Algebraic proof
Edexcel GCSE Maths revision on Algebraic proof. Aligned to the Pearson Edexcel GCSE Mathematics 1MA1 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 expression used to represent any even integer?
- A) Two multiplied by n because it is divisible by two
- B) Two multiplied by n plus one because it is odd now
- C) Two multiplied by n plus two because it is a prime
- D) Two multiplied by n plus four because it is a cube
Show answer
Answer: Two multiplied by n because it is divisible by two
The correct answer is 'Two multiplied by n because it is divisible by two'. Any integer n multiplied by two results in a product that must be divisible by two, which is the definition of an even number.
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Question 2
When expanding the expression for the product of two consecutive odd integers, what is the resulting constant term?
Show answer
Answer: -1
The correct answer is -1. Expanding (2n-1)(2n+1) gives 4n^2 - 1, meaning the constant term is -1.
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Question 3
Which of these statements correctly describes the sum of any three consecutive integers?
- A) It is always a multiple of three as shown by 3n+3
- B) It is always a multiple of two as shown by 2n+2
- C) It is always a multiple of four as shown by 4n+4
- D) It is always a multiple of five as shown by 5n+5
Show answer
Answer: It is always a multiple of three as shown by 3n+3
The correct answer is 'It is always a multiple of three as shown by 3n+3'. Adding (n-1) + n + (n+1) simplifies to 3n, which is a multiple of three; the distractor 3n+3 is a common error from incorrect algebraic setup.
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.