SAT Math · Advanced Math
Equivalent expressions practice questions
Each free question on this page comes with its answer and a full explanation, and each one is marked easy, medium or hard.
- Question 9 · mediumThe function f(x) = x² - 8x + 19 is equivalent to which of the following, where the minimum value of f is visible directly from…
- Question 16 · easyIf (x+3)(x-5) = x² + bx + c for all values of x, what is the value of b?
- Question 32 · easyFor x ≠ 4, which expression is equivalent to (x² - 16)/(x - 4)?
- Question 61 · hardLet u = x² - 1. If u² - 7u + 10 = 0, how many distinct real values of x satisfy this equation?
- Question 62 · mediumIf x + y = 7 and xy = 10, what is the value of x² + y²?
- Question 74 · mediumIn the expansion of (x+5)(2x-3), what is the coefficient of the x term?
- Question 75 · mediumWhich expression is equivalent to x^3/2 for x > 0?
- Question 76 · mediumWhen the polynomial x³ - 2x² + 5 is divided by x - 1, what is the remainder?
- Question 93 · mediumWhat is the product of the two solutions to x² - 5x - 24 = 0?
- Question 94 · mediumFor which values of x is the expression (x²-4)/(x²-2x) undefined?
- Question 135 · mediumWhat is the minimum value of the function f(x) = x² - 6x + 5?
- Question 153 · mediumWhat is the maximum value of the function f(x) = -x² + 10x - 21?
- Question 158 · hardWhich expression is equivalent to x^-2/3 for x > 0?
- Question 172 · mediumWhat is the sum of the two solutions to x² - 5x - 24 = 0?
- Question 178 · hardFor x ≠ 2 and x ≠ -2, which expression is equivalent to (x^4 - 16)/(x² - 4)?
- Question 179 · mediumIf x + y = 9 and xy = 14, what is the value of (x-y)²?
- Question 180 · mediumIf (x+2)(x-4) = x² + bx + c for all values of x, what is the value of b + c?
- Question 193 · mediumWhen the polynomial x³ + 3x² - x + 2 is divided by x - 2, what is the remainder?
- Question 198 · mediumWhat is the value of 8^2/3?
- Question 214 · easyWhat is the x-coordinate of the vertex of the graph of f(x) = x² + 12x + 40?
- Question 232 · easyWhat is the y-intercept of the graph of f(x) = x² - 8x + 21?
- Question 236 · hardWhich expression is equivalent to x^-3/2 for x > 0?
- Question 254 · mediumWhat is the product of the two solutions to x² - 2x - 35 = 0?
- Question 258 · mediumIf (x-6)(x+2) = x² + bx + c for all values of x, what is the value of b - c?
- Question 266 · easyIf (x-4)(x+9) = x² + bx + c for all values of x, what is the value of c?
- Question 272 · mediumThe function f(x) = x² - 4x - 5 can be written in vertex form as f(x) = (x-h)² + k. What is the value of h + k?
- Question 274 · mediumWhen the polynomial x³ + 4x² - 2x + 1 is divided by x - 1, what is the remainder?
- Question 295 · mediumWhat is the sum of the two solutions to x² - 3x - 40 = 0?
- Question 298 · easyFor x ≠ 6, which expression is equivalent to (x² - 36)/(x - 6)?
- Question 312 · mediumWhat is the product of the two solutions to x² + 3x - 40 = 0?