## Algebra

## A1

Find the roots of the quadratic equation \(x^2 - 4x + 4 = 0\).

## A2

Determine the value of \(y\) in the equation \(2y + 3 = 7\).

## Combinatorics

## C1

How many ways can 3 objects be arranged in a line?

## A1

Find the roots of the quadratic equation \(x^2 - 4x + 4 = 0\).

Solution. The equation simplifies to \((x - 2)^2 = 0\), so the root is \(x = 2\).

## A2

Determine the value of \(y\) in the equation \(2y + 3 = 7\).

Solution 1. Subtracting 3 from both sides gives \(2y = 4\).

Solution 2. Dividing both sides by 2 gives \(y = 2\).

## C1

How many ways can 3 objects be arranged in a line?

Solution. The number of permutations of 3 objects is \(3! = 6\).