Inequalities with polynomials and rational expressions

Inequalities with polynomials and rational expressions Quiz

Spec D8–D9 · AQA A-Level Further Maths: Quiz

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5 questions, one answer each

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  1. 1. Solve (x−1)(x+2)(x−3)>0(x-1)(x+2)(x-3)>0.

    • A. x<−2x<-2 or 1<x<31<x<3
    • B. −2<x<1-2<x<1 or x>3x>3
    • C. x<−2x<-2 or x>3x>3
    • D. −2<x<3-2<x<3

  2. 2. Solve (x−2)2(x+1)≥0(x-2)^2(x+1)\ge0.

    • A. x>−1x>-1
    • B. x≥−1x\ge-1
    • C. x≥−1x\ge-1, x≠2x\ne2
    • D. x≤−1x\le-1

  3. 3. Solve ∣x−1∣<2x|x-1|<2x.

    • A. x>1x>1
    • B. −1<x<13-1<x<\frac13
    • C. x>0x>0
    • D. x>13x>\frac13

  4. 4. Solve x4−1≤0x^4-1\le0.

    • A. −1≤x≤1-1\le x\le1
    • B. x≤−1x\le-1 or x≥1x\ge1
    • C. −1<x<1-1<x<1
    • D. x≤1x\le1

  5. 5. Why must you be careful multiplying an inequality by x−1x-1?

    • A. it creates extra roots
    • B. its sign may be negative, which reverses the inequality
    • C. it is never allowed
    • D. it changes a strict inequality to a non-strict one

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