OCR MEI C4 2012 June — Question 4 4 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Year2012
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicReciprocal Trig & Identities
TypeProve algebraic trigonometric identity
DifficultyModerate -0.5 This is a straightforward trigonometric identity proof requiring only basic manipulation of sec and cosec definitions. Students need to express everything in terms of sin and cos, find a common denominator, and apply the Pythagorean identity sin²θ + cos²θ = 1. It's slightly easier than average because it's a direct proof with a clear path and no problem-solving insight required, though worth 4 marks for showing all algebraic steps.
Spec1.05p Proof involving trig: functions and identities

Prove that \(\sec^2\theta + \cosec^2\theta = \sec^2\theta \cosec^2\theta\). [4]

Question 4:
AnswerMarks
4Age group 2010 2030 2050 2070
80+ 1
60–79 10
40–59 20
20–39 20
0–19 20

Total 71

As in Table 6, the figures are in millions.
AnswerMarks Guidance
Age group2010 2030
80+1
60–7910
40–5920
20–3920
0–1920
Total71
Question 4:
4 | Age group 2010 2030 2050 2070
80+ 1
60–79 10
40–59 20
20–39 20
0–19 20
Total 71
As in Table 6, the figures are in millions.
Age group | 2010 | 2030 | 2050 | 2070
80+ | 1
60–79 | 10
40–59 | 20
20–39 | 20
0–19 | 20
Total | 71
Prove that $\sec^2\theta + \cosec^2\theta = \sec^2\theta \cosec^2\theta$. [4]

\hfill \mbox{\textit{OCR MEI C4 2012 Q4 [4]}}