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1. Evaluating a function by substitution ●○○○○ 10 ptsIf $g(2x - 5) = 3x + 9$ for all real $x$, find $g(1)$.
2. Maximum burning time of a candle ●○○○○ 10 ptsA candle with an original length of $12\ \text{cm}$ burns so that its remaining length depends on the burning time as shown in the table below: | Burning time (minutes) | $10$ | $20$ | $30$ | $40$ | $50$ | $\ldots$ | |---|---|---|---|---|---|---| | Remaining length (cm) | $11.2$ | $10.4$ | $9.6$ | $8.8$ | $8$ | $\ldots$ | Assuming the remaining length decreases linearly with burning time, find the maximum number of minutes the candle can burn.
3. Linear function avoiding the second quadrant ●●○○○ 20 ptsTwo different numbers are chosen from $-2,-1,1,2,3$, the first as $k$ and the second as $b$, to form the linear function $y=kx+b$. Find the probability that the resulting line does not pass through the second quadrant. Give your answer as a decimal.
4. Input value of a linear function ●●○○○ 20 ptsGiven that $f\left(\frac{x}{2} - 1\right) = 2x + 3$ for all $x$, and $f(m) = 6$, find the value of $m$. Give your answer as a decimal.