Worksheet: Evaluating Expressions Involving Absolute Values

In this worksheet, we will practice determining the value of expressions involving absolute values.

Q1:

Given that ๐‘ฅ = โˆ’ 1 6 , evaluate | | | โˆ’ 8 ๐‘ฅ ๏Šจ + 1 6 ๐‘ฅ ๏Šฉ โˆ’ 8 ๐‘ฅ | | | .

Q2:

Given that ๐‘Ž = 6 5 and ๐‘ = โˆ’ 2 4 5 , find | | ๐‘Ž รท ๐‘ | | 2 2 .

  • A 1 4
  • B โˆ’ 1 1 6
  • C โˆ’ 1 4
  • D 1 1 6

Q3:

Evaluate 3 | ๐‘ | + ๐‘ for ๐‘ = 9 and ๐‘ = โˆ’ 6 .

Q4:

Evaluate | ๐‘Ž + 9 | for ๐‘Ž = โˆ’ 8 .

Q5:

If ( | ๐‘ฅ | , 4 9 ) = ( 9 , ๐‘ฆ ) 2 , and the point ( ๐‘ฅ , ๐‘ฆ ) lies in the second quadrant, find 7 ๐‘ฅ โˆ’ 1 0 ๐‘ฆ .

Q6:

Given that | ๐‘ฆ | = 1 2 , determine ๐‘ฆ .

  • A ๐‘ฆ = 1 1 2 or ๐‘ฆ = โˆ’ 1 1 2
  • B ๐‘ฆ = 1 4 4 or ๐‘ฆ = โˆ’ 1 4 4
  • C ๐‘ฆ = | 1 2 | or ๐‘ฆ = | โˆ’ 1 2 |
  • D ๐‘ฆ = 1 2 or ๐‘ฆ = โˆ’ 1 2

Q7:

Evaluate | ๐‘Ž โˆ’ 1 9 | for ๐‘Ž = 2 .

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