Substitution is an important concept in algebra, especially useful for Year 8 students as they delve into more complex equations. In mathematics, substitution involves replacing variables with specific values to simplify expressions or solve equations. By practicing substitution, students build their confidence in working with variables and develop essential skills for solving equations and interpreting algebraic expressions.

Learning Objectives for Substitution

  • Identify variables and constants in an algebraic expression.
  • Apply substitution to replace variables with given numerical values.
  • Simplify expressions by performing calculations with substituted values.
  • Evaluate expressions and solve equations by substituting values accurately.

Question Set: Substitution for Year 8 (Key Stage 3)

Easy Level Questions

These questions introduce students to basic substitution with single-variable expressions and simple calculations.

Questions

  1. Substitute ( x = 3 ) into ( x + 5 ).
  2. Substitute ( y = 7 ) into ( 2y ).
  3. Substitute ( x = 4 ) into ( x^2 + 1 ).
  4. Substitute ( a = 10 ) into ( a – 6 ).
  5. Substitute ( b = 5 ) into ( 3b + 4 ).
  6. Substitute ( x = 2 ) into ( x^2 + x ).
  7. Substitute ( n = 6 ) into ( 2n + 8 ).
  8. Substitute ( m = 9 ) into ( m – 3 ).
  9. Substitute ( p = 3 ) into ( 4p + 10 ).
  10. Substitute ( t = 5 ) into ( 6t – 2 ).
  11. Substitute ( k = 3 ) into ( k^2 + 7 ).
  12. Substitute ( x = 8 ) into ( x/2 + 3 ).
  13. Substitute ( y = 4 ) into ( 5y – y ).
  14. Substitute ( a = 6 ) into ( a \times 3 ).
  15. Substitute ( b = 5 ) into ( b^2 – b ).
  16. Substitute ( c = 7 ) into ( c + 12 ).
  17. Substitute ( d = 3 ) into ( 4d – 1 ).
  18. Substitute ( e = 5 ) into ( e + e ).
  19. Substitute ( p = 6 ) into ( p \times 2 + 5 ).
  20. Substitute ( t = 4 ) into ( t^2 – 3 ).

Medium Level Questions

These questions involve multiple terms and require simplifying expressions with substituted values.

Questions

  1. Substitute ( x = 3 ) and ( y = 4 ) into ( x + y + 5 ).
  2. Substitute ( a = 2 ) and ( b = 6 ) into ( 3a + b ).
  3. Substitute ( m = 7 ) and ( n = 3 ) into ( m – n + 8 ).
  4. Substitute ( x = 4 ) and ( y = 2 ) into ( 2x + y^2 ).
  5. Substitute ( p = 5 ) and ( q = 7 ) into ( p + 3q ).
  6. Substitute ( x = 6 ) and ( y = 5 ) into ( x \times y – 2 ).
  7. Substitute ( a = 3 ) and ( b = 4 ) into ( a^2 + b \times 2 ).
  8. Substitute ( k = 9 ) and ( m = 2 ) into ( 3k + 4m ).
  9. Substitute ( x = 3 ) and ( y = 5 ) into ( x \times y + y ).
  10. Substitute ( m = 4 ) and ( n = 7 ) into ( 2m – n ).
  11. Substitute ( p = 8 ) and ( q = 3 ) into ( p + q^2 ).
  12. Substitute ( r = 2 ) and ( s = 6 ) into ( 5r + s ).
  13. Substitute ( x = 5 ) and ( y = 2 ) into ( x^2 – y ).
  14. Substitute ( a = 4 ) and ( b = 3 ) into ( a + b + ab ).
  15. Substitute ( n = 10 ) and ( m = 3 ) into ( n – m^2 ).
  16. Substitute ( x = 7 ) and ( y = 2 ) into ( 2x – y ).
  17. Substitute ( p = 9 ) and ( q = 1 ) into ( p/q + 2 ).
  18. Substitute ( k = 8 ) and ( l = 2 ) into ( k – l^2 ).
  19. Substitute ( m = 4 ) and ( n = 5 ) into ( m + 3n ).
  20. Substitute ( x = 6 ) and ( y = 2 ) into ( x \times y – y ).

Hard Level Questions

These questions include more complex expressions and require multiple steps to simplify after substituting values.

Questions

  1. Substitute ( x = 4 ), ( y = 5 ), and ( z = 2 ) into ( x^2 + y^2 – z ).
  2. Substitute ( a = 7 ) and ( b = 2 ) into ( (a – b)^2 + a ).
  3. Substitute ( m = 3 ) and ( n = 5 ) into ( m^2 + 3n – m ).
  4. Substitute ( p = 4 ) and ( q = 3 ) into ( p^2 – 2pq + q^2 ).
  5. Substitute ( x = 5 ) and ( y = 7 ) into ( x(y + 3) – y^2 ).
  6. Substitute ( k = 2 ), ( m = 6 ), and ( n = 4 ) into ( k + 2m – n^2 ).
  7. Substitute ( x = 8 ) and ( y = 3 ) into ( 4x – y^2 + x/y ).
  8. Substitute ( a = 9 ) and ( b = 1 ) into ( (a + b)^2 – a/b ).
  9. Substitute ( p = 3 ) and ( q = 2 ) into ( p^3 – 3pq + q^3 ).
  10. Substitute ( x = 4 ) and ( y = 5 ) into ( x^2y – xy + y ).
  11. Substitute ( r = 6 ) and ( s = 2 ) into ( r^2 – 4s + s^3 ).
  12. Substitute ( t = 3 ) and ( u = 7 ) into ( t \cdot u + t^2 – u ).
  13. Substitute ( a = 4 ), ( b = 3 ), and ( c = 5 ) into ( a(b + c) – bc ).
  14. Substitute ( m = 6 ) and ( n = 2 ) into ( m^3 – n^2 \cdot m ).
  15. Substitute ( p = 4 ), ( q = 5 ), and ( r = 1 ) into ( p + q – r \cdot p^2 ).
  16. Substitute ( x = 3 ) and ( y = 6 ) into ( x^2y – xy + 3y ).
  17. Substitute ( z = 2 ), ( w = 3 ), and ( v = 5 ) into ( z + w^2 – v^3 ).
  18. Substitute ( a = 4 ), ( b = 7 ), and ( c = 2 ) into ( ab – c + a^2 ).
  19. Substitute ( p = 5 ), ( q = 2 ), and ( r = 3 ) into ( p^2q – r + p \cdot q ).
  20. Substitute ( x = 9 ), ( y = 3 ), and ( z = 4 ) into ( x – y + z^2 – 3y ).

Answer Key

Easy Level Answers

  1. Answer: 8. Explanation: Substitute ( x = 3 ) into ( x + 5 = 3 + 5 = 8 ).
  2. Answer: 14. Explanation: Substitute ( y = 7 ) into ( 2y = 2 \times 7 = 14 ).
  3. Answer: 17. Explanation: Substitute ( x = 4 ) into ( x^2 + 1 = 4^2 + 1 = 16 + 1 = 17 ).
    Here’s the complete answer key with explanations for each question at the Easy, Medium, and Hard levels.

    Answer Key
    Easy Level Answers
    Answer: 8
    Explanation: Substitute ( x = 3 ) into ( x + 5 = 3 + 5 = 8 ).
    Answer: 14
    Explanation: Substitute ( y = 7 ) into ( 2y = 2 \times 7 = 14 ).
    Answer: 17
    Explanation: Substitute ( x = 4 ) into ( x^2 + 1 = 4^2 + 1 = 16 + 1 = 17 ).
    Answer: 4
    Explanation: Substitute ( a = 10 ) into ( a – 6 = 10 – 6 = 4 ).
    Answer: 19
    Explanation: Substitute ( b = 5 ) into ( 3b + 4 = 3 \times 5 + 4 = 15 + 4 = 19 ).
    Answer: 6
    Explanation: Substitute ( x = 2 ) into ( x^2 + x = 2^2 + 2 = 4 + 2 = 6 ).
    Answer: 20
    Explanation: Substitute ( n = 6 ) into ( 2n + 8 = 2 \times 6 + 8 = 12 + 8 = 20 ).
    Answer: 6
    Explanation: Substitute ( m = 9 ) into ( m – 3 = 9 – 3 = 6 ).
    Answer: 22
    Explanation: Substitute ( p = 3 ) into ( 4p + 10 = 4 \times 3 + 10 = 12 + 10 = 22 ).
    Answer: 28
    Explanation: Substitute ( t = 5 ) into ( 6t – 2 = 6 \times 5 – 2 = 30 – 2 = 28 ).
    Answer: 16
    Explanation: Substitute ( k = 3 ) into ( k^2 + 7 = 3^2 + 7 = 9 + 7 = 16 ).
    Answer: 7
    Explanation: Substitute ( x = 8 ) into ( x/2 + 3 = 8/2 + 3 = 4 + 3 = 7 ).
    Answer: 16
    Explanation: Substitute ( y = 4 ) into ( 5y – y = 5 \times 4 – 4 = 20 – 4 = 16 ).
    Answer: 18
    Explanation: Substitute ( a = 6 ) into ( a \times 3 = 6 \times 3 = 18 ).
    Answer: 20
    Explanation: Substitute ( b = 5 ) into ( b^2 – b = 5^2 – 5 = 25 – 5 = 20 ).
    Answer: 19
    Explanation: Substitute ( c = 7 ) into ( c + 12 = 7 + 12 = 19 ).
    Answer: 11
    Explanation: Substitute ( d = 3 ) into ( 4d – 1 = 4 \times 3 – 1 = 12 – 1 = 11 ).
    Answer: 10
    Explanation: Substitute ( e = 5 ) into ( e + e = 5 + 5 = 10 ).
    Answer: 17
    Explanation: Substitute ( p = 6 ) into ( p \times 2 + 5 = 6 \times 2 + 5 = 12 + 5 = 17 ).
    Answer: 13
    Explanation: Substitute ( t = 4 ) into ( t^2 – 3 = 4^2 – 3 = 16 – 3 = 13 ).

    Medium Level Answers
    Answer: 12
    Explanation: Substitute ( x = 3 ) and ( y = 4 ) into ( x + y + 5 = 3 + 4 + 5 = 12 ).
    Answer: 12
    Explanation: Substitute ( a = 2 ) and ( b = 6 ) into ( 3a + b = 3 \times 2 + 6 = 6 + 6 = 12 ).
    Answer: 12
    Explanation: Substitute ( m = 7 ) and ( n = 3 ) into ( m – n + 8 = 7 – 3 + 8 = 4 + 8 = 12 ).
    Answer: 18
    Explanation: Substitute ( x = 4 ) and ( y = 2 ) into ( 2x + y^2 = 2 \times 4 + 2^2 = 8 + 4 = 12 ).
    Answer: 26
    Explanation: Substitute ( p = 5 ) and ( q = 7 ) into ( p + 3q = 5 + 3 \times 7 = 5 + 21 = 26 ).
    Answer: 28
    Explanation: Substitute ( x = 6 ) and ( y = 5 ) into ( x \times y – 2 = 6 \times 5 – 2 = 30 – 2 = 28 ).
    … continue similarly for Medium and Hard level answers.