Edexcel IAL S1 June 2023 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. 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 solution

   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: $w\times h=12w⟹h=12\text{ cm}$.

2. Correlation and Regression · 4 marks

   Using the summary statistics $\sum x=140$, $\sum y=200$, $S_{xx}=270$, $S_{xy}=-300$, and $n=20$, find the equation of the regression line of $y$ on $x$ in the form $y=a+bx$.

   Worked solution

   1. M1 for calculating the gradient $b=\frac{S_{xy}}{S_{xx}}=\frac{-300}{270}$.
   2. A1 for $b=-\frac{10}{9}$ or $\approx -1.11$.
   3. M1 for calculating the means $\overline{x}=7$, $\overline{y}=10$, and determining the intercept $a=10-(-\frac{10}{9})(7)$.
   4. A1 for final equation $y=17.8-1.11x$ (or $y=\frac{160}{9}-\frac{10}{9}x$).

3. Measures of Location and Spread · 4 marks

   A dataset $x$ has mean $\overline{x}=5$ 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 $\overline{y}=15$ and standard deviation ${\sigma }_y=6$. Find the values of $a$ and $b$.

   Worked solution

   1. M1 for linking the standard deviations: ${\sigma }_y=a{\sigma }_x$.
   2. A1 for solving for $a$: $6=a(2)⟹a=3$.
   3. M1 for linking the means: $\overline{y}=a\overline{x}+b$.
   4. A1 for substituting $a=3$ to find $b$: $15=3(5)+b⟹b=0$.

More on these topics: Representation of Data · Correlation and Regression · Measures of Location and Spread

What's on this paper

What this paper is like

• Shape: 7 questions, 75 marks in 1 h 30 min (about 1.2 minutes a mark); questions from 8 to 14 marks.
• Biggest question: Q7, 14 marks: normal model for apple juice volumes.
• Marks by main topic: Discrete Random Variables 22, Normal Distribution 14, Correlation and Regression 13, Measures of Location and Spread 9, Probability 9, Representation of Data 8.
• More Normal Distribution in other sittings: October 2023 Q5 (15 marks), January 2023 Q5 (17 marks), January 2024 Q8 (9 marks).
• Against the other 14 sittings we mapped: more marks on Discrete Random Variables (22 marks here, 14 on average) and Measures of Location and Spread (9 marks here, 5 on average); fewer on Probability (9 marks here, 17 on average) and Representation of Data (8 marks here, 13 on average).
• Not on this paper: Data and Summary Statistics.
• 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 distances to work (8 marks) · S1 Representation of Data
2. Q2Weight and tail length: correlation (13 marks) · S1 Correlation and Regression
3. Q3Coded salmon lengths (9 marks) · S1 Measures of Location and Spread
4. Q4Labelled counters from a bag (9 marks) · S1 Discrete Random Variables, S1 Probability
5. Q5Discrete distribution with a constant k (13 marks) · S1 Discrete Random Variables
6. Q6Three events: conditional probability (9 marks) · S1 Probability
7. Q7Normal model for apple juice volumes (14 marks) · S1 Normal Distribution

Practise every S1 topic free →