Lesson H6
H6 Integration using partial fractions Quiz: AQA Maths, Unit 8
20 questions
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Lesson H6, Integration using partial fractions: 20 multiple choice questions for the AQA Maths (7357), Unit 8: Integration, written with Revision Ninja.
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The 20 questions
-
Which partial fraction form is correct for (px + q)/((x - a)(x - b)) when a and b are distinct?
- Ax/(x - a) + B
- A/(x - a) + B/(x - b)
- A/((x - a)(x - b))
- A/(x - a) + B/(x - a)^2
-
Write 1/((x - 1)(x + 2)) as A/(x - 1) + B/(x + 2). What is A?
- -1/2
- 1/3
- 1/2
- -1/3
-
Write 1/((x - 1)(x + 2)) as A/(x - 1) + B/(x + 2). What is B?
- 1/2
- -1/3
- -1/2
- 1/3
-
Which expression is an integral of 1/((x - 1)(x + 2)) with respect to x?
- -(1/3)ln|x - 1| - (1/3)ln|x + 2| + C
- ln|x - 1| - ln|x + 2| + C
- (1/3)ln|x - 1| + (1/3)ln|x + 2| + C
- (1/3)ln|x - 1| - (1/3)ln|x + 2| + C
-
Evaluate the integral from 2 to 3 of 1/((x - 1)(x + 2)) dx in exact form.
- (1/3) ln(8/5)
- ln(8/5)
- (1/3) ln 2
- (1/3) ln(5/8)
-
For (3x + 5)/((x + 1)(x + 2)) = A/(x + 1) + B/(x + 2), what is A?
- 2
- -2
- 1
- 3
-
For (5x - 1)/((x - 1)(x + 3)) = A/(x - 1) + B/(x + 3), what is B?
- -1
- 1
- -4
- 4
-
Which expression is an integral of 4/(x^2 - 4) with respect to x, for |x| > 2?
- ln|x^2 - 4| + C
- 4 ln|x| + C
- ln|(x + 2)/(x - 2)| + C
- ln|(x - 2)/(x + 2)| + C
-
Before splitting (x^2 + 1)/((x - 1)(x + 1)) into partial fractions, what step is needed first?
- Substitute x = 0 only
- Divide to write it as a polynomial plus a proper fraction
- Factorise the numerator
- Multiply top and bottom by x
-
Find B in 1/(x(x + 1)(x + 2)) = A/x + B/(x + 1) + C/(x + 2).
- 1
- -1/2
- -1
- 1/2
-
Evaluate the integral from 1 to 2 of 1/(x(x + 1)) dx in exact form.
- ln(2/3)
- ln 2
- ln(4/3)
- ln(3/4)
-
For (x + 7)/((x - 1)(x + 2)) = A/(x - 1) + B/(x + 2), what is A?
- 3
- 5/3
- 8/3
- -5/3
-
Which is an integral of (x + 7)/((x - 1)(x + 2)) with respect to x?
- (8/3)ln|x - 1| - (5/3)ln|x + 2| + C
- 8 ln|x - 1| - 5 ln|x + 2| + C
- (5/3)ln|x - 1| - (8/3)ln|x + 2| + C
- (8/3)ln|x - 1| + (5/3)ln|x + 2| + C
-
What is the main purpose of partial fractions in integration?
- To make the denominator equal to 1
- To write a rational function as a sum of simpler fractions that can each be integrated
- To evaluate the limit at infinity only
- To find the derivative of a rational function
-
Which is an integral of 1/(x^2 - 1) with respect to x, for |x| > 1?
- ln|(x - 1)/(x + 1)| + C
- (1/2)ln|x^2 - 1| + C
- (1/2)ln|(x - 1)/(x + 1)| + C
- (1/2)ln|(x + 1)/(x - 1)| + C
-
Evaluate the integral from 0 to 1 of 2/((x + 1)(x + 3)) dx in exact form.
- ln(3/2)
- ln 2
- ln(3/4)
- ln(2/3)
-
If (5x + 3)/((x - 3)(x + 1)) = A/(x - 3) + B/(x + 1), what is A + B?
- 4
- 5
- 6
- 5/2
-
For 2x/((x - 2)(x - 4)) = A/(x - 2) + B/(x - 4), what is A?
- -4
- 4
- 2
- -2
-
Which is an integral of (2x + 3)/(x^2 + 3x + 2) with respect to x, for x not equal to -1 or -2?
- ln|(x + 1)/(x + 2)| + C
- 2 ln|x + 1| + C
- (2x + 3)^2/2 + C
- ln|(x + 1)(x + 2)| + C
-
For (3x + 1)/((x - 2)(x + 1)) = A/(x - 2) + B/(x + 1), what is B?
- 2/3
- 7/3
- -7/3
- -2/3
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