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Lesson: Substitution to Manipulate Expressions into Quadratics

Worksheet • 12 Questions

Q1:

Find the solution set of 5 + 1 2 5 5 = 3 0 π‘₯ π‘₯ .

  • A { 1 , 2 }
  • B { 5 , 2 5 }
  • C { 1 0 , 1 0 0 }
  • D { 4 , 4 4 }

Q2:

Find the solution set of 3 + 7 2 9 3 = 9 0 π‘₯ π‘₯ .

  • A { 2 , 4 }
  • B { 9 , 8 1 }
  • C { 3 6 , 3 6 0 }
  • D { 8 , 8 4 }

Q3:

Factorise fully ( 𝑧 + 3 ) βˆ’ 1 9 ( 𝑧 + 3 ) + 9 0 2 .

  • A ( 𝑧 βˆ’ 6 ) ( 𝑧 βˆ’ 7 )
  • B ( 𝑧 βˆ’ 9 ) ( 𝑧 βˆ’ 1 0 )
  • C ( 𝑧 + 8 ) ( 𝑧 + 2 1 )
  • D ( 𝑧 + 3 ) ( 𝑧 + 3 0 )

Q4:

Factorise fully ( π‘₯ βˆ’ 7 ) + 6 ( π‘₯ βˆ’ 7 ) βˆ’ 7 2 2 .

  • A ( π‘₯ + 5 ) ( π‘₯ βˆ’ 1 3 )
  • B ( π‘₯ βˆ’ 3 ) ( π‘₯ βˆ’ 2 5 )
  • C ( π‘₯ + 1 2 ) ( π‘₯ βˆ’ 6 )
  • D ( π‘₯ + 3 ) ( π‘₯ βˆ’ 2 4 )
  • E ( π‘₯ βˆ’ 1 9 ) ( π‘₯ βˆ’ 1 )

Q5:

Factorise fully ( 𝑦 βˆ’ 4 ) βˆ’ 1 8 ( 𝑦 βˆ’ 4 ) + 8 0 2 .

  • A ( 𝑦 βˆ’ 1 4 ) ( 𝑦 βˆ’ 1 2 )
  • B ( 𝑦 βˆ’ 1 0 ) ( 𝑦 βˆ’ 8 )
  • C ( 𝑦 + 1 ) ( 𝑦 + 1 2 )
  • D ( 𝑦 + 4 ) ( 𝑦 + 2 0 )

Q6:

Factorise fully 2 4 π‘₯ βˆ’ 3 4 π‘₯ + 1 2 π‘₯ 5 3 .

  • A 2 π‘₯ ο€Ή 3 π‘₯ βˆ’ 2  ο€Ή 4 π‘₯ βˆ’ 3  2 2
  • B 2 π‘₯ ο€Ή 3 π‘₯ + 2  ο€Ή 4 π‘₯ + 3  2 2
  • C π‘₯ ο€Ή 1 2 π‘₯ + 4  ο€Ή 2 π‘₯ βˆ’ 3  2 2
  • D 2 π‘₯ ο€Ή 3 π‘₯ βˆ’ 2  ο€Ή 4 π‘₯ + 3  2 2

Q7:

Consider the equation π‘₯ + 2 = 2 π‘₯ . Adding π‘₯ + π‘₯  to both sides produces

Is the solution set of the equation formed the same as that of the original equation?

  • Ano
  • Byes

Q8:

Find the solution set of π‘₯ βˆ’ 3 3 π‘₯ + 3 2 = 0 5 5 2 .

  • A { 1 , 4 }
  • B { 1 , 3 2 }
  • C { 4 , 1 6 }
  • D { 2 }
  • E { 1 , 2 }

Q9:

Find the solution set of π‘₯ βˆ’ 7 3 0 π‘₯ + 7 2 9 = 0 1 2 5 6 5 .

  • A { 1 , 2 4 3 , βˆ’ 1 , βˆ’ 2 4 3 }
  • B { βˆ’ 5 , βˆ’ 1 5 }
  • C { 1 , 3 , βˆ’ 1 , βˆ’ 3 }
  • D { βˆ’ 1 , βˆ’ 3 }
  • E { 5 , 1 5 , βˆ’ 5 , βˆ’ 1 5 }

Q10:

Find the solution set of π‘₯ βˆ’ 9 π‘₯ + 1 4 = 0 2 3 1 3 .

  • A { 3 4 3 , 8 }
  • B { βˆ’ 2 1 , βˆ’ 6 }
  • C { 7 , 2 }
  • D { βˆ’ 7 , βˆ’ 2 }
  • E { 2 1 , 6 }

Q11:

Find the solution set of 2 βˆ’ 2 0 Γ— 2 + 2 5 6 = 0 2 π‘₯ + 2 π‘₯ + 2 .

  • A { 2 , 4 }
  • B { 2 , βˆ’ 2 }
  • C { 4 , 1 6 }
  • D { 6 , βˆ’ 6 }
  • E { 3 , βˆ’ 3 }

Q12:

Find the solution set of 2 + 8 = 6 Γ— 2 2 π‘₯ π‘₯ .

  • A { 1 , 2 }
  • B { 2 , 4 }
  • C { βˆ’ 1 , βˆ’ 2 }
  • D { 1 , βˆ’ 1 }
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