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Worksheet: Evaluating Polynomials at Given Values

Q1:

Evaluate π‘₯ 𝑧 βˆ’ 3 𝑦 + 6 , given that π‘₯ = 5 , 𝑦 = 6 , and 𝑧 = 1 0 .

Q2:

Evaluate 5 𝑑 βˆ’ 2 𝑑 + 9 2 for 𝑑 = 3 .

Q3:

Evaluate 2 𝑑 βˆ’ 𝑑 βˆ’ 1 2 for 𝑑 = 6 .

Q4:

Evaluate 𝑧 + 4 𝑦 βˆ’ 1 2 , given that 𝑦 = 2 and 𝑧 = 4 .

Q5:

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

Q6:

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

Q7:

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

Q8:

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

Q9:

Given that π‘₯ = βˆ’ 1 3 , 𝑦 = βˆ’ 1 2 , and 𝑧 = 3 2 , find the numerical value of 6 π‘₯ 𝑦 𝑧 2 2 3 .

  • A 3 5 2 2
  • B 3 2
  • C βˆ’ 3 1 6
  • D 9 1 6
  • E 2 7 8

Q10:

Given that π‘₯ = 2 3 , 𝑦 = βˆ’ 3 2 , and 𝑧 = βˆ’ 2 3 , find the numerical value of 2 3 π‘₯ 𝑦 βˆ’ 𝑦 𝑧 βˆ’ 3 2 π‘₯ 𝑧 2 3 2 2 .

  • A βˆ’ 2 6 3
  • B βˆ’ 1
  • C βˆ’ 1 7 2 7
  • D 1 9
  • E 3 7 5 4

Q11:

Given that π‘₯ = 3 2 , 𝑦 = βˆ’ 1 2 , and 𝑧 = 1 3 , find the numerical value of 2 π‘₯ 𝑦 βˆ’ 2 𝑦 𝑧 βˆ’ 3 π‘₯ 𝑧 2 2 2 .

  • A βˆ’ 1 3
  • B βˆ’ 8 3
  • C 2 3 7 2
  • D 1 1 2
  • E βˆ’ 1 1 6

Q12:

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

Q13:

The distance, in feet, an object falls 𝑑 seconds after it is released is given by the expression 𝑔 𝑑 2 2 , where 𝑔 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 𝑔 = 3 2 feet per second squared.

Q14:

The expression 6 𝑠 2 can be used to determine the surface area of a cube, where 𝑠 is the edge length of the cube. Determine the surface area of a cube whose edge is 11 centimeters long.

Q15:

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

Q16:

A group of friends is planning to go to a concert, and the cost in dollars for 𝑛 tickets is 2 1 𝑛 . 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.

  • A$651, $945
  • B$35, $52
  • C$294, $434
  • D$294, $651
  • E$35, $45

Q17:

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

Q18:

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

Q19:

A company produces greetings cards with an initial cost of 2 000 LE and an extra cost of 1 2 L E per card. The total cost is given by 𝐢 = 1 2 π‘₯ + 2 0 0 0 , where π‘₯ is the number of produced cards. Find the total cost of producing 15 000 cards.

Q20:

If π‘₯ = βˆ’ 6 and 𝑦 = βˆ’ 1 , what is the value of π‘₯ βˆ’ 3 π‘₯ 𝑦 βˆ’ 1 0 𝑦 2 2 ?

Q21:

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

Q22:

If π‘₯ = 3 and 𝑦 = 5 , is 6 π‘₯ βˆ’ 𝑦 prime or composite?

  • Aprime
  • Bcomposite

Q23:

If 𝑝 = 6 and 𝑛 = βˆ’ 2 , evaluate 𝑝 𝑛 2 2 .

Q24:

Evaluate the following expression βˆ’ 𝑝 Γ· 𝑛 2 if 𝑝 = βˆ’ 8 and 𝑛 = 2 .