Solving quadratic, radical, rational, and exponential equations, plus systems that mix a line with a curve — including discriminant reasoning.
86
Total questions
40
Easy
15
Medium
31
Hard
This skill covers solving quadratics (factoring, quadratic formula, completing the square), radical and rational equations, and mixed systems where a line meets a parabola or circle. Discriminant questions — for what value of k does the equation have exactly one real solution — are a hard-difficulty staple.
For quadratics, try factoring first, but know the quadratic formula without hesitation. For "exactly one solution" questions, set the discriminant b² − 4ac = 0 and solve for the unknown constant. For line-meets-curve systems, substitute the linear equation into the nonlinear one and analyze the resulting quadratic. Desmos verifies almost all of these graphically in seconds.
Straight from the Grind1600 question bank — try each one before revealing the answer.
Correct answer: C
Choice C is correct. It's given that x² = 64. Substituting: x² + 10 = 64 + 10 = 74. Choice A is incorrect and may result from using x = 8, then computing 8 + 10. Choice B is incorrect and may result from computing 64 - 10. Choice D is incorrect and may result from computing (8 + 10)² or similar errors.
Correct answer: A
Choice A is correct. Starting with d = (1/2)at². Multiplying both sides by 2: 2d = at². Dividing both sides by a: t² = 2d/a. Taking the positive square root: t = √(2d/a). Choice B is incorrect; this doesn't account for the square root. Choice C is incorrect; this divides by 2a instead of first multiplying by 2. Choice D is incorrect; this has a in the numerator.
Equivalent Expressions
Rewriting algebraic expressions — factoring, expanding, combining rational expressions, and applying exponent rules to show two forms are equivalent.
Nonlinear Functions
Quadratic, exponential, and polynomial functions: vertex form, growth and decay, end behavior, and interpreting key features in context.
Function Notation
Evaluating and composing functions written as f(x), interpreting what f(a) = b means, and translating between notation, tables, and graphs.
86 Nonlinear Equations & Systems questions with step-by-step explanations, woven into a day-by-day study plan built for your test date.
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