Worksheet: Evaluating Polynomials at Given Values

In this worksheet, we will practice identifying and evaluating polynomials at given values using direct substitution.

Q1:

Evaluate ๐‘ฅ ๐‘ง โˆ’ 3 ๐‘ฆ + 6 , given that ๐‘ฅ = 5 , ๐‘ฆ = 6 , and ๐‘ง = 1 0 .

Q2:

Evaluate 5 ๐‘ก โˆ’ 2 ๐‘ก + 9 2 for ๐‘ก = 3 .

Q3:

Evaluate ๐‘ง + 4 ๐‘ฆ โˆ’ 1 2 , given that ๐‘ฆ = 2 and ๐‘ง = 4 .

Q4:

The expression 9 ๐ถ + 1 6 0 5 can be used to convert the temperature in degrees Celsius, ๐ถ , into degrees Fahrenheit. If a thermometer shows a temperature of 6 0 โˆ˜ C , determine the temperature in degrees Fahrenheit.

Q5:

The height of an object dropped from the top of a 150-foot-tall building can be described by the expression 1 5 0 โˆ’ 1 6 ๐‘ก ๏Šจ , where ๐‘ก is the time in seconds during which the object is falling. Determine the height of the object 2 seconds after it has been dropped.

Q6:

Given that ๐‘ฅ = โˆ’ 1 3 , ๐‘ฆ = โˆ’ 1 2 , and ๐‘ง = 3 2 , find the numerical value of 6 ๐‘ฅ ๐‘ฆ ๐‘ง 2 2 3 .

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

Q7:

Given that ๐‘ฅ = 2 3 , ๐‘ฆ = โˆ’ 3 2 , and ๐‘ง = โˆ’ 2 3 , find the numerical value of 2 3 ๐‘ฅ ๐‘ฆ โˆ’ ๐‘ฆ ๐‘ง โˆ’ 3 2 ๐‘ฅ ๐‘ง 2 3 2 2 .

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

Q8:

The cost, in dollars, of using the wireless internet at an airport is calculated using the expression 3 . 5 + ๐‘š 2 0 , where ๐‘š is the number of minutes spent online. How much will it cost to be online for 40 minutes?

Q9:

The distance, in feet, an object falls ๐‘ก seconds after it is released is given by the expression ๐‘” ๐‘ก 2 2 , where ๐‘” 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 ๐‘” = 3 2 feet per second squared.

Q10:

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.

Q11:

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.

Q12:

A group of friends is planning to go to a concert, and the cost in dollars for ๐‘› tickets is 2 1 ๐‘› . 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

Q13:

The surface area, ๐‘† , of a cube of edge ๐‘ฅ is given by ๐‘† = 6 ๐‘ฅ 2 . What is the surface area of a cube of edge 0.3 length units?

Q14:

Given that 2 7 ๐‘ฅ + 2 2 ๐‘ฆ = 1 4 , what is the value of 1 5 ๐‘ฅ + 1 6 ๐‘ฆ + 1 2 ๐‘ฅ + 6 ๐‘ฆ ?

Q15:

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 ๐ถ = 1 2 ๐‘ฅ + 2 , 0 0 0 , where ๐‘ฅ is the number of produced cards. Find the total cost of producing 15,000 cards.

Q16:

If ๐‘ฅ = โˆ’ 6 and ๐‘ฆ = โˆ’ 1 , what is the value of ๐‘ฅ โˆ’ 3 ๐‘ฅ ๐‘ฆ โˆ’ 1 0 ๐‘ฆ 2 2 ?

Q17:

A donut shop charges $4 to make a customized frosting and $4 for each donut with the same frosting. The expression 4 ๐‘› + 4 represents the cost of ๐‘› donuts with customized frosting. Determine the total cost of 8 of these donuts.

Q18:

If ๐‘ฅ = 3 and ๐‘ฆ = 5 , is 6 ๐‘ฅ โˆ’ ๐‘ฆ prime or composite?

  • Aprime
  • Bcomposite

Q19:

If ๐‘ = 6 and ๐‘› = โˆ’ 2 , evaluate ๐‘ ๐‘› 2 2 .

Q20:

Evaluate the following expression โˆ’ ๐‘ รท ๐‘› 2 if ๐‘ = โˆ’ 8 and ๐‘› = 2 .

Q21:

The expression 9 ๐ถ + 1 6 0 5 can be used to convert the temperature in degrees Celsius, ๐ถ , into degrees Fahrenheit. If a thermometer shows a temperature of 8 0 โˆ˜ C , determine the temperature in degrees Fahrenheit.

Q22:

The height of an object dropped from the top of a 350-foot-tall building can be described by the expression 3 5 0 โˆ’ 1 6 ๐‘ก ๏Šจ , where ๐‘ก is the time in seconds during which the object is falling. Determine the height of the object 4 seconds after it has been dropped.

Q23:

Evaluate 2 ๐‘ก โˆ’ ๐‘ก โˆ’ 1 2 for ๐‘ก = 6 .

Q24:

Given that ๐‘ฅ = 3 2 , ๐‘ฆ = โˆ’ 1 2 , and ๐‘ง = 1 3 , find the numerical value of 2 ๐‘ฅ ๐‘ฆ โˆ’ 2 ๐‘ฆ ๐‘ง โˆ’ 3 ๐‘ฅ ๐‘ง 2 2 2 .

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

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