Problem-solving practice 2 (AQA GCSE Maths): Revision Notes
Problem-solving practice 2
This practice focuses on three key areas of probability and statistics: comparing data sets, interpreting scatter graphs, and calculating probabilities. Each problem requires different mathematical skills and problem-solving strategies.
Problem 3: Comparing data sets
When you need to compare two groups of data, you must calculate and compare both averages and measures of spread. This gives you a complete picture of how the groups differ.
Worked Example: Comparing Boys' and Girls' Weights
Step 1: Calculate statistics for both groups Boys' weights: 70, 65, 45, 52, 63, 72, 63 kg Girls' weights: 65, 45, 47, 61, 44, 67, 55, 56, 63 kg
Step 2: Find means and ranges
- Calculate the mean for both data sets
- Calculate the range for both data sets
Step 3: Write comparative conclusions using your calculations
Key strategy for data comparison
You should always calculate your statistics first, then use these numbers to write meaningful comparisons. When writing conclusions, use complete sentences that clearly state which group has higher averages or greater spread. This approach ensures you get full marks for both the calculations and the interpretation.
Problem 4: Using scatter graphs and line of best fit
Scatter graphs help you identify relationships between two variables and make predictions. The key skill is drawing and using a line of best fit to estimate unknown values.
In this example, Jade's French mark was 42, and you need to estimate her German mark using the scatter graph pattern.
Worked Example: Reading Values from Scatter Graphs
Step 1: Draw the line of best fit through the data points
Step 2: Find your starting point - locate the known value on the appropriate axis
Step 3: Draw a vertical line from this point to meet your line of best fit
Step 4: Draw a horizontal line from this intersection to the other axis
Step 5: Read your answer to the nearest small square on the grid
Important tip for reading graphs
When reading information from any graph, always give your answer to the nearest small square. This shows you understand the limitations of reading from a graph and helps avoid unnecessary precision errors.
Problem 5: Calculating probability with independent events
Probability questions often involve multiple events happening together. There are two main approaches you can use to solve these problems.
The setup: Amy picks one card from group A (cards 1, 2, 3) and one card from group B (cards 4, 5), then adds the numbers together.
Worked Example: Method 1 - List All Possible Outcomes
Write down every possible combination when picking two cards:
- Card 1 + Card 4 = 5
- Card 1 + Card 5 = 6
- Card 2 + Card 4 = 6
- Card 2 + Card 5 = 7
- Card 3 + Card 4 = 7
- Card 3 + Card 5 = 8
Count the outcomes that match what you're looking for, then calculate the probability.
Worked Example: Method 2 - Use Independent Events
Calculate the probability of each pick separately, then multiply them together. This works because picking from group A doesn't affect what you can pick from group B.
Essential probability strategy
Always make sure you've identified all possible outcomes before calculating your probability. List them systematically to avoid missing any combinations. This methodical approach helps you get the right answer and shows clear working for full marks.
Key Points to Remember:
- For data comparison: Calculate averages and spread measures first, then write comparative conclusions using these values
- For scatter graphs: Draw your line of best fit carefully, then use the step-by-step line method to read estimates accurately
- For probability: List all possible outcomes systematically before calculating - this prevents errors and shows clear reasoning
- Always show your working: Problem-solving questions reward clear methods and logical steps, not just correct final answers
- Use complete sentences: When writing conclusions or comparisons, full sentences demonstrate your understanding more effectively than brief phrases