. Correlation and Regression · 4 marks

   A dataset of 20 observations produced the following summary statistics: $\sum x = 140$, $\sum y = 200$, $\sum x^2 = 1250$, $\sum y^2 = 2600$, and $\sum xy = 1100$. Calculate the product moment correlation coefficient.

   Worked answer

   1. M1 for calculating $S_{xx} = 1250 - \frac{140^2}{20} = 270$ and $S_{yy} = 2600 - \frac{200^2}{20} = 600$.
   2. M1 for calculating $S_{xy} = 1100 - \frac{140 \times 200}{20} = -300$.
   3. M1 for setting up the PMCC calculation $r = \frac{-300}{\sqrt{270 \times 600}}$.
   4. A1 for evaluating the final correlation coefficient as $r \approx -0.745$ (to 3 s.f.).

3. 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 $a = 0.4$.

More on these topics: Representation of Data · Correlation and Regression · Discrete Random Variables

S1 topics this paper can test

Every S1 paper can test any of the 7 S1 topics in the specification.

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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 (Q4); Outliers (Q8); Histograms (Q5). 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)