GRE Graduate Record Exam Sample Test

Try 5 free practice questions with instant feedback. See how ready you are.

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Sample Questions

Question 1

What is the formula for the area of a triangle given two sides and the included angle?

Answer: Area = (1/2) × a × b × sin(C), where a and b are two sides and C is the included angle between them.

Question 2

In a 30-60-90 triangle, if the shortest side has length x, what are the lengths of the other two sides?

Answer: The side opposite 60° is x√3, and the hypotenuse (opposite 90°) is 2x.

Question 3

What does the Triangle Inequality Theorem state?

Answer: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Question 4

What is the relationship between the sides of a 45-45-90 triangle?

Answer: If each leg has length x, then the hypotenuse has length x√2.

Question 5

How do you find the area of a triangle using Heron's formula?

Answer: Area = √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2 is the semi-perimeter and a, b, c are the side lengths.