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.

  • A7โˆ’โˆš10
  • Bโˆ’21
  • C7โˆ’โˆš7
  • Dโˆ’3
  • E7+โˆš10

Q3:

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

Make ๐‘Ÿ the subject.

  • A๐‘Ÿ=๏„ž3๐‘‰4๐œ‹๏Žข
  • B๐‘Ÿ=๏„ž3๐‘‰4๐œ‹
  • C๐‘Ÿ=3๐‘‰4๐œ‹
  • D๐‘Ÿ=๏„ž4๐œ‹๐‘‰3๏Žข
  • E๐‘Ÿ=๏„ž4๐‘‰3๐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.

  • A502227
  • Bโˆ’167681
  • C84
  • Dโˆ’502227
  • E167681

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.

  • Aโˆ’25
  • Bโˆ’59
  • Cโˆ’19
  • D29
  • Eโˆ’23

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.

  • A2494
  • B1232
  • C14
  • D2814

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?

  • A๐‘ฅโˆ’๐‘ฆ๏Šจ
  • B๐‘ฅ+๐‘ฆ๏Šจ๏Šจ
  • C๐‘ฅ+๐‘ฆ๏Šจ
  • D๐‘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.

  • A116
  • B16
  • C12
  • D2

Q16:

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

  • Aโˆ’118
  • B32
  • Cโˆ’4736
  • Dโˆ’518
  • E76

Q17:

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

  • A3625
  • B56
  • C2536
  • D1

Q18:

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

  • Aโˆ’114
  • Bโˆ’34
  • C114
  • Dโˆ’12
  • E34

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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