Chapter 1: Introduction to the Math Challenge

In previous articles, I frequently emphasize the critical gap in mathematical proficiency among Data Scientists. I often express concern that many practitioners execute methodologies without a fundamental grasp of the underlying principles. Recently, while assisting my daughter with her preparations for the GCSE Mathematics exam—a test administered to 16-year-olds in England, Wales, and Northern Ireland—I contemplated how individuals engaged in Data Science might fare on such questions.

She posed an intriguing question: how would Data Scientists perform on her exam? This prompted me to share a set of ten progressively difficult questions with the Medium community, inviting them to tackle these challenges. For context, these questions are representative and do not require complex formatting or diagrams, such as those found in trigonometry.

If you want to replicate exam conditions, attempt to solve these ten questions within a 25-minute timeframe, without calculators and providing full workings for your answers. At the end, you can compare your responses to see how well you did. Are you ready? Let's dive in!

Section 1.1: The Questions

1. David is tiling his bathroom wall. The tiles measure 1 cm in width and b cm in height, and he requires a total of 20 tiles. Determine an expression for the area of the wall being tiled.

2. Sara has six dogs in her kennels, weighing 32 kg, 23 kg, 31 kg, 28 kg, 36 kg, and 26 kg. After two dogs wander off, the average weight of the remaining dogs is 27.25 kg. Identify the weights of the two dogs that left.

3. Demonstrate that the difference between the mean and the median of five consecutive integers is always zero.

4. In 2018, Mohammed completed a long-distance race in time t. The following year, he finished the same race 10% faster. Calculate the percentage increase in his average speed, rounded to two decimal places.

5. A hairdresser noted that the ratio of children to adults was 3:7. If 60% of the children and 20% of the adults had blonde hair, what percentage of all customers had blonde hair?

6. Express the recurring decimal 0.590909090… as a simplified fraction a/b.

7. Given p = 2³ * 3² * 5 * 7, q = (6/7)*p, and r =(4/15)*p, calculate the highest common factor (HCF) of q and r.

8. A tea shop had 100 customers, each purchasing at least one type of tea: English Breakfast, Earl Grey, and Darjeeling. With 28 customers buying Earl Grey (12 of whom also bought Darjeeling) and 43 customers purchasing English Breakfast (10 of whom also bought Earl Grey and 7 also bought Darjeeling), compute:

   8A. The probability that a randomly selected customer bought English Breakfast or Darjeeling.

   8B. The probability that a customer who bought Darjeeling also purchased at least one other type of tea.

9. Tammy and Mae-Li each think of a number. Tammy's number is negative, and Mae-Li's is one more than Tammy's. When they take the reciprocal of their numbers and add them, the result is 5/6. Determine Tammy's original number using algebra.

10. The speed x (in meters per second) of object A after t seconds is described by the equation x = 18(s + 2t²)/5t, where s is the distance traveled in t seconds. Object B travels s meters in t seconds, and s is directly proportional to t², completing 160 meters in 8 seconds. After 6 seconds, both objects have traveled the same distance. Find the value of x at this time.

Chapter 2: Video Resources

To further enhance your understanding of high school mathematics, here are some useful video resources.

The first video titled "How To ACE Your Math Class" offers valuable strategies for excelling in mathematics.

Next, the video "Can you Pass High School MATH (12 question quick test)" provides a quick math quiz that challenges your skills.

Conclusion: Evaluating Your Performance

If you found yourself struggling with these questions, particularly those toward the end, here's a rough guide for self-assessment assuming you adhered to the 25-minute limit:

• Correctly answered 3 or fewer questions: Unfortunately, you wouldn't meet the basic passing criteria.
• Correctly answered between 4 and 6 questions: You passed, but further mathematical study may not be advisable.
• Correctly answered 7 or 8 questions: A solid performance, though high grades in upper-level mathematics will require extra effort.
• Correctly answered 9 or more questions: You likely possess a natural aptitude for mathematics, positioning you for success in future studies.

Feel free to share your results in the comments.

As a former Pure Mathematician turned Psychometrician and Data Scientist, I am dedicated to applying the rigor of these fields to complex human questions. I invite you to connect with me on LinkedIn or Twitter, and check out my blog at drkeithmcnulty.com, where I discuss topics from my recent books: "Handbook of Regression Modeling in People Analytics" and "Handbook of Graphs and Networks in People Analytics."