Welcome to Identifying Cases!

Have you ever tried to filter for the perfect pair of shoes online? You select your size, your favorite color, and your budget. By doing this, you are performing a fundamental "Thinking Skill": identifying cases that satisfy given criteria. In the Cambridge 9694 syllabus, this is a core part of problem-solving. It’s all about being a data detective—taking a list of rules and finding out which options "pass the test" and which ones "fail."

In this chapter, we will learn how to systematically check data against rules and, importantly, how to explain exactly why a solution doesn't work when it misses the mark.

1. What are "Criteria"?

In Thinking Skills, criteria are simply the rules or conditions that a piece of information must meet. Think of them as a "security checkpoint" at an airport. To pass through, you must have a ticket, a passport, and no prohibited items. If you are missing even one, you don't get through!

Criteria can be presented in many ways:

  • Numbers: "The cost must be less than \( \$50 \)."
  • Categories: "The fruit must be citrus."
  • Time/Dates: "The delivery must arrive before \( 14:00 \)."
  • Logical Relationships: "If the item is heavy, it must also have wheels."

Quick Tip: Look out for "Threshold" words. Words like "at least", "no more than", "minimum", and "maximum" are the most common ways criteria are phrased in your exam.

2. The Systematic Approach (The "Checklist" Method)

When you are given a long list of data and several criteria, it’s easy to get overwhelmed. Don't worry! The best way to handle this is to create a mental or physical checklist. Follow these steps:

Step A: List the Criteria

Read the scenario and identify every single rule. For example, if you are looking for a flight, your criteria might be:
1. Price \( < \$400 \)
2. Duration \( < 5 \) hours
3. Departure after \( 09:00 \)

Step B: Test Each Case One-by-One

Pick the first "case" (e.g., Flight A) and compare it against Rule 1. If it passes, move to Rule 2. If it fails even one rule, you can stop immediately—that case is disqualified!

Step C: Confirm the Finalist

Once you find a case that satisfies all the criteria, double-check it. It’s easy to miss a small detail like a "greater than" vs "greater than or equal to" sign.

3. Identifying Why a Solution Fails

The 2027 syllabus specifically mentions "identifying criteria not met by a proposed solution." This means the exam might give you a "potential answer" and ask you why it is wrong.

To do this, you must pinpoint the exact rule that was broken. It is not enough to say "it doesn't fit"; you must show the math or the logic.

Example Scenario:
A club requires members to be at least \( 18 \) years old and live within \( 10km \) of the city center.
Proposed Solution: John is \( 20 \) years old and lives \( 12km \) away.
Identification of Failure: John satisfies the age criterion (\( 20 \ge 18 \)), but he fails the distance criterion because \( 12km \) is greater than the allowed \( 10km \).

Memory Aid: Think of it as a "Trial." You are the prosecutor, and you must provide "Evidence" (the data) of which "Law" (the criterion) was broken.

4. Common Pitfalls to Avoid

Even the best students can make simple mistakes in this section. Watch out for these "traps":

  • The "Exclusive" vs "Inclusive" Trap: If a rule says "less than \( 10 \)", then \( 10 \) is not allowed. If it says "at most \( 10 \)", then \( 10 \) is allowed.
  • Ignoring "Hidden" Criteria: Sometimes a rule is tucked away in the introductory text rather than the bullet points. Read the whole scenario!
  • The "One-Hit" Wonder: Don't stop checking just because a case meets the first rule. It must meet all of them to satisfy the criteria.
  • Mixing Units: If the criteria are in minutes but the data is in hours, you must convert them before comparing (e.g., \( 1.5 \) hours \( = 90 \) minutes).

5. Case Study: The Weekend Job

Let's look at a quick example to see this in action.

The Criteria:
Anish wants a job that:
1. Pays at least \( \$12 \) per hour.
2. Is on a Saturday.
3. Does not require him to start before \( 08:00 \).

The Options:
- Option A: Dog walking. \( \$15 \) per hour, Saturday, starts at \( 07:30 \).
- Option B: Car washing. \( \$10 \) per hour, Saturday, starts at \( 10:00 \).
- Option C: Tutoring. \( \$20 \) per hour, Saturday, starts at \( 09:00 \).

The Process:
- Option A fails Criterion 3 (\( 07:30 \) is before \( 08:00 \)).
- Option B fails Criterion 1 (\( \$10 \) is less than \( \$12 \)).
- Option C satisfies all criteria! (\( \$20 \ge \$12 \), Saturday, and \( 09:00 \ge 08:00 \)).

Key Takeaways

1. Be Precise: Pay close attention to the wording of the rules.

2. Stay Organised: Check one case at a time against every rule.

3. Explain the Failure: When a solution is wrong, be ready to state exactly which rule it broke and why.

4. Cross-Reference: Remember that this skill is often combined with other chapters. For instance, once you identify the cases that fit, you might then be asked to Search for solutions in more complicated situations or Find optimal solutions. Keep those tools in your belt!