Worksheet: Evaluating Higher-Degree Algebraic Expressions

In this worksheet, we will practice evaluating algebraic expressions of more than one degree with one or multiple variables and applying this in real-world problems.

Q1:

Find the value of (๐‘Žโˆ’๐‘)๏Šจ given ๐‘Ž=389 and ๐‘=โˆ’79.

Q2:

Given that ๐‘Ž=โˆš5 and ๐‘=โˆš2, find the value of ๐‘+๐‘Ž๐‘+๐‘Ž๏Šฉ๏Šฉ.

  • A 7 โˆ’ โˆš 1 0
  • B โˆ’ 2 1
  • C 7 โˆ’ โˆš 7
  • D โˆ’ 3
  • E 7 + โˆš 1 0

Q3:

The formula to calculate the volume of a sphere is ๐‘‰=43๐œ‹๐‘Ÿ๏Šฉ.

Make ๐‘Ÿ the subject.

  • A ๐‘Ÿ = ๏„ž 3 ๐‘‰ 4 ๐œ‹ ๏Žข
  • B ๐‘Ÿ = ๏„ž 3 ๐‘‰ 4 ๐œ‹
  • C ๐‘Ÿ = 3 ๐‘‰ 4 ๐œ‹
  • D ๐‘Ÿ = ๏„ž 4 ๐œ‹ ๐‘‰ 3 ๏Žข
  • E ๐‘Ÿ = ๏„ž 4 ๐‘‰ 3 ๐œ‹ ๏Žข

Find the radius of a sphere with a volume of 900 cubic centimeters. Give your answer accurate to two decimal places.

Q4:

Evaluate (3๐‘ก+8)รท2๏Šจ for ๐‘ก=โˆ’2.

Q5:

Given that ๐‘=213, ๐‘=โˆ’223, and ๐‘‘=412, evaluate ๏€ผโˆ’13๐‘๏ˆโ‹…3๐‘๐‘‘๏Šฉ.

  • A 5 0 2 2 2 7
  • B โˆ’ 1 6 7 6 8 1
  • C84
  • D โˆ’ 5 0 2 2 2 7
  • E 1 6 7 6 8 1

Q6:

Given that ๐‘=๐‘š(1+๐‘Ÿ)๏Š, find ๐‘ when ๐‘š=7.4ร—10๏Šฉ, ๐‘Ÿ=5.8ร—10๏Šฑ๏Šฉ, and ๐‘›=6.

Q7:

Given that ๐‘ฅ=12,๐‘ฆ=โˆ’23, and ๐‘ง=โˆ’13, find the numerical value of ๐‘ฅ๐‘ฆ๐‘ฆ+๐‘ง๏Šจ๏Šจ.

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

Q8:

Given that ๐‘ฅ=8(5+9)โˆ’6 and ๐‘ฆ=(7ร—2)โˆ’9๏Šจ๏Šจ, evaluate (๐‘ฅโˆ’๐‘ฆ)โˆ’7๏Šจ๏Šจ.

Q9:

Given that ๐‘š+1๐‘š=โˆ’6, what is the value of ๐‘š+1๐‘š๏Šจ๏Šจ?

Q10:

Given that ๐‘Ž=โˆ’4, ๐‘=12, and ๐‘=โˆ’5, determine the numerical value of the expression ๐‘Ž๐‘+๐‘๐‘+6๐‘Ž๐‘๐‘๏Šจ๏Šจ๏Šจ๏Šจ.

  • A 2 4 9 4
  • B 1 2 3 2
  • C 1 4
  • D 2 8 1 4

Q11:

Evaluate ๐‘Žร—๐‘๏Šจ๏Šฉ, given that ๐‘Ž=4 and ๐‘=3.

Q12:

Given that ๐‘Ž=โˆ’5๐‘ฅ+2, ๐‘=๐‘ฅ+2, and ๐‘=2๐‘ฅโˆ’4, evaluate ๐‘Ž๐‘โˆ’๐‘๏Šจ when ๐‘ฅ=0.

Q13:

Given that ๐‘ฅ=2 and ๐‘ฆ=โˆ’5, which of the following choices is a negative number?

  • A ๐‘ฅ โˆ’ ๐‘ฆ ๏Šจ
  • B ๐‘ฅ + ๐‘ฆ ๏Šจ ๏Šจ
  • C ๐‘ฅ + ๐‘ฆ ๏Šจ
  • D ๐‘ฅ + ๐‘ฆ ๏Šจ

Q14:

Given that ๐‘ฆ=2๏Šฉ and ๐‘š=3๏Šจ, find the value of (๐‘ฆโˆ’๐‘š)๏Šฉ.

Q15:

Given that ๐‘Ž=43 and ๐‘=23, evaluate ๏€ป๐‘Ž๐‘๏‡๏Šช.

  • A 1 1 6
  • B16
  • C 1 2
  • D2

Q16:

Given that ๐‘Ž=1โˆš3 and ๐‘=โˆ’3, find the value of 4๐‘Žโˆ’(3โˆ’๐‘)๏Šจ๏Šฑ๏Šง.

  • A โˆ’ 1 1 8
  • B 3 2
  • C โˆ’ 4 7 3 6
  • D โˆ’ 5 1 8
  • E 7 6

Q17:

If ๐‘Ž=โˆ’๐‘ and ๐‘Ž=1, what is the value of ๏€ผ56๏ˆ๏Œบ๏Šฑ๏Œป?

  • A1
  • B 2 5 3 6
  • C 3 6 2 5
  • D 5 6

Q18:

Evaluate 15๐‘“๐‘”๏Šจ for ๐‘“=112 and ๐‘”=โˆ’123.

  • A โˆ’ 1 1 4
  • B โˆ’ 3 4
  • C 1 1 4
  • D โˆ’ 1 2
  • E 3 4

Q19:

Given that ๐‘ฅ=13 and ๐‘ฆ=20, evaluate (๐‘ฆโˆ’๐‘ฅ)+3๏Šจ.

Q20:

The height of an object dropped from the top of a 150-foot-tall building can be described by the expression 150โˆ’16๐‘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.

Q21:

The distance, in feet, an object falls ๐‘ก seconds after it is released is given by the expression ๐‘”๐‘ก2๏Šจ, 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‘”=32 feet per second squared.

Q22:

The expression 6๐‘ ๏Šจ can be used to determine the surface area of a cube, where ๐‘  is the edge length of the cube. Determine the surface area of a cube whose edge is 11 centimeters long.

Q23:

Evaluate 5๐‘กโˆ’2๐‘ก+9๏Šจ for ๐‘ก=3.

Q24:

The surface area, ๐‘†, of a cube of edge ๐‘ฅ is given by ๐‘†=6๐‘ฅ๏Šจ. What is the surface area of a cube of edge 9 length units?

Q25:

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

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