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{                                 Time (s)\par
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{33.}{\tab }\plain \f0
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{Create a factorable difference of squares. Factor your expression.}\plain \f0
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{               Cost to Produce Blankets\par
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{                              Number of Blankets}\plain \f0
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{\par
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{h}\plain \f0
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{ = \'96
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{ \'96
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{ + 17, \par
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{h}\plain \f0
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{ is the height of the soccer ball and }\plain \i \f0
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{x}\plain \f0
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{ is the distance the soccer ball is kicked. \par
}\plain \f0
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{Both distances are measured in metres. How far was the ball kicked?}\plain \f0
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{\par
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{45.}{\tab }\plain \f0
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{Two integers differ by 13 and the sum of their squares is 2197. Determine the in
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{\par
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{46.}{\tab }\plain \f0
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{Liz says that the greatest common factor of }\plain \i \f0
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{y}\plain \f0
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{ = \'96
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{x}\plain \super \f0
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{3}\plain \f0
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{ + 42}\plain \i \f0
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{2}\plain \f0
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{ \'96
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{x }\plain \f0
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{is 6}\plain \i \f0
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{x}\plain \f0
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{. \par
}\plain \f0
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\ql{Becky says that the greatest common factor is \'96
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{x}\plain \f0
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{. \par
}\plain \f0
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{Explain why both Liz and Becky are correct.}\plain \f0
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{\par
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{\par
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{\tab }\plain \f0
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{47.}{\tab }\plain \f0
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{A professional cliff diver\'92
s height above the water can be modelled by \par
}\plain \f0
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\pard
\widctlpar\keep\hyphpar0
\li0\ri0\fi0
\ql{the equation }\plain \i \f0
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{h}\plain \f0
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{ = \'96
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{t}\plain \super \f0
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{2}\plain \f0
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{ + 36, where }\plain \i \f0
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{h}\plain \f0
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{ is the diver\'92
s height in metres and \par
}\plain \f0
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\plain \i \f0
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{r}\plain \f0
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{ is the elapsed time in seconds.\par
}\plain \f0
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{a) Draw a height versus time graph.\par
}\plain \f0
\fs22
\cf1
{b) Determine the height of the cliff that the diver jumped from.\par
}\plain \f0
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\cf1
{c) Determine when the diver will enter the water. Explain.}\plain \f0
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{\par
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{\par
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{\tab }\plain \f0
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{48.}{\tab }\plain \f0
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{A tennis ball is thrown from the top of a building and falls to the ground below
. \par
}\plain \f0
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\pard
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\ql{The height of the ball above the ground is approximated by the relation \par
}\plain \f0
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\plain \i \f0
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{h}\plain \f0
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{ = \'96
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{t}\plain \super \f0
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{2}\plain \f0
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{ + 8}\plain \i \f0
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{t}\plain \f0
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{ + 32, where }\plain \i \f0
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{h}\plain \f0
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{ is the height above the ground in metres and \par
}\plain \f0
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\plain \i \f0
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{t}\plain \f0
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{ is the elapsed time in seconds. Determine the maximum height that is reached\par
}\plain \f0
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{by the ball. Explain.}\plain \f0
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{\par
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{\tab }\plain \f0
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{49.}{\tab }\plain \f0
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{The area of a rectangle is given by the relation }\plain \i \f0
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{A}\plain \f0
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{ = }\plain \i \f0
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{x}\plain \super \f0
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{2}\plain \f0
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{ + 7}\plain \i \f0
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{ \'96
 18. \par
}\plain \f0
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\ql{a) Determine the expressions for the possible dimensions of this rectangle. Expl
ain.\par
}\plain \f0
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{b) Determine the dimensions and area of this rectangle if }\plain \i \f0
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{x}\plain \f0
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{ = 3 cm. Explain.}\plain \f0
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{\par
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{\par
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{\tab }\plain \f0
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{50.}{\tab }\plain \f0
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{The area of a rectangle is given by the relation }\plain \i \f0
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{A}\plain \f0
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{ = 20}\plain \i \f0
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{x}\plain \super \f0
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{2}\plain \f0
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{ + 3}\plain \i \f0
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{ \'96
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}\plain \f0
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\ql{a) Determine the expressions for the possible dimensions of this rectangle. Expl
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}\plain \f0
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{b) Determine the dimensions and area of this rectangle if }\plain \i \f0
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{x}\plain \f0
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{ = 1 cm. Explain.}\plain \f0
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{\par
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{\tab }\plain \f0
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{51.}{\tab }\plain \f0
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{The area of a circle is given by the relation }\plain \i \f0
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{A}\plain \f0
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{ = }\plain \f3
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{p}\plain \i \f0
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{x}\plain \super \f0
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{2}\plain \f0
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{ + 6}\plain \f3
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{. \par
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\ql{a) Determine an expression for the radius of this circle. Explain.\par
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{b) Determine the radius and area of this circle if }\plain \i \f0
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{x}\plain \f0
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{ = 9 cm. Explain.}\plain \f0
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{\par
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{\tab }\plain \f0
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{52.}{\tab }\plain \f0
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{Anne kicked a soccer ball. The height of the ball, }\plain \i \f0
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{h}\plain \f0
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{, in metres, can be modelled \par
}\plain \f0
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{ = \'96
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{x}\plain \super \f0
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{2}\plain \f0
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{ + 12}\plain \i \f0
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{x}\plain \f0
\fs22
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{, where }\plain \i \f0
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{x}\plain \f0
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{ is the horizontal distance from where she kicked the ball.\par
}\plain \f0
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{a) What was the initial height of the ball when she kicked it? How do you know?\par
}\plain \f0
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{b) Complete the square to write the relation in vertex form.\par
}\plain \f0
\fs22
\cf1
{c) State the vertex of the relation.\par
}\plain \f0
\fs22
\cf1
{d) What does each coordinate of the vertex represent in this situation?\par
}\plain \f0
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{e) How far did Anne kick the ball?}\plain \f0
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{\par
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{\tab }\plain \f0
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{53.}{\tab }\plain \f0
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{Lily has just opened her own nail salon. Based on experience, \par
}\plain \f0
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{P}\plain \f0
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{, can be modelled by the relation \par
}\plain \f0
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\plain \i \f0
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{P}\plain \f0
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{ = \'96
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{x}\plain \super \f0
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{2}\plain \f0
\fs22
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{ + 168}\plain \i \f0
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{x}\plain \f0
\fs22
\cf1
{ \'96
 510, where }\plain \i \f0
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\cf1
{x}\plain \f0
\fs22
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{ is the number of clients per day. \par
}\plain \f0
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{How many clients should she book each day to maximize her profit? \par
}\plain \f0
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{Show your work.}\plain \f0
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{\par
}\plain \f0
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{\par
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{\tab }\plain \f0
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{54.}{\tab }\plain \f0
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{The cost, }\plain \i \f0
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{C}\plain \f0
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{, in dollars, to hire workers to build a new playground at a park \par
}\plain \f0
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{C}\plain \f0
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{ = 5}\plain \i \f0
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{x}\plain \super \f0
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{2}\plain \f0
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{ \'96
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{x}\plain \f0
\fs22
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{ + 700, where }\plain \i \f0
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{x}\plain \f0
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{ is the number of workers \par
}\plain \f0
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{hired to do the work. How many workers should be hired to minimize the cost? \par
}\plain \f0
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{Show your work.}\plain \f0
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\cf1
{\par
}\plain \f0
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\cf1
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{\par
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{\tab }\plain \f0
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{55.}{\tab }\plain \f0
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{A square lawn is surrounded by a concrete walkway that is 3.0 m wide.\par
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\ql{If the area of the walkway equals the area of the lawn, what are the \par
}\plain \f0
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{dimensions of the lawn? Express the dimensions to the nearest tenth of a metre. \par
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{Explain.}\plain \f0
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{\par
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{\tab }\plain \f0
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{56.}{\tab }\plain \f0
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{The height of a super ball, }\plain \i \f0
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{h}\plain \f0
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{, in metres, can be modelled \par
}\plain \f0
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{h}\plain \f0
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{ = \'96
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{t}\plain \super \f0
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{2}\plain \f0
\fs22
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{ + 7.42}\plain \i \f0
\fs22
\cf1
{t}\plain \f0
\fs22
\cf1
{ + 2.809, where }\plain \i \f0
\fs22
\cf1
{t}\plain \f0
\fs22
\cf1
{ is the time in seconds. \par
}\plain \f0
\fs22
\cf1
{How many times do you think the ball will pass through \par
}\plain \f0
\fs22
\cf1
{a height of 4 m and a height of 8 m? Explain.}\plain \f0
\fs2
\cf1
{\par
}\plain \f0
\fs2
\cf1
\pard
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{\par
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{57.}{\tab }\plain \f0
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{The height of a trampoline jumper, }\plain \i \f0
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\cf1
{h}\plain \f0
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{, in metres, can be modelled \par
}\plain \f0
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{ = \'96
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{t}\plain \super \f0
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{2}\plain \f0
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{ + 9.17}\plain \i \f0
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{t}\plain \f0
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{ + 1.997, where }\plain \i \f0
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{t}\plain \f0
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{ is the time in seconds. \par
}\plain \f0
\fs22
\cf1
{How many times do you think the ball will pass through \par
}\plain \f0
\fs22
\cf1
{a height of 3 m and a height of 5 m? Explain.}\plain \f0
\fs2
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{\par
}\plain \f0
\fs2
\cf1
\pard
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{\tab }\plain \f0
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{58.}{\tab }\plain \f0
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{Ashley went bungee jumping from a bridge last summer. \par
}\plain \f0
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\pard
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{the water, }\plain \i \f0
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\cf1
{h}\plain \f0
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{, in metres, was modelled by }\plain \i \f0
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{h}\plain \f0
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{ = \'96
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{t}\plain \super \f0
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{2}\plain \f0
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{ + 5}\plain \i \f0
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{t}\plain \f0
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{ + 203, \par
}\plain \f0
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{where }\plain \i \f0
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{t}\plain \f0
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{ is the time in seconds.\par
}\plain \f0
\fs22
\cf1
{a) How high above the water is the platform from \par
}\plain \f0
\fs22
\cf1
{which he jumped? Explain.\par
}\plain \f0
\fs22
\cf1
{b) Show that if his hair just touches the water on his first jump, \par
}\plain \f0
\fs22
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{the corresponding quadratic equation has two solutions. Explain what the solutio
ns mean.}\plain \f0
\fs2
\cf1
{\par
}\plain \f0
\fs2
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\pard
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{\par
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{\tab }\plain \f0
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{59.}{\tab }\plain \f0
\fs22
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{Water from a garden hose is sprayed on a plant that is growing up the side of a 
house.\par
}\plain \f0
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\cf1
\pard
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}\plain \f0
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{The equation }\plain \i \f0
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{H}\plain \f0
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{ = \'96
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{x}\plain \super \f0
\fs22
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{2}\plain \f0
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{ + 0.08}\plain \i \f0
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{x}\plain \f0
\fs22
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{ + 1.9 models the height of the jet of water, }\plain \i \f0
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{H}\plain \f0
\fs22
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{, \par
}\plain \f0
\fs22
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{and the horizontal distance it can travel from the nozzle, }\plain \i \f0
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{x}\plain \f0
\fs22
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{, both in metres. \par
}\plain \f0
\fs22
\cf1
{a) What is the maximum height that the water can reach? Explain.\par
}\plain \f0
\fs22
\cf1
{b) How far back could a gardener stand, but still have the water reach the windo
w? Explain.}\plain \f0
\fs2
\cf1
{\par
}\plain \f0
\fs2
\cf1
\pard
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{\par
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{\tab }\plain \f0
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{60.}{\tab }\plain \f0
\fs22
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{The cost, }\plain \i \f0
\fs22
\cf1
{C}\plain \f0
\fs22
\cf1
{, in dollars per hour, to run a machine can be modelled \par
}\plain \f0
\fs22
\cf1
\pard
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{C}\plain \f0
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{ = 0.03}\plain \i \f0
\fs22
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{x}\plain \super \f0
\fs22
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{2}\plain \f0
\fs22
\cf1
{ \'96
 2.4}\plain \i \f0
\fs22
\cf1
{x}\plain \f0
\fs22
\cf1
{ + 96.27, where }\plain \i \f0
\fs22
\cf1
{x}\plain \f0
\fs22
\cf1
{ is the minimum number of items \par
}\plain \f0
\fs22
\cf1
{produced per hour. \par
}\plain \f0
\fs22
\cf1
{a) How many items should be produced each hour to minimize the cost? Explain.\par
}\plain \f0
\fs22
\cf1
{b) What production rate will keep the cost below $55? Explain.\sect
\par
}\sectd\sbkpage
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{Lesson 4.11\par
}\plain \b \f0
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\cf1
{Answer Section}\plain \f0
\fs2
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{\par
}\plain \f0
\fs2
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{MULTIPLE CHOICE}\plain \f0
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{\par
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{\par
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{B\tab }\plain \f0
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{DIF:\tab }\plain \f0
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{Grade 10 Academic\tab }\plain \f0
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{\par
}\plain \f0
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\pard
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{REF:\tab }\plain \f0
\fs22
\cf1
{4.1 Common Factors in Polynomials\tab }\plain \f0
\fs22
\cf1
{\tab }\plain \f0
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{\tab }\plain \f0
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{\par
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{OBJ:\tab }\plain \f0
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{TOP:\tab }\plain \f0
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{Knowledge and Understanding\par
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{KEY:\tab }\plain \f0
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{factor}\plain \f0
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{\par
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{\tab }\plain \f0
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{DIF:\tab }\plain \f0
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{Grade 10 Academic\tab }\plain \f0
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{\par
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{REF:\tab }\plain \f0
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{4.1 Common Factors in Polynomials\tab }\plain \f0
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{\tab }\plain \f0
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{\tab }\plain \f0
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{\par
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{OBJ:\tab }\plain \f0
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{factor}\plain \f0
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{A\tab }\plain \f0
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{Grade 10 Academic\tab }\plain \f0
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{\par
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{REF:\tab }\plain \f0
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{4.2 Exploring the Factorization of Trinomials\tab }\plain \f0
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{\par
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{OBJ:\tab }\plain \f0
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{Grade 10 Academic\tab }\plain \f0
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{\par
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{REF:\tab }\plain \f0
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{4.3 Factoring Quadratics: x^2 + bx + c\tab }\plain \f0
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{\tab }\plain \f0
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{\par
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{OBJ:\tab }\plain \f0
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{Grade 10 Academic\tab }\plain \f0
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{\tab }\plain \f0
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{DIF:\tab }\plain \f0
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{\tab }\plain \f0
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{\par
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{Solve quadratic equations that have real roots, using a variety of methods (i.e.
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{Interpret real and non-real roots of quadratic equations, through investigation 
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{Interpret real and non-real roots of quadratic equations, through investigation 
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{Interpret real and non-real roots of quadratic equations, through investigation 
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{Each factor is a dimension for the rectangle. \par
}\plain \f0
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{Therefore, the dimensions of the rectangle are (}\plain \i \f0
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{ \'96
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{ + 9).\par
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{b) Substitute }\plain \i \f0
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{x}\plain \f0
\fs22
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{ = 3 into (}\plain \i \f0
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{x}\plain \f0
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{ \'96
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{ + 9).\par
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{ \'96
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{x}\plain \f0
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{ + 9 = 3 + 9\par
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{         = 1                                         = 12\par
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{Therefore, the dimensions of the rectangle are 1 cm by 12 cm and the area is \par
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{Each factor is a dimension for the rectangle. \par
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{Therefore, the dimensions of the rectangle are (4}\plain \i \f0
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{x}\plain \f0
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{ \'96
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{x}\plain \f0
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{ + 2).\par
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{b) Substitute }\plain \i \f0
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{x}\plain \f0
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{x}\plain \f0
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{4}\plain \i \f0
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{ \'96
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{x}\plain \f0
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{ + 2 = 5(1) + 2\par
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{        = 12                                              = }\plain \f3
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{                                                            {\dn1 {\pict \wmetafile8\picw0\pich0\picwgoal119\pichgoal209\picscalex100\picscaley100\picbmp\picbpp4
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{The solutions mean that Ashley\'92
s hair touches the water on his initial jump, as 
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m its graph (i.e., using graphing calculators or graphing software) or from its d
efining equation (i.e., by applying algebraic techniques). | Solve quadratic equa
tions that have real roots, using a variety of methods (i.e., factoring, using th
e quadratic formula, graphing). | Solve problems arising from a realistic situati
on represented by a graph or an equation of a quadratic relation, with and withou
t the use of technology.\par
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{TOP:\tab }\plain \f0
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{\par
}\plain \f0
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{MSC:\tab }\plain \f0
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{Problem Solving | Selecting Tools and Computational Strategies | Connecting | Co
mmunicating\par
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