GRE Math Domain 3: Additional Math Topics

A set contains all integers \( x \) such that \( -2 < x < 3 \). How many elements are in this set?

In a class of 30 students, 18 are studying French, 15 are studying German, and 7 are studying both. How many students are not studying either language?

What is the area of a triangle with sides of length 13, 14, and 15?

If the sum of the first \( n \) terms of an arithmetic sequence is given by \( S_n = 3n^2 + 5n \), what is the first term of the sequence?

In a certain sequence, the term \( a_n = \frac{1}{n(n+1)} \) for \( n \geq 1 \). What is the sum of the first 10 terms of this sequence?

What is the remainder when \( 2^{100} \) is divided by 7?

A rectangle is inscribed in a circle of radius \( r \). If the perimeter of the rectangle is \( 20 \), what is the maximum possible area of the rectangle?

If \( x \) and \( y \) are integers such that \( x^2 + y^2 = 25 \), what is the maximum possible value of \( x \)?

A fair six-sided die is rolled twice. What is the probability that the sum of the two rolls is 9?

What is the value of \( n \) in the permutation equation \( P(n, 3) = 60 \)?

A circle has a circumference of \( 8\pi \). What is the area of the circle?

If \( a, b, \) and \( c \) are the angles of a triangle, and \( a = 2b \) and \( b = 2c \), what is the measure of angle \( c \)?

What is the hundredth term of the arithmetic sequence 3, 6, 9, ... ?

If \( 2x + 3y = 12 \) and \( 4x - 5y = 1 \), what is the value of \( x \)?

If \( \sin \theta = \frac{3}{5} \) and \( 0 < \theta < \frac{\pi}{2} \), what is \( \cos \theta \)?

What is the equation of the line perpendicular to \( y = 2x + 3 \) and passing through the point (1, -2)?

If a set contains all numbers \( x \) such that \( 1 < x^2 < 9 \), what is the range of \( x \)?

The sum of the interior angles of a polygon is 1260 degrees. How many sides does the polygon have?

A cylinder has a radius of 3 and a height of 4. What is the volume of the cylinder?

If \( \log_2 x + \log_2 y = 5 \) and \( \log_2 x - \log_2 y = 1 \), what is the value of \( x \)?