Worksheet: Evaluating Algebraic Expressions of More Than One Degree

In this worksheet, we will practice evaluating algebraic expressions given integer and fractional inputs.

Q1:

If โˆ’ 6 ๐‘ฅ = 2 4 , what is the value of 6 ๐‘ฅ โˆ’ 1 ?

Q2:

Evaluate โˆ’ 5 ( ๐‘‘ โˆ’ 7 ) when ๐‘‘ = โˆ’ 3 .

Q3:

Find the value of ( ๐‘Ž โˆ’ ๐‘ ) ๏Šจ given ๐‘Ž = 3 8 9 and ๐‘ = โˆ’ 7 9 .

Q4:

Given that ๐‘Ž = โˆš 5 and ๐‘ = โˆš 2 , find the value of ๐‘ + ๐‘Ž ๐‘ + ๐‘Ž ๏Šฉ ๏Šฉ .

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

Q5:

The formula to calculate the volume of a sphere is ๐‘‰ = 4 3 ๐œ‹ ๐‘Ÿ 3 .

Make ๐‘Ÿ the subject.

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

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

Q6:

Evaluate ( 3 ๐‘ก + 8 ) รท 2 ๏Šจ for ๐‘ก = โˆ’ 2 .

Q7:

Given that ๐‘ = 2 1 3 , ๐‘ = โˆ’ 2 2 3 , and ๐‘‘ = 4 1 2 , evaluate ๏€ผ โˆ’ 1 3 ๐‘ ๏ˆ โ‹… 3 ๐‘ ๐‘‘ ๏Šฉ .

  • A 5 0 2 2 2 7
  • B โˆ’ 1 6 7 6 8 1
  • C โˆ’ 5 0 2 2 2 7
  • D 1 6 7 6 8 1
  • E84

Q8:

Given that ๐‘ = ๐‘š ( 1 + ๐‘Ÿ ) ๏Š , find ๐‘ when ๐‘š = 7 . 4 ร— 1 0 ๏Šฉ , ๐‘Ÿ = 5 . 8 ร— 1 0 ๏Šฑ ๏Šฉ , and ๐‘› = 6 .

Q9:

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

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

Q10:

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

Q11:

Given that ๐‘š + 1 ๐‘š = โˆ’ 6 , what is the value of ๐‘š + 1 ๐‘š ๏Šจ ๏Šจ ?

Q12:

Find the value of ( ๐‘ฅ + ๐‘ง ) รท ( ๐‘ฆ โˆ’ ๐‘ง ) given ๐‘ฅ = โˆ’ 5 2 , ๐‘ฆ = โˆ’ 7 6 , and ๐‘ง = 1 .

  • A 3 2
  • B 3 1 3
  • C 3 7
  • D 9 1 3

Q13:

Given that , , and , determine the numerical value of the expression .

  • A
  • B
  • C
  • D

Q14:

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

Q15:

Given that ๐‘Ž = โˆ’ 5 ๐‘ฅ + 2 , ๐‘ = ๐‘ฅ + 2 , and ๐‘ = 2 ๐‘ฅ โˆ’ 4 , evaluate ๐‘Ž ๐‘ โˆ’ ๐‘ ๏Šจ when ๐‘ฅ = 0 .

Q16:

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

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

Q17:

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

Q18:

Given that ๐‘Ž = 4 3 and ๐‘ = 2 3 , evaluate ๏€ป ๐‘Ž ๐‘ ๏‡ ๏Šช .

  • A2
  • B 1 1 6
  • C 1 2
  • D16

Q19:

Given that ๐‘Ž = 1 โˆš 3 and ๐‘ = โˆ’ 3 , find the value of 4 ๐‘Ž โˆ’ ( 3 โˆ’ ๐‘ ) ๏Šจ ๏Šฑ ๏Šง .

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

Q20:

If ๐‘Ž = โˆ’ ๐‘ and ๐‘Ž = 1 , what is the value of ๏€ผ 5 6 ๏ˆ ๏Œบ ๏Šฑ ๏Œป ?

  • A 3 6 2 5
  • B1
  • C 5 6
  • D 2 5 3 6

Q21:

Evaluate 1 5 ๐‘“ ๐‘” ๏Šจ for ๐‘“ = 1 1 2 and ๐‘” = โˆ’ 1 2 3 .

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

Q22:

Find the value of 1 ๐‘ฅ ๐‘ฆ ๐‘ง given ๐‘ฅ = 4 3 , ๐‘ฆ = 3 2 , and ๐‘ง = โˆ’ 5 .

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

Q23:

Find the value of ๐‘ฅ ๐‘ฆ ๐‘ง given ๐‘ฅ = โˆ’ 5 2 , ๐‘ฆ = โˆ’ 1 2 and ๐‘ง = โˆ’ 2 .

  • A โˆ’ 5 2
  • B 5 4
  • C 5 8
  • D โˆ’ 5 8
  • E โˆ’ 5 4

Q24:

Find the value of ๐‘ฅ ๐‘ฆ ๐‘ง given ๐‘ฅ = 1 4 , ๐‘ฆ = 4 3 , and ๐‘ง = 4 .

  • A 1 6 3
  • B 1 3
  • C 1 6 7
  • D 4 3
  • E 2 0 7

Q25:

Substitute ๐‘ฅ = 2 and ๐‘ฆ = 1 into ๏€น ๐‘ฅ + ๐‘ฆ ๏… = ๏€น ๐‘ฅ โˆ’ ๐‘ฆ ๏… + ( 2 ๐‘ฅ ๐‘ฆ ) 2 2 2 2 2 2 2 to generate a Pythagorean triple.

  • A 5 = 3 + 2 2 2 2
  • B 3 = 2 + 1 2 2 2
  • C 5 = 1 + 4 2 2 2
  • D 5 = 3 + 4 2 2 2
  • E 3 = 4 โˆ’ 1 2 2 2

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