Worksheet: Evaluating Simple Algebraic Expressions

In this worksheet, we will practice evaluating simple and rational algebraic expressions with one or multiple variables and applying this to real-world problems.

Q1:

If ๐‘š = 2 1 . 4 , ๐‘ = 2 3 . 4 , and ๐‘› = 9 , evaluate ๐‘š + ๐‘› + ๐‘ ๐‘ to the nearest tenth.

Q2:

Evaluate 1 4 + ๐‘ฆ ๏Šจ if ๐‘ฆ = 6 .

Q3:

Given that ๐‘› = 4 , determine the value of ๐‘› โˆ’ 8 ๏Šฉ .

Q4:

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

Q5:

Evaluate 7 ๐‘ž ๐‘ž + 2 ( ๐‘ + 5 ) for ๐‘ = 3 and ๐‘ž = 1 2 .

Q6:

Evaluate ๐‘ ( ๐‘› โˆ’ ๐‘ก ) for ๐‘› = 2 , ๐‘ = 6 , and ๐‘ก = 1 .

Q7:

Evaluate ๐‘ ๐‘› ๐‘ก + 1 1 ๏Šจ for ๐‘› = 4 , ๐‘ = 5 , and ๐‘ก = 5 .

Q8:

Evaluate 5 + ๐‘ฅ 2 if ๐‘ฅ = 3 .

Q9:

Given that ๐‘ฅ = 6 and ๐‘ฆ = 1 , find the value of 4 ๐‘ฅ + 3 ๐‘ฆ .

  • A 25
  • B 22
  • C 9
  • D 27

Q10:

If 7 ๐‘ฆ = 3 5 , what is the value of 8 ๐‘ฆ ?

Q11:

Evaluate 1 0 ๐‘š + 5 ๐‘˜ , given that ๐‘š = 9 and ๐‘˜ = 3 .

Q12:

Given that ๐‘Ž = 2 and ๐‘ = 5 , evaluate the expression ๐‘Ž ๐‘ + 8 ร— 9 .

Q13:

Evaluate 4 ๐‘ฆ รท ( 2 ๐‘ฅ + 2 ) , given that ๐‘ฅ = 3 and ๐‘ฆ = 2 0 .

Q14:

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

  • A 0
  • B โˆ’ 3 2
  • C 1 2
  • D 3 8

Q15:

Given that ๐‘ฅ = 3 and ๐‘ฆ = 1 , evaluate 2 ๐‘ฅ + 5 ๐‘ฆ รท 4 ๐‘ฅ ๐‘ฆ .

  • A 12
  • B 1 1 1 2
  • C 4 3
  • D 7 7 1 2

Q16:

Evaluate 9 ๐‘ โ‹… 6 ๏Šจ , given that ๐‘ = 1 0 .

Q17:

A square has a side length of ( 5 ๐‘Ž + ๐‘ ) cm. Write an expression for its area and evaluate its area when ๐‘Ž = 1 and ๐‘ = 6 .

  • A ( 5 ๐‘Ž + ๐‘ ) ๏Šจ cm2, 22 cm2
  • B 4 ( 5 ๐‘Ž + ๐‘ ) cm2, 121 cm2
  • C ( 5 ๐‘Ž + ๐‘ ) ๏Šจ cm2, 11 cm2
  • D ( 5 ๐‘Ž + ๐‘ ) ๏Šจ cm2, 121 cm2

Q18:

Evaluate 6 ( ๐‘Ž + ๐‘ โˆ’ ๐‘ ) ๏Šจ given that ๐‘Ž = 2 , ๐‘ = 7 , and ๐‘ = 6 .

Q19:

Evaluate ๐‘š ๐‘ โˆ’ ๐‘› if ๐‘š = 5 6 , ๐‘ = โˆ’ 8 , and ๐‘› = โˆ’ 4 .

Q20:

Given that โˆš ๐‘š = 1 5 , find ๐‘š + 4 .

Q21:

Evaluate 7 ๐‘’ ๐‘“ ( โˆ’ ๐‘” โ„Ž ) for ๐‘’ = 1 1 3 , ๐‘“ = โˆ’ 1 1 2 , โ„Ž = 2 1 2 , and ๐‘” = โˆ’ 1 1 2 .

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

Q22:

Evaluate ๐‘Ž ๐‘ โˆ’ ๐‘ ๏Šจ for ๐‘Ž = โˆ’ 8 , ๐‘ = โˆ’ 7 , and ๐‘ = โˆ’ 9 .

Q23:

Evaluate ๐‘‘ โˆ’ ๐‘” โˆ’ ๐‘“ if ๐‘‘ = 1 5 , ๐‘“ = โˆ’ 1 5 , and ๐‘” = 1 7 .

Q24:

Evaluate 6 ๐‘Ž + ๐‘ ๐‘ if ๐‘Ž = โˆ’ 8 , ๐‘ = โˆ’ 6 , and ๐‘ = 9 .

Q25:

Evaluate the expression ๐‘’ โ„Ž ๏Šจ ๏Šจ if ๐‘’ = โˆ’ 1 2 5 and โ„Ž = 1 2 3 .

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

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