Algebraic proof
AQA GCSE Maths revision on Algebraic proof. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
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Question 1
What is the standard algebraic representation for any even integer?
- A) 2n is the form
- B) 3n is the form
- C) 4n is the form
- D) 5n is the form
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Answer: 2n is the form
The correct answer is 2n is the form. Any integer multiplied by 2 will always result in an even number, whereas 3n or 5n would produce multiples of those primes.
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Question 2
Which expression represents an odd integer if n is an integer?
- A) 2n plus one
- B) 2n minus zero
- C) 3n plus zero
- D) 4n plus zero
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Answer: 2n plus one
The correct answer is 2n plus one. Since 2n is always even, adding 1 to it guarantees an odd result, while the other options remain even or depend on the value of n.
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Question 3
If x and y are odd integers, what must their product be?
- A) Always odd value
- B) Often even value
- C) Could be zeroing
- D) Never odd result
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Answer: Always odd value
The correct answer is Always odd value. Multiplying (2m+1) by (2n+1) results in 4mn + 2m + 2n + 1, which factorises to 2(2mn + m + n) + 1, proving it is always odd.
Want to test yourself on the remaining cards for this topic?
13 more questions on Algebraic proof — plus mistakes tracking and spaced repetition across the whole Maths spec.