IMO Algebra and Equations 3

Question 1

If 2(x + 3) = 18, what is x?

Accepted Answer

6

Answer

2(x + 3) = 18 → x + 3 = 9 → x = 6.

Question 2

What is the product of (x + 2)(x + 3)?

Accepted Answer

x² + 5x + 6

Answer

(x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6.

Question 3

Which value of x satisfies 3x > 12?

Accepted Answer

x = 5

Answer

3x > 12 → x > 4, so x = 5 is the only option greater than 4.

Question 4

If the area of a rectangle is 3x + 6 and one side is 3, what is the other side?

Accepted Answer

x + 2

Answer

Other side = (3x + 6) ÷ 3 = x + 2.

Question 5

What is the value of 4k² when k = 2?

Accepted Answer

16

Answer

4k² = 4 × 2² = 4 × 4 = 16.

IMO - International Mathematics Olympiad Practice Test