Identity and inverses

Identity and inverses Quiz

Spec DG5–DG6 · AQA A-Level Further Maths: Quiz

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5 questions, one answer each

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  1. 1. a∗b=a+b−5a*b=a+b-5 on R\mathbb{R}. Find the identity.

    • A. 00
    • B. −5-5
    • C. 1010
    • D. 55

  2. 2. a∗b=a+b−5a*b=a+b-5 on R\mathbb{R}. Find the inverse of 88.

    • A. 22
    • B. −8-8
    • C. 1313
    • D. 18\frac18

  3. 3. a∗b=2aba*b=2ab on the non-zero rationals. Find the identity.

    • A. 11
    • B. 12\frac12
    • C. 22
    • D. 00

  4. 4. Find the inverse of 44 in {1,2,…,10}\{1,2,\dots,10\} under multiplication modulo 1111.

    • A. 22
    • B. 55
    • C. 33
    • D. 77

  5. 5. Which is true for the non-negative integers {0,1,2,… }\{0,1,2,\dots\} under addition?

    • A. The identity is 00 and every element has an inverse.
    • B. The identity is 00 and only 00 has an inverse.
    • C. The identity is 11 and only 11 has an inverse.
    • D. There is no identity.

Quiz