Edexcel AS Paper 1 Specimen — Question 5 5 marks

Exam BoardEdexcel
ModuleAS Paper 1 (AS Paper 1)
SessionSpecimen
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicIndefinite & Definite Integrals
TypeShow definite integral equals value
DifficultyModerate -0.3 This is a straightforward integration question requiring students to integrate a polynomial plus a power of x (x^{-2}), then substitute limits. The algebraic manipulation of the result involves surds but is routine. Slightly easier than average as it's a 'show that' question with a clear target and uses standard AS integration techniques.
Spec1.08b Integrate x^n: where n != -1 and sums1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)

Given that $$f(x) = 2x + 3 + \frac{12}{x^2}, \quad x > 0$$ show that \(\int_1^{2\sqrt{2}} f(x)\,dx = 16 + 3\sqrt{2}\) [5]

Question 5:
AnswerMarks Guidance
5f(x) = 2x + 3 + 12 x –2 B1
Attempts to integrateM1 1.1a
(cid:180)(cid:167) 12(cid:183) 12
(cid:181)(cid:168) (cid:14)2x(cid:14)3(cid:14) (cid:184) dx = x2 (cid:14)3x (cid:16)
AnswerMarks Guidance
(cid:182)(cid:169) x2 (cid:185) xA1 1.1b
(cid:167) 12( 2)(cid:183)
(cid:168)(2 2)2 (cid:14)3(2 2) (cid:16) (cid:184)(cid:16)(cid:11)(cid:16)8(cid:12)
(cid:168) (cid:184)
2(cid:117)2
AnswerMarks Guidance
(cid:169) (cid:185)M1 1.1b
(cid:32)16(cid:14)3 2*A1* 1.1b
(5 marks)
Notes:
B1: Correct function with numerical powers
M1: Allow for raising power by one. xn (cid:111)xn(cid:14)1
A1: Correct three terms
M1: Substitutes limits and rationalises denominator
A1*: Completely correct, no errors seen
AnswerMarks Guidance
QuestionScheme Marks
Question 5:
5 | f(x) = 2x + 3 + 12 x –2 | B1 | 1.1b
Attempts to integrate | M1 | 1.1a
(cid:180)(cid:167) 12(cid:183) 12
(cid:181)(cid:168) (cid:14)2x(cid:14)3(cid:14) (cid:184) dx = x2 (cid:14)3x (cid:16)
(cid:182)(cid:169) x2 (cid:185) x | A1 | 1.1b
(cid:167) 12( 2)(cid:183)
(cid:168)(2 2)2 (cid:14)3(2 2) (cid:16) (cid:184)(cid:16)(cid:11)(cid:16)8(cid:12)
(cid:168) (cid:184)
2(cid:117)2
(cid:169) (cid:185) | M1 | 1.1b
(cid:32)16(cid:14)3 2* | A1* | 1.1b
(5 marks)
Notes:
B1: Correct function with numerical powers
M1: Allow for raising power by one. xn (cid:111)xn(cid:14)1
A1: Correct three terms
M1: Substitutes limits and rationalises denominator
A1*: Completely correct, no errors seen
Question | Scheme | Marks | AOs
Given that
$$f(x) = 2x + 3 + \frac{12}{x^2}, \quad x > 0$$
show that $\int_1^{2\sqrt{2}} f(x)\,dx = 16 + 3\sqrt{2}$
[5]

\hfill \mbox{\textit{Edexcel AS Paper 1  Q5 [5]}}