WJEC Further Unit 4 2022 June — Question 4 5 marks

Exam BoardWJEC
ModuleFurther Unit 4 (Further Unit 4)
Year2022
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVolumes of Revolution
TypeVolume with trigonometric functions
DifficultyStandard +0.3 This is a straightforward volume of revolution question about the y-axis using a standard formula. While it requires careful setup (recognizing x = sin y means the formula is π∫x² dy), the integration itself is routine (∫sin²y dy using the double angle formula). The calculation is mechanical with no conceptual challenges beyond applying the correct formula, making it slightly easier than average.
Spec4.08d Volumes of revolution: about x and y axes
The region \(R\) is bounded by the curve \(x = \sin y\), the \(y\)-axis and the lines \(y = 1\), \(y = 3\). Find the volume of the solid generated when \(R\) is rotated through four right angles about the \(y\)-axis. Give your answer correct to two decimal places. [5]
AnswerMarks Guidance
B1Correct notation required
Volume= \(\pi\int_1^3 \sin^2 y \, dy\)M1 Integrable form with no more than 1 slip
\(\pi\int_1^3 \frac{1-\cos 2y}{2} \, dy\)A1 oe cao
\(\pi\left[\frac{1}{2}y - \frac{1}{4}\sin 2y\right]_1^3\)m1 Attempt to substitute in correct limits
\(\pi\left[\left(\frac{3}{2} - \frac{1}{4}\sin 6\right) - \left(\frac{1}{2} - \frac{1}{4}\sin 2\right)\right]\)A1 cao
Volume = 4.08A1 cao 
| B1 | Correct notation required

Volume= $\pi\int_1^3 \sin^2 y \, dy$ | M1 | Integrable form with no more than 1 slip

$\pi\int_1^3 \frac{1-\cos 2y}{2} \, dy$ | A1 | oe cao

$\pi\left[\frac{1}{2}y - \frac{1}{4}\sin 2y\right]_1^3$ | m1 | Attempt to substitute in correct limits

$\pi\left[\left(\frac{3}{2} - \frac{1}{4}\sin 6\right) - \left(\frac{1}{2} - \frac{1}{4}\sin 2\right)\right]$ | A1 | cao

Volume = 4.08 | A1 | cao

---
The region $R$ is bounded by the curve $x = \sin y$, the $y$-axis and the lines $y = 1$, $y = 3$. Find the volume of the solid generated when $R$ is rotated through four right angles about the $y$-axis. Give your answer correct to two decimal places. [5]

\hfill \mbox{\textit{WJEC Further Unit 4 2022 Q4 [5]}}
This paper (14 questions)
View full paper
Q1 8 Q2 4 Q3 9 Q4 5 Q5 5 Q6 6 Q7 8 Q8 6 Q9 12 Q10 9 Q11 15 Q12 12 Q13 11 Q14 10