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GRE Unit 1A1: Relations, Functions and Graphs — practice questions

Explore 73 free Unit 1A1: Relations, Functions and Graphs questions in GRE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Unit 1A1: Relations, Functions and Graphs questions and exercises with answers

Showing questions 1–30 of 73.

A rational number is any number that can be written in the form p/q, where p and q are integers and:Read the answer and worked solution →Which of the following is NOT a rational number?Read the answer and worked solution →The additive identity for rational numbers is:Read the answer and worked solution →The multiplicative identity for rational numbers is:Read the answer and worked solution →Which property is shown by: (−2/3) + (3/5) = (3/5) + (−2/3)?Read the answer and worked solution →The additive inverse of 5/8 is:Read the answer and worked solution →Which statement is TRUE for the set of rational numbers?Read the answer and worked solution →Find 3/4 − 5/6.Read the answer and worked solution →Using distributivity, the value of (7/5) × (−3/12) + (7/5) × (5/12) is:Read the answer and worked solution →The mean of two rational numbers a and b is (a + b)/2. The mean of 1/3 and 1/2 is:Read the answer and worked solution →Find (−4/5) × (3/7) × (15/16) × (−14/9).Read the answer and worked solution →Simplify using commutativity and distributivity: (2/5) × (−3/7) − (1/14) − (3/7) × (3/5)Read the answer and worked solution →How many rational numbers exist between 1/3 and 1/2?Read the answer and worked solution →Does the rational number 0 have a multiplicative inverse?Read the answer and worked solution →Which of the following is the WHOLE NUMBER that is closest to 0 but is NOT a natural number?Read the answer and worked solution →Using distributivity, find: (3/5) × [(−7/9) + (4/9)].Read the answer and worked solution →For which rational number a is the statement 'a is its own additive inverse' TRUE?Read the answer and worked solution →Three rational numbers a, b, c are given. Which of the following is ALWAYS true?Read the answer and worked solution →The MAXIMUM possible measure of an exterior angle of a regular polygon is:Read the answer and worked solution →Which of the following is NOT a perfect square?Read the answer and worked solution →Which of the following is a perfect square?Read the answer and worked solution →The sum 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 equals:Read the answer and worked solution →Using prime factorisation, √324 equals:Read the answer and worked solution →How many PERFECT SQUARES lie strictly between 100 and 200?Read the answer and worked solution →$\csc\theta$ (cosecant) is the reciprocal of:Read the answer and worked solution →$\sec\theta \cdot \cos\theta$ equals (where defined):Read the answer and worked solution →Express $40^{\circ} 20'$ in degrees as a fraction.Read the answer and worked solution →$\dfrac{\pi}{6}$ radian = ?Read the answer and worked solution →$\dfrac{3\pi}{2}$ radian = ?Read the answer and worked solution →Which of the following is a perfect cube?Read the answer and worked solution →

Worked practice questions

A rational number is any number that can be written in the form p/q, where p and q are integers and:

  1. p ≠ 0
  2. q ≠ 0
  3. p = q
  4. p > q
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Correct answer: B. q ≠ 0

Division by zero is undefined, so the denominator q must be non-zero. The numerator p may be any integer (including 0, since 0/5 = 0 is rational).

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Which of the following is NOT a rational number?

  1. −2/3
  2. 0
  3. 7/0
  4. 9/(−5)
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Correct answer: C. 7/0

7/0 is undefined because division by zero is not allowed. The other three are all valid rational numbers (recall 0 = 0/1 is rational).

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The additive identity for rational numbers is:

  1. 0
  2. 1
  3. −1
  4. Any rational number
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Correct answer: A. 0

For any rational number a, a + 0 = 0 + a = a. **So 0 leaves every rational number unchanged under addition and is the additive identity.**

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More Mathematics topics

MathematicsStatistics and ProbabilityArithmetic ProgressionSets and RelationsQuadratic EquationsReal Numbers and PolynomialsUnit 6B: Definite Integration & Riemann SumsUnit 1B1: Limit Concepts and Graphical Limits