AP EAPCET (Engineering) Algebra: Partial Fractions — practice questions
47 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP EAPCET (Engineering) Algebra: Partial Fractions in the app →Which of these is a proper rational fraction?Which sum equals 1/((x-1)(x-2))?Find the partial fractions of (3x+5)/((x+1)(x+2)).Express 1/(x(x+1)) as a difference of two simple fractions.For (x+1)/(x-2)^2 split as A/(x-2) + B/(x-2)^2, B equalsWhich template fits (x+2)/((x+1)(x^2+1))?Choose the correct form for 1/(x^2(x-1)).Divide and decompose (x^2+1)/(x-1).What is the polynomial part of x^3/(x^2-1)?Which quadratic is irreducible over the real numbers?Count the constants for three distinct linear factors, as in 1/((x-1)(x-2)(x-3)).2x/(x^2-1) is identical to which sum?For (5x-1)/((x-1)(x+1)) written as A/(x-1) + B/(x+1), the value of B isIntegrating 1/(x(x+1)) with respect to x givesFind the value of the integral of 1/((x-1)(x-2)) dx.Which expression equals (x^2+1)/(x^2-1) after splitting?With x/((x-1)(x-2)) split as A/(x-1) + B/(x-2), the sum A + B isThe term in 1/x in the split of 1/(x^3-x) has coefficientFor a nonzero constant a, 1/(x^2-a^2) has coefficient of 1/(x-a) equal toWhich difference of simple fractions equals 3/((x+1)(x+4))?For 1/((x-1)(x-2)(x-3)), the middle fraction has numeratorAdding 1/(1x2) + 1/(2x3) + 1/(3x4) + ... without end givesA partial sum of the first N terms of 1/(n(n+1)) equalsSumming 1/(n(n+2)) over all positive integers n givesHow many constants does (x^2+1)/(x-1)^3 need in its decomposition?The constant A when 1/((x-1)(x^2+x+1)) is split with a quadratic term isIf (3x+5)/(1-2x)^2 = A/(1-2x)^2 + B/(1-2x), find A.Partial fraction decomposition expresses a rational fraction as aEach denominator in a partial fraction decomposition is a power ofWhat is the first step for an improper rational fraction?Over the complex numbers, every irreducible denominator factor has degreeOver the real numbers, irreducible factors in denominators can beEuclidean division of numerator by denominator yields which part?In symbolic integration, the sum whose antiderivative is a combination of logarithms is called thePartial fractions help invert which transform of rational functions?If (x-a)^3 divides the denominator exactly, how many terms involve powers of (x-a)?In the residue method, the coefficient of 1/(x - xi) is called theWhat is the discriminant of x^2 - 4x + 8?Multiplying a decomposition through by the common denominator givesEquating coefficients to find the constants is a variant of the method ofSplitting a fraction with coprime denominator factors relies on which identity?The first derivative at x = a of (x-a)^2 p(x) equalsWhich fraction needs long division before it can be decomposed?Real-variable integral calculus uses partial fractions to find antiderivatives ofx/((x+1)(x+2)) breaks into which pair of fractions?Which pair of fractions adds up to (2x+1)/(x^2+x-2)?How many constants split 1/((x-1)^2 (x+2))?