ESAT · Maths and science modules

ESAT 'which statements are correct' questions

Decide which of several numbered statements are true, then choose the matching combination.

How to spot it

Which of the following statements is/are correct?
I ... II ... III ...

Try one

Original example

A ball is thrown straight up and caught again at the same height. Air resistance is negligible.

I. At the highest point the ball's velocity is zero.II. At the highest point the ball's acceleration is zero.III. The time taken to rise equals the time taken to fall back.

Which of the statements is/are correct?

The method

Judge each statement on its own and mark it true or false.
Find a counterexample fast for any statement that says "always".
Only then read the options and pick the combination.

The trap

Watch forReading the options first and choosing a combination that looks balanced.

Now a harder one

Harder

The function $f$ is given by $f(x)$ $= x^2 - 6x + 10$ .

I. $f(x)$ $> 0$ for all real $x$ .II. The minimum value of $f(x)$ is $3$ .III. $f(x)$ $= f(x + 6)$ for all real $x$ .

Which of the statements is/are true?