IB Maths AI HL Sl 5 7 Optimization Questions

width of the square is $70-x \quad \mathbf{OR}$ the length of the square is $\frac{-x^{2}}{50}+2 x+30$
(M1)
Note: Award (M1) for 70-x seen anywhere. Accept $\frac{-x^{2}}{50}+2 x+30$ but only if this expression is explicitly identified as a dimension of the square.
in term of x, equating the length to the width ED
$\frac{-x^{2}}{50}+2 x+30=70-x$
( $x=14.7920 \ldots$ or 135.21)
$(x=) 14.8 \mathrm{~m}(14.7920 \ldots)$

Note: Award MOMOAO for an unsupported answer of 15. Award at most M1M0A0 for an approach which leads to $A^{\prime}(x)=0$. This will lead to a square base which extends beyond the east boundary of the property. Similar for any solution where F is not on the northern boundary, or GH is not on the east boundary.

EITHER
$(70-14.7920 \ldots)^{2}$

OR
$(55.2079 \ldots)^{2}$

OR
$\left(\frac{-(14.7920 \ldots)^{2}}{50}+2(14.7920 \ldots)+30\right)^{2}$

THEN
(Area = ) $3050 \mathrm{~m}^{2}$ (3047.92…)

Note: Follow through from part (d)(i), provided x is between 0 and 70 . Award at most M1A0 if their answer is outside the range of their [0, 4713.33...] from part (b).