Partial fractions

Partial fractions Quiz

Spec 2.10 · Edexcel A-Level Maths: Quiz

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  1. 1. Which is the correct form for 4x+1(x+3)(x−2)2\frac{4x+1}{(x+3)(x-2)^2}?

    • A. Ax+3+B(x−2)2\frac{A}{x+3}+\frac{B}{(x-2)^2}
    • B. Ax+3+Bx+C(x−2)2\frac{A}{x+3}+\frac{Bx+C}{(x-2)^2}
    • C. Ax+3+Bx−2+C(x−2)2\frac{A}{x+3}+\frac{B}{x-2}+\frac{C}{(x-2)^2}
    • D. Ax+3+Bx−2\frac{A}{x+3}+\frac{B}{x-2}

  2. 2. Find AA in x+7(x+1)(x+3)≡Ax+1+Bx+3\frac{x+7}{(x+1)(x+3)}\equiv\frac{A}{x+1}+\frac{B}{x+3}.

    • A. 33
    • B. −3-3
    • C. 66
    • D. 32\frac32

  3. 3. ∫32x+1 dx=\int\frac{3}{2x+1}\,dx=

    • A. 3ln⁡∣2x+1∣+c3\ln|2x+1|+c
    • B. 32ln⁡∣2x+1∣+c\frac32\ln|2x+1|+c
    • C. 6ln⁡∣2x+1∣+c6\ln|2x+1|+c
    • D. 32ln⁡∣x∣+c\frac{3}{2}\ln|x|+c

  4. 4. The expansion of 11+3x\frac{1}{1+3x} is valid for

    • A. ∣x∣<1|x|<1
    • B. ∣x∣<3|x|<3
    • C. ∣x∣<13|x|<\frac13
    • D. ∣x∣<12|x|<\frac12

  5. 5. If f(x)=2x+1+3x−2f(x)=\frac{2}{x+1}+\frac{3}{x-2}, then f′(x)=f'(x)=

    • A. −2(x+1)2−3(x−2)2-\frac{2}{(x+1)^2}-\frac{3}{(x-2)^2}
    • B. 2(x+1)2+3(x−2)2\frac{2}{(x+1)^2}+\frac{3}{(x-2)^2}
    • C. 2ln⁡∣x+1∣+3ln⁡∣x−2∣2\ln|x+1|+3\ln|x-2|
    • D. −2x+1−3x−2-\frac{2}{x+1}-\frac{3}{x-2}

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