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

3 S1 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. Data and Summary Statistics · 9 marks

   The mean of three numbers, $a$, $b$, and $c$, is exactly $8$. The variance of these three numbers is $10$.

   1. Using the formula for variance, prove that $a^2+b^2+c^2=222$.

   2. Given that $c=10$, find the mean and the variance of the remaining two numbers, $a$ and $b$.

   Worked solution

   1. Let the sum of squares be $\sum x^2=a^2+b^2+c^2$.
      Using the variance formula: $\text{Var}(X)=\frac{\sum x^2}{n}-{\mu }^2$. M1
      $10=\frac{a^2+b^2+c^2}{3}-8^2$. M1
      $10=\frac{a^2+b^2+c^2}{3}-64⟹74=\frac{a^2+b^2+c^2}{3}$. A1
      $a^2+b^2+c^2=3\times 74=222$. A1 *

   2. If $c=10$, then $a+b+10=3\times 8=24⟹a+b=14$. M1
      New mean for just $a$ and $b$: $\frac{14}{2}=7$. A1
      Substitute $c=10$ into sum of squares: $a^2+b^2+100=222⟹a^2+b^2=122$. M1
      New Variance for $a$ and $b$ $=\frac{a^2+b^2}{2}-(\text{New Mean}{)}^2$. M1
      $=\frac{122}{2}-7^2=61-49=12$. A1

2. Representation of Data · 5 marks

   The data in a histogram is grouped into classes. A bar representing the class $100\le x<150$ has a width of $2.5\text{ cm}$ and a height of $4\text{ cm}$. The total area of all bars in the histogram is $90{\text{ cm}}^2$. If the bar for $100\le x<150$ represents a frequency of $20$, calculate the total frequency of the entire data set.

   Worked solution

   1. M1 for calculating the area of the specified bar: $2.5\times 4=10{\text{ cm}}^2$.
   2. M1 for establishing the relationship between area and frequency: $10{\text{ cm}}^2$ represents a frequency of $20$.
   3. A1 for calculating the scale factor: $1{\text{ cm}}^2$ represents $2$ items (since $20/10=2$).
   4. M1 for using the total area to find total frequency: $90{\text{ cm}}^2\times 2$.
   5. A1 for the final answer: $180$ items.

3. Probability · 3 marks

   Given $P(A|B)=0.5$, $P(B)=0.4$, $P(A)=0.3$, find $P(B|A)$.

   Worked solution

   $P(A\cap B)=P(A|B)P(B)=0.5\times 0.4=0.2$ M1
   $P(B|A)=\frac{P(A\cap B)}{P(A)}=\frac{0.2}{0.3}$ M1
   $=\frac{2}{3}$ A1

   Answer: $\frac{2}{3}$

More on these topics: Data and Summary Statistics · Representation of Data · Probability

What's on this paper

What this paper is like

• Shape: 8 questions, 75 marks in 1 h 30 min (about 1.2 minutes a mark); questions from 7 to 12 marks.
• Biggest question: Q2, 12 marks: monthly temperatures: regression.
• Marks by main topic: Correlation and Regression 24, Probability 17, Normal Distribution 16, Discrete Random Variables 10, Representation of Data 8.
• More Correlation and Regression in other sittings: October 2023 Q6 (12 marks), June 2024 Q4 (13 marks), June 2023 Q2 (13 marks).
• Against the other 14 sittings we mapped: more marks on Correlation and Regression (24 marks here, 13 on average) and Normal Distribution (16 marks here, 12 on average); fewer on Measures of Location and Spread (0 marks here, 5 on average) and Discrete Random Variables (10 marks here, 15 on average).
• Not on this paper: Data and Summary Statistics, Measures of Location and Spread.
• Calculator: allowed.

WST01/01: question by question

Labels and topics are ours, read from the WST01/01 paper (checked 2026-11-01); marks as printed. Tap a number to practise that topic.

1. Q1Histogram of heights (8 marks) · S1 Representation of Data
2. Q2Monthly temperatures: regression (12 marks) · S1 Correlation and Regression
3. Q3Left- and right-handed students (8 marks) · S1 Probability
4. Q4French and Spanish marks: correlation (12 marks) · S1 Correlation and Regression
5. Q5Normal model for discus throws (7 marks) · S1 Normal Distribution
6. Q6Two events with unknown probabilities (9 marks) · S1 Probability
7. Q7Cumulative distribution function (10 marks) · S1 Discrete Random Variables
8. Q8Normal distribution with an unknown mean (9 marks) · S1 Normal Distribution

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