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).