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GRE Quadratic Equations — practice questions — page 2

Explore 78 free Quadratic Equations questions in GRE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Quadratic Equations questions and exercises with answers

Showing questions 31–60 of 78.

tan(A + B) equals:Read the answer and worked solution →sin(180° - θ) equals:Read the answer and worked solution →In triangle ABC with sides a, b, c opposite to angles A, B, C: sine rule states:Read the answer and worked solution →If sin θ + cos θ = 1, then sin θ × cos θ equals:Read the answer and worked solution →General solution of cos θ = 0:Read the answer and worked solution →If tan θ + cot θ = 2, find sin 2θ:Read the answer and worked solution →If sin θ = 12/13 (acute θ in Q1), find tan(θ/2):Read the answer and worked solution →Minimum value of sin²θ + cos⁴θ:Read the answer and worked solution →If sin θ = 12/13 (acute), find tan(θ/2):Read the answer and worked solution →In triangle with sides 7, 8, 9, find cos of the angle opposite to side 9 (use cosine rule):Read the answer and worked solution →General solution of sin θ = sin α:Read the answer and worked solution →In radian measure, $\pi$ radians equals:Read the answer and worked solution →One radian is approximately equal to:Read the answer and worked solution →In a circle of radius $r$, an arc of length $l$ subtends at the centre an angle (in radians) of:Read the answer and worked solution →The identity $\sin^2\theta + \cos^2\theta$ equals:Read the answer and worked solution →The identity $1 + \tan^2\theta$ equals:Read the answer and worked solution →The period of the function $\sin x$ is:Read the answer and worked solution →The radian measure of $45^\circ$ is:Read the answer and worked solution →$\sin(90^\circ - \theta)$ equals:Read the answer and worked solution →The standard form of a quadratic equation in the variable x is:Read the answer and worked solution →For a quadratic equation $ax^2+bx+c=0$, the discriminant is:Read the answer and worked solution →A quadratic equation has two distinct real roots when its discriminant is:Read the answer and worked solution →A quadratic equation has two equal real roots when its discriminant is:Read the answer and worked solution →A quadratic equation has no real roots when its discriminant is:Read the answer and worked solution →For $ax^2+bx+c=0$, the sum of the roots equals:Read the answer and worked solution →For $ax^2+bx+c=0$, the product of the roots equals:Read the answer and worked solution →The roots of the equation $x^2 - 5x + 6 = 0$ are:Read the answer and worked solution →The roots of $x^2 + 4x + 4 = 0$ are:Read the answer and worked solution →The value(s) of k for which $x^2 + kx + 9 = 0$ has two equal roots is/are:Read the answer and worked solution →The discriminant of $2x^2 - 4x + 3 = 0$ is −8, so the equation has:Read the answer and worked solution →

Worked practice questions

tan(A + B) equals:

  1. tanA + tanB
  2. tanA tanB
  3. (tanA + tanB)/(1 - tanA tanB)
  4. (tanA - tanB)/(1 + tanA tanB)
Show answer and solution

Correct answer: C. (tanA + tanB)/(1 - tanA tanB)

tan(A + B) = (tanA + tanB)/(1 - tanA tanB). *Note: when tanA tanB = 1, denominator is 0 — that's when A + B = 90° + 180°k.*

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sin(180° - θ) equals:

  1. cos θ
  2. -cos θ
  3. -sin θ
  4. sin θ
Show answer and solution

Correct answer: D. sin θ

sin is positive in Q2: sin(180° - θ) = sin θ. (Compare: cos(180° - θ) = -cos θ; tan(180° - θ) = -tan θ.)

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In triangle ABC with sides a, b, c opposite to angles A, B, C: sine rule states:

  1. a/sinA = b/sinB = c/sinC
  2. a + b + c = 0
  3. sinA = sinB
  4. a²+b² = c²
Show answer and solution

Correct answer: A. a/sinA = b/sinB = c/sinC

**Sine rule:** a/sinA = b/sinB = c/sinC = 2R (where R is circumradius). Useful for solving triangles when you know any side + opposite angle + one more piece.

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More Mathematics topics

MathematicsStatistics and ProbabilityArithmetic ProgressionSets and RelationsReal Numbers and PolynomialsUnit 1A1: Relations, Functions and GraphsUnit 6B: Definite Integration & Riemann SumsUnit 1B1: Limit Concepts and Graphical Limits