UPCAT 2026 Math & Logic Review

Question-and-answer flashcards summarizing core math, probability, and logic points extracted from the lecture transcript.

How do you determine whether a quadratic equation ax² + bx + c = 0 has two real roots?

Check the discriminant b² − 4ac; if it is positive, the two roots are real and unequal.

What does a zero discriminant (b² − 4ac = 0) tell you about the roots of a quadratic?

The quadratic has exactly one real root of multiplicity two (a repeated real root).

If a quartic polynomial has a double root at x = k, what test can you use to find out whether the other two roots are real?

Factor out (x − k)² and examine the discriminant of the remaining quadratic factor.

When comparing total profits of two restaurants across several months, what is the first computational step?

Add up each restaurant’s monthly profits separately to obtain their respective totals.

If Restaurant Y’s total profit is ₱20,000 greater than Restaurant X’s from January to May, which restaurant earned more overall?

Restaurant Y earned more; its total exceeds Restaurant X’s by ₱20,000.

In a contingency table of gender (male/female) and smoking status (smoker/non-smoker), how do you find P(Male ∩ Smoker)?

Divide the number of male smokers by the grand total of individuals in the table.

What is the formula for the probability that a randomly chosen individual is male given that the person is a smoker?

P(Male | Smoker) = (Number of male smokers) ÷ (Total number of smokers).

How many distinct sets of three products can be formed from n different products?

The number of sets is the combination C(n, 3) = n(n − 1)(n − 2) ⁄ 6.

A store has exactly 8 distinct 3-product sets and displays one set per day. How many days are needed to showcase every set once?

8 days—one day for each distinct set.

Syllogism: If ‘No mascot is a clown,’ what can you conclude about ‘Some mascots are not clowns’?

It must be true; if zero mascots are clowns, then certainly some (in fact all) mascots are not clowns.

Which statement is logically stronger—‘Some mascots are not clowns’ or ‘No mascot is a clown’?

‘No mascot is a clown’ is stronger because it excludes every mascot from the category of clowns, not just some.

What logical test shows that ‘Some mascots are not clowns’ does not contradict ‘No mascot is a clown’?

Verify that the universal statement (‘No mascot is a clown’) implies the existential statement; if the universal holds, the existential is automatically satisfied.