Challenge your understanding of core GRE math formulas with these key questions designed to assess your grasp of equations, shapes, and algebraic concepts. Strengthen your quantitative reasoning for the GRE by identifying the correct applications and components of must-know formulas.
Which of the following correctly represents the quadratic formula used to find the roots of ax² + bx + c = 0?
Explanation: The correct quadratic formula is x = (-b ± √(b² - 4ac))/(2a), which solves for x in the standard quadratic equation. Option B incorrectly reverses the order of 4ac and b², while C misses the negative sign in front of b. Option D incorrectly adds 4ac to b² and divides by a instead of 2a. Only the first option correctly applies the signs and components.
Given a circle with radius r, what is the formula to calculate its area?
Explanation: The area of a circle is found using the formula Area = πr², where r is the radius of the circle. Option B, 2πr, is actually the circumference formula. Option C incorrectly uses the diameter squared instead of radius. Option D falsely multiplies the diameter by π. Thus, only the correct area formula uses radius squared multiplied by pi.
For two points on a coordinate plane, (x₁, y₁) and (x₂, y₂), which formula gives the slope m of the line passing through them?
Explanation: The formula for the slope of a line is m = (y₂ - y₁)/(x₂ - x₁), expressing how much y changes for each unit change in x. Option B inverts numerator and denominator, which gives the reciprocal of the correct value. Option C reverses the order and signs. Option D adds coordinates, which is not the method for calculating slope. Thus, only the first choice defines slope properly.
If a right triangle has legs of lengths 3 and 4, what is the formula to find the length of the hypotenuse c?
Explanation: Applying the Pythagorean Theorem, the hypotenuse c is found by c² = a² + b². For this triangle, that results in c² = 3² + 4². Option B mistakenly adds the sides, which is not the correct way to find hypotenuse. Option C multiplies instead of adding squares. Option D subtracts squares, which is incorrect for the Pythagorean Theorem. Only the correct answer provides the proper formula.
What is the correct formula for calculating simple interest I earned on a principal P at rate r for time t years?
Explanation: Simple interest is calculated by multiplying the principal by the rate and the time, I = Prt. Option B adds instead of multiplying, which gives an incorrect value. Option C divides rate by time, which does not yield interest. Option D subtracts, which is not correct for interest calculations. Thus, only 'I = Prt' produces the correct interest amount.