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Worksheet: Evaluating Algebraic Expressions of More Than One Degree

Q1:

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

Make π‘Ÿ the subject.

  • A π‘Ÿ = 3 𝑉 4 πœ‹
  • B π‘Ÿ = ο„ž 4 𝑉 3 πœ‹ 3
  • C π‘Ÿ = ο„ž 3 𝑉 4 πœ‹
  • D π‘Ÿ = ο„ž 3 𝑉 4 πœ‹ 3
  • E π‘Ÿ = ο„ž 4 πœ‹ 𝑉 3 3

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

Q2:

Evaluate ( 3 𝑑 + 8 ) Γ· 2 2 for 𝑑 = βˆ’ 2 .

Q3:

Evaluate 1 5 𝑓 𝑔 2 for 𝑓 = 1 1 2 and 𝑔 = βˆ’ 1 2 3 .

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

Q4:

Given that 𝑏 = 2 1 3 , 𝑐 = βˆ’ 2 2 3 , and 𝑑 = 4 1 2 , evaluate ο€Ό βˆ’ 1 3 𝑏  β‹… 3 𝑐 𝑑 3 .

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

Q5:

Given that 𝑐 = π‘š ( 1 + π‘Ÿ ) 𝑛 , find 𝑐 when π‘š = 7 . 4 Γ— 1 0 3 , π‘Ÿ = 5 . 8 Γ— 1 0 βˆ’ 3 , and 𝑛 = 6 .

Q6:

Find the value of ( π‘Ž βˆ’ 𝑏 ) 2 given π‘Ž = 3 8 9 and 𝑏 = βˆ’ 7 9 .

Q7:

Find the value of 1 π‘₯ 𝑦 𝑧 given π‘₯ = 4 3 , 𝑦 = 3 2 , and 𝑧 = βˆ’ 5 .

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

Q8:

Given that π‘₯ = 1 2 , 𝑦 = βˆ’ 2 3 , and 𝑧 = βˆ’ 1 3 , find the numerical value of π‘₯ 𝑦 𝑦 + 𝑧 2 2 .

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

Q9:

Find the value of π‘₯ 𝑦 𝑧 given π‘₯ = βˆ’ 5 2 , 𝑦 = βˆ’ 1 2 and 𝑧 = βˆ’ 2 .

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

Q10:

Given that π‘₯ = 8 ( 5 + 9 ) βˆ’ 6 and 𝑦 = ( 7 Γ— 2 ) βˆ’ 9 2 2 , evaluate ( π‘₯ βˆ’ 𝑦 ) βˆ’ 7 2 2 .

Q11:

Given that π‘₯ = 2 and 𝑦 = βˆ’ 5 , which of the following choices is a negative number?

  • A π‘₯ βˆ’ 𝑦 2
  • B π‘₯ + 𝑦 2 2
  • C π‘₯ + 𝑦 2
  • D π‘₯ + 𝑦 2

Q12:

Given that 𝑦 = 2 3 and π‘š = 3 2 , find the value of ( 𝑦 βˆ’ π‘š ) 3 .

Q13:

Given that π‘Ž = 1 √ 3 and 𝑏 = βˆ’ 3 , find the value of 4 π‘Ž βˆ’ ( 3 βˆ’ 𝑏 ) 2 βˆ’ 1 .

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

Q14:

Find the value of π‘₯ 𝑦 𝑧 given π‘₯ = 1 4 , 𝑦 = 4 3 , and 𝑧 = 4 .

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

Q15:

Given that π‘š + 1 π‘š = βˆ’ 6 , what is the value of π‘š + 1 π‘š 2 2 ?

Q16:

If π‘Ž = βˆ’ 𝑏 and π‘Ž = 1 , what is the value of ο€Ό 5 6  π‘Ž βˆ’ 𝑏 ?

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

Q17:

If βˆ’ 6 π‘₯ = 2 4 , what is the value of 6 π‘₯ βˆ’ 1 ?

Q18:

Find the value of ( π‘₯ + 𝑧 ) Γ· ( 𝑦 βˆ’ 𝑧 ) given π‘₯ = βˆ’ 5 2 , 𝑦 = βˆ’ 7 6 , and 𝑧 = 1 .

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

Q19:

Substitute π‘₯ = 2 and 𝑦 = 1 into ο€Ή π‘₯ + 𝑦  = ο€Ή π‘₯ βˆ’ 𝑦  + ( 2 π‘₯ 𝑦 ) 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 βˆ’ 1 2 2 2

Q20:

Determine the value of π‘š 𝑛 , given that π‘š = βˆ’ 1 2 and 𝑛 = βˆ’ 1 0 .

Q21:

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

  • A
  • B
  • C
  • D

Q22:

Evaluate π‘Ž Γ— 𝑏 2 3 , given that π‘Ž = 4 and 𝑏 = 3 .

Q23:

Given that π‘Ž = √ 5 and 𝑏 = √ 2 , find the value of 𝑏 + π‘Ž 𝑏 + π‘Ž 3 3 .

  • A βˆ’ 3
  • B 7 + √ 1 0
  • C βˆ’ 2 1
  • D 7 βˆ’ √ 1 0
  • E 7 βˆ’ √ 7

Q24:

Given that π‘Ž = 4 3 and 𝑏 = 2 3 , evaluate ο€» π‘Ž 𝑏  4 .

  • A2
  • B 1 1 6
  • C 1 2
  • D16

Q25:

Given that π‘Ž = βˆ’ 5 π‘₯ + 2 , 𝑏 = π‘₯ + 2 , and 𝑐 = 2 π‘₯ βˆ’ 4 , evaluate π‘Ž 𝑏 βˆ’ 𝑐 2 when π‘₯ = 0 .