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In this lesson, we will learn how to identify and evaluate polynomials at given values using direct substitution.

Q1:

The cost, in dollars, of using the wireless internet at an airport is calculated using the expression 3 . 5 + π 2 0 , where π is the number of minutes spent online. How much will it cost to be online for 40 minutes?

Q2:

The expression 9 πΆ + 1 6 0 5 can be used to convert the temperature in degrees Celsius, πΆ , into degrees Fahrenheit. If a thermometer shows a temperature of 6 0 β C , determine the temperature in degrees Fahrenheit.

Q3:

The expression 9 πΆ + 1 6 0 5 can be used to convert the temperature in degrees Celsius, πΆ , into degrees Fahrenheit. If a thermometer shows a temperature of 8 0 β C , determine the temperature in degrees Fahrenheit.

Q4:

The height of an object dropped from the top of a 150-foot-tall building can be described by the expression 1 5 0 β 1 6 π‘ 2 , where π‘ is the time in seconds during which the object is falling. Determine the height of the object 2 seconds after it has been dropped.

Q5:

The height of an object dropped from the top of a 350-foot-tall building can be described by the expression 3 5 0 β 1 6 π‘ 2 , where π‘ is the time in seconds during which the object is falling. Determine the height of the object 4 seconds after it has been dropped.

Q6:

The distance, in feet, an object falls π‘ seconds after it is released is given by the expression π π‘ 2 2 , where π is the acceleration due to gravity. Determine how many feet a stone will fall 5 seconds after it is released from the top of a cliff. Assume π = 3 2 feet per second squared.

Q7:

The expression can be used to determine the surface area of a cube, where is the edge length of the cube. Determine the surface area of a cube whose edge is 11 centimetres long.

Q8:

Fares intends to buy 8 coins to add to his collection. Older coins are $7 each, while newer ones are $3 each. If of the 8 coins he buys are old, the total cost, in dollars, is . Evaluate the expression to find the total cost if he buys 4 old coins.

Q9:

A group of friends is planning to go to a concert, and the cost in dollars for π tickets is 2 1 π . Given that as few as 14 people or as many as 31 people might go, find the minimum and maximum costs that the group of friends might pay.

Q10:

Evaluate 5 π‘ β 2 π‘ + 9 2 for π‘ = 3 .

Q11:

Evaluate 2 π‘ β π‘ β 1 2 for π‘ = 6 .

Q12:

The surface area, π , of a cube of edge π₯ is given by π = 6 π₯ 2 . What is the surface area of a cube of edge 0.3 length units?

Q13:

Given that 2 7 π₯ + 2 2 π¦ = 1 4 , what is the value of 1 5 π₯ + 1 6 π¦ + 1 2 π₯ + 6 π¦ ?

Q14:

If π = 6 and π = β 2 , evaluate π π 2 2 .

Q15:

If π₯ = 3 and π¦ = 5 , is 6 π₯ β π¦ prime or composite?

Q16:

A company produces greetings cards with an initial cost of 2β000 LE and an extra cost of 1 2 L E per card. The total cost is given by πΆ = 1 2 π₯ + 2 0 0 0 , where π₯ is the number of produced cards. Find the total cost of producing 15β000 cards.

Q17:

Given that π₯ = β 1 3 , π¦ = β 1 2 , and π§ = 3 2 , find the numerical value of 6 π₯ π¦ π§ 2 2 3 .

Q18:

Evaluate the following expression β π Γ· π 2 if π = β 8 and π = 2 .

Q19:

Given that π₯ = 2 3 , π¦ = β 3 2 , and π§ = β 2 3 , find the numerical value of 2 3 π₯ π¦ β π¦ π§ β 3 2 π₯ π§ 2 3 2 2 .

Q20:

Given that π₯ = 3 2 , π¦ = β 1 2 , and π§ = 1 3 , find the numerical value of 2 π₯ π¦ β 2 π¦ π§ β 3 π₯ π§ 2 2 2 .

Q21:

Evaluate π₯ π§ β 3 π¦ + 6 , given that π₯ = 5 , π¦ = 6 , and π§ = 1 0 .

Q22:

If π₯ = β 6 and π¦ = β 1 , what is the value of π₯ β 3 π₯ π¦ β 1 0 π¦ 2 2 ?

Q23:

Evaluate π§ + 4 π¦ β 1 2 , given that π¦ = 2 and π§ = 4 .

Q24:

A donut shop charges $4 to make a customized frosting and $4 for each donut with the same frosting. The expression 4 π + 4 represents the cost of π donuts with customized frosting. Determine the total cost of 8 of these donuts.

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