The class of 2024 has proven to be exceptional at mathematics, showcasing their skills through the challenging A-level exams. As we delve into the questions that these pupils faced, it’s an opportunity for us to test our own mathematical prowess. Let’s explore some of the questions from last year’s A-level exams and see if we can rise to the challenge.

### Question 1: Product Moment Correlation Coefficient

In this question, we are presented with a set of values and asked to determine which of them is not a possible value for a product moment correlation coefficient. The options provided are -6/5, -3/5, 0, and 1. To solve this question, we need to understand the concept of the product moment correlation coefficient and its possible range of values.

The product moment correlation coefficient, often denoted by r, measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.

In this case, the possible values for a product moment correlation coefficient are within the range of -1 to 1. Therefore, the correct answer to this question is -6/5, as it falls outside the valid range of values for the correlation coefficient.

### Question 2: Probability and Statistics

Moving on to the next question, we are introduced to a scenario involving the passing rate of drivers taking their driving test at a local test center. It is stated that, on average, 40% of drivers pass their driving test at this center. With this information, we are tasked with calculating the standard deviation of the number of drivers who pass their test each day.

To tackle this question, we first need to understand the concept of variance and standard deviation. Variance measures the spread of data points from the mean, while standard deviation is the square root of the variance, providing a more intuitive understanding of the spread of data.

Given that the passing rate is 40%, we can calculate the variance by multiplying the number of drivers (32) by the probability of passing (0.4) and failing (0.6). This yields a variance of 7.68. Taking the square root of the variance gives us the standard deviation, which is approximately 2.773 in this scenario.

### Question 3: Probability and Combinatorics

The final question presents a probability scenario involving two types of coins in a money box: bronze coins comprising 20% of the total and silver coins making up the remaining 80%. The task is to determine the probability that both coins drawn randomly are bronze, given that at least one of them is bronze.

To solve this question, we first calculate the probability of drawing at least one bronze coin, which is 1 minus the probability of drawing two silver coins (0.8 x 0.8 = 0.64), resulting in a probability of 0.36. Next, we calculate the probability of drawing both bronze coins, given that at least one is bronze. This is achieved by multiplying the individual probabilities of drawing bronze coins and dividing by the probability of drawing at least one bronze coin. The final probability is 1/9.

In conclusion, the A-level mathematics questions from the class of 2024 exemplify the depth and complexity of mathematical concepts tested in these exams. As we reflect on these questions and answers, it’s a reminder of the importance of critical thinking and problem-solving skills in the field of mathematics. Whether you aced these questions or found them challenging, they serve as a testament to the rigorous academic standards upheld in A-level examinations.