10th Class Mathematics Test Unit 4 - Partial Fractions

Unit 4 – Partial Fractions

Quiz

 

1. 1. What is the purpose of partial fraction decomposition?
   1.   To simplify complex numbers
   2.   To split a rational expression into simpler fractions
   3.   To factorize polynomials
   4.   To solve quadratic equations
2. 2. A proper rational function is defined as:
   1.   Degree of numerator is less than the degree of denominator
   2.   Degree of numerator is greater than the degree of denominator
   3.   Degree of numerator is equal to the degree of denominator
   4.   None of the above
3. 3. If the degree of the numerator is greater than or equal to the degree of the denominator, the first step is to:
   1.   Factorize the denominator
   2.   Divide the numerator by the denominator
   3.   Apply partial fraction directly
   4.   Multiply by a constant
4. 4. For the partial fraction decomposition of P(x)Q(x)\frac{P(x)}{Q(x)}Q(x)P(x), Q(x)Q(x)Q(x) must be:
   1.   ) A polynomial of lower degree than P(x)P(x)P(x)
   2.   A polynomial of higher degree than P(x)P(x)P(x)
   3.   A factorizable polynomial
   4.   A constant
5. 5. If Q(x)Q(x)Q(x) contains non-repeated linear factors, the partial fraction decomposition takes the form:
   1.   A(x−a)+B(x−b)\frac{A}{(x-a)} + \frac{B}{(x-b)}(x−a)A+(x−b)B
   2.   A(x−a)2+B(x−a)\frac{A}{(x-a)^2} + \frac{B}{(x-a)}(x−a)2A+(x−a)B
   3.   Ax+B(x2−a)\frac{Ax+B}{(x^2-a)}(x2−a)Ax+B
   4.   None of the above
6. 6. For repeated linear factors, such as (x−a)2(x-a)^2(x−a)2, the partial fraction decomposition is:
   1.   Ax−a+B(x−a)2\frac{A}{x-a} + \frac{B}{(x-a)^2}x−aA+(x−a)2B
   2.   Ax−a+Bx+a\frac{A}{x-a} + \frac{B}{x+a}x−aA+x+aB
   3.   Ax+B(x−a)2\frac{Ax+B}{(x-a)^2}(x−a)2Ax+B
   4.   None of the above
7. 7. If Q(x)Q(x)Q(x) contains an irreducible quadratic factor, the partial fraction decomposition involves:
   1.   A constant numerator
   2.   A linear numerator
   3.   A quadratic numerator
   4.   A cubic numerator
8. 8. In the decomposition of 1(x−1)(x−2)\frac{1}{(x-1)(x-2)}(x−1)(x−2)1, the partial fractions are:
   1.   1x−1+1x−2\frac{1}{x-1} + \frac{1}{x-2}x−11+x−21
   2.   Ax−1+Bx−2\frac{A}{x-1} + \frac{B}{x-2}x−1A+x−2B
   3.   A(x−1)2+B(x−2)2\frac{A}{(x-1)^2} + \frac{B}{(x-2)^2}(x−1)2A+(x−2)2B
   4.   None of the above
9. 9. For the decomposition of 1(x−1)2\frac{1}{(x-1)^2}(x−1)21, the partial fractions are:
   1.   Ax−1+B(x−1)2\frac{A}{x-1} + \frac{B}{(x-1)^2}x−1A+(x−1)2B
   2.   Ax−1\frac{A}{x-1}x−1A
   3.   B(x−1)2\frac{B}{(x-1)^2}(x−1)2B
   4.   Ax−1−B(x−1)2\frac{A}{x-1} - \frac{B}{(x-1)^2}x−1A−(x−1)2B
10. 10. The partial fraction decomposition of 5x+7(x−1)(x+2)\frac{5x+7}{(x-1)(x+2)}(x−1)(x+2)5x+7 takes the form:
    1.   Ax−1+Bx+2\frac{A}{x-1} + \frac{B}{x+2}x−1A+x+2B
    2.   Ax+2+Bx−1\frac{A}{x+2} + \frac{B}{x-1}x+2A+x−1B
    3.   Ax+Bx−1\frac{Ax+B}{x-1}x−1Ax+B
    4.   None of the above