AQA Further Paper 1 2020 June — Question 1 1 marks

Exam BoardAQA
ModuleFurther Paper 1 (Further Paper 1)
Year2020
SessionJune
Marks1
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndefinite & Definite Integrals
TypeImproper integral evaluation
DifficultyEasy -1.8 This is a pure recognition/definition question requiring students to identify which integral has no discontinuities or infinite limits. It tests only conceptual understanding of what makes an integral 'improper' with no calculation required—significantly easier than typical A-level questions.
Spec4.08c Improper integrals: infinite limits or discontinuous integrands
1 Which of the integrals below is not an improper integral?
Circle your answer. \(\int _ { 0 } ^ { \infty } e ^ { - x } d x\) \(\int _ { 0 } ^ { 2 } \frac { 1 } { 1 - x ^ { 2 } } \mathrm {~d} x\) \(\int _ { 0 } ^ { 1 } \sqrt { x } \mathrm {~d} x\) \(\int _ { 0 } ^ { 1 } \frac { 1 } { \sqrt { x } } \mathrm {~d} x\)
Question 1:
AnswerMarks Guidance
AnswerMarks Guidance
Circles \(\int_{0}^{1} \sqrt{x} \, dx\)B1 AO 2.2a
Total: 1 mark
## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| Circles $\int_{0}^{1} \sqrt{x} \, dx$ | B1 | AO 2.2a |

**Total: 1 mark**

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1 Which of the integrals below is not an improper integral?\\
Circle your answer.\\
$\int _ { 0 } ^ { \infty } e ^ { - x } d x$\\
$\int _ { 0 } ^ { 2 } \frac { 1 } { 1 - x ^ { 2 } } \mathrm {~d} x$\\
$\int _ { 0 } ^ { 1 } \sqrt { x } \mathrm {~d} x$\\
$\int _ { 0 } ^ { 1 } \frac { 1 } { \sqrt { x } } \mathrm {~d} x$

\hfill \mbox{\textit{AQA Further Paper 1 2020 Q1 [1]}}
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Q1 1 Q2 1 Q3 1 Q4 6 Q5 9 Q6 9 Q7 7 Q8 6 Q9 13 Q10 10 Q11 11 Q12 8 Q13 12 Q14 6