The diagram below shows a plan of the patio Eric wants to build.

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\includegraphics[max width=\textwidth, alt={}]{72bb1603-edbd-4e2e-bf2b-f33bb667e61b-2_517_746_1505_632}
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The walls $O A$ and $O C$ are perpendicular. The straight line $A B$ is of length 4 m and is perpendicular to $O A$. The shape $O B C$ is a sector of a circle with centre $O$ and radius OC.\\
The angle $B O C$ is $\frac { \pi } { 3 }$ radians. Calculate the area of the patio $O A B C$. Give your answer correct to 2 decimal places.

The sum to infinity of a geometric series with first term $a$ and common ratio $r$ is 120 . The sum to infinity of another geometric series with first term $a$ and common ratio $4 r ^ { 2 }$ is $112 \frac { 1 } { 2 }$. Find the possible values of $r$ and the corresponding values of $a$.

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0 & 5 \\
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The function $f ( x )$ is defined by

$$f ( x ) = \frac { 6 x + 4 } { ( x - 1 ) ( x + 1 ) ( 2 x + 3 ) }$$

a) Express $f ( x )$ in terms of partial fractions.\\
b) Find $\int \frac { 3 x + 2 } { ( x - 1 ) ( x + 1 ) ( 2 x + 3 ) } \mathrm { d } x$, giving your answer in the form $a \ln | g ( x ) |$, where $a$ is a real number and $g ( x )$ is a function of $x$.

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0 & 6 \\
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Geraint opens a savings account. He deposits $\pounds 10$ in the first month. In each subsequent month, the amount he deposits is 20 pence greater than the amount he deposited in the previous month.\\
a) Find the amount that Geraint deposits into the savings account in the 12th month.\\
b) Determine the number of months it takes for the total amount in the savings account to reach $\pounds 954$.\\
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0\\
The diagram below shows a sketch of the curves $y = x ^ { 2 }$ and $y = 8 \sqrt { x }$.\\
\includegraphics[max width=\textwidth, alt={}, center]{72bb1603-edbd-4e2e-bf2b-f33bb667e61b-3_508_869_2094_623}

Find the area of the region bounded by the two curves.

\hfill \mbox{\textit{WJEC Unit 3 2022 Q3}}