Edexcel IAL S1 January 2022 question paper and mark scheme (WST01/01)

Try 3 S1 questions like these

Written and checked by us, not taken from the Pearson paper. Tap "Worked answer" to see every step.

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. 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: $0.21 + 0.14 + 0.09 = 0.44$.

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 · Probability · Discrete Random Variables

S1 topics this paper can test

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

We haven't mapped this paper question by question yet. Each topic below opens our S1 page at that topic: what it covers, a worked example with its mark scheme, then practice questions.

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

Practise these topics (opens the practice engine)

• IAL S1

Practise every S1 topic free →

Formula booklet

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