Lesson 2.19

2.19 Algebraic proof Quiz: AQA Further Maths, Unit 2

20 questions

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Lesson 2.19, Algebraic proof: 20 multiple choice questions for the AQA GCSE Further Maths (8365), Unit 2: Algebra, written with Revision Ninja.

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The 20 questions

  1. What expression is obtained by fully expanding and simplifying (n + 1)^2 - (n - 1)^2?

    • 4n
    • 2n^2 + 2
    • 2n
    • 4n + 2
  2. Which expression represents any even integer?

    • n + 1
    • n^2
    • 2n + 1
    • 2n
  3. Which expression represents three consecutive integers?

    • n, n^2, n^3
    • n, n + 1, n + 2
    • n, 2n, 3n
    • n, n + 2, n + 4
  4. What is the primary purpose of a counterexample in mathematical proof?

    • Disprove a statement
    • Simplify an expression
    • Prove a statement
    • Solve an equation
  5. Which expression shows that the sum of two even numbers, 2a and 2b, is even?

    • 4(a + b)
    • 2a + b
    • 2(a + b)
    • 2ab
  6. Which number is a counterexample to the claim that every square number is even?

    • 4
    • 9
    • 36
    • 16
  7. Simplify (n + 4)^2 − n^2.

    • 4n + 16
    • 8n + 16
    • 8n^2
    • 8n + 8
  8. Which expression represents the sum of three consecutive integers n, n + 1 and n + 2?

    • 3n + 4
    • 3(n + 1)
    • 3n + 2
    • 3n + 1
  9. Why is the product of two consecutive integers always even?

    • Both are prime
    • One is even
    • Both are even
    • Difference is even
  10. Simplify (2n + 1)^2.

    • 2n^2 + 1
    • 4n^2 + 4n + 1
    • 2n^2 + 4n + 1
    • 4n^2 + 1
  11. Simplify the sum (2n + 1) + (2m + 1) to show the result is even.

    • 2n + 2m + 1
    • 2(n + m)
    • 4(n + m)
    • 2(n + m + 1)
  12. Which expression shows that 6n + 3 is divisible by 3?

    • 2(3n + 1)
    • 3(2n + 1)
    • 3(n + 1)
    • 6(n + 1)
  13. Which expression proves that x^2 − 2x + 2 is always positive?

    • (x − 1)^2 + 1
    • (x − 1)^2 − 1
    • (x − 2)^2 + 2
    • (x + 1)^2 + 2
  14. Let x = 0.6666... Using 10x − x = 6, what is x?

    • 2/9
    • 6/10
    • 2/3
    • 3/2
  15. Simplify n^2 − (n − 2)^2.

    • 2n − 4
    • 4n + 4
    • 4n − 4
    • 4n
  16. For any integer n, which integer is always a factor of (n + 1)^2 - (n - 1)^2?

    • 3
    • 5
    • 4
    • 6
  17. Factorise n^3 − n.

    • n^2(n − 1)
    • (n − 1)(n + 1)^2
    • n(n − 1)(n + 1)
    • n(n^2 + 1)
  18. Simplify (2n + 1)^2 + (2n + 3)^2.

    • 4n^2 + 16n + 10
    • 8n^2 + 12n + 10
    • 8n^2 + 16n + 8
    • 8n^2 + 16n + 10
  19. Which factorisation of 9n^2 + 6n shows that it is divisible by 3?

    • 9n(n + 1)
    • 3n(3n + 6)
    • 3n(3n + 2)
    • 6n(n + 1)
  20. Simplify n^2 + (n + 1)^2 to show it is always odd.

    • 2n^2 + 2n + 1
    • n^2 + 2n + 1
    • 2n^2 + 2n
    • 2n^2 + 1

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