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
-
What expression is obtained by fully expanding and simplifying (n + 1)^2 - (n - 1)^2?
- 4n
- 2n^2 + 2
- 2n
- 4n + 2
-
Which expression represents any even integer?
- n + 1
- n^2
- 2n + 1
- 2n
-
Which expression represents three consecutive integers?
- n, n^2, n^3
- n, n + 1, n + 2
- n, 2n, 3n
- n, n + 2, n + 4
-
What is the primary purpose of a counterexample in mathematical proof?
- Disprove a statement
- Simplify an expression
- Prove a statement
- Solve an equation
-
Which expression shows that the sum of two even numbers, 2a and 2b, is even?
- 4(a + b)
- 2a + b
- 2(a + b)
- 2ab
-
Which number is a counterexample to the claim that every square number is even?
- 4
- 9
- 36
- 16
-
Simplify (n + 4)^2 − n^2.
- 4n + 16
- 8n + 16
- 8n^2
- 8n + 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
-
Why is the product of two consecutive integers always even?
- Both are prime
- One is even
- Both are even
- Difference is even
-
Simplify (2n + 1)^2.
- 2n^2 + 1
- 4n^2 + 4n + 1
- 2n^2 + 4n + 1
- 4n^2 + 1
-
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)
-
Which expression shows that 6n + 3 is divisible by 3?
- 2(3n + 1)
- 3(2n + 1)
- 3(n + 1)
- 6(n + 1)
-
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
-
Let x = 0.6666... Using 10x − x = 6, what is x?
- 2/9
- 6/10
- 2/3
- 3/2
-
Simplify n^2 − (n − 2)^2.
- 2n − 4
- 4n + 4
- 4n − 4
- 4n
-
For any integer n, which integer is always a factor of (n + 1)^2 - (n - 1)^2?
- 3
- 5
- 4
- 6
-
Factorise n^3 − n.
- n^2(n − 1)
- (n − 1)(n + 1)^2
- n(n − 1)(n + 1)
- n(n^2 + 1)
-
Simplify (2n + 1)^2 + (2n + 3)^2.
- 4n^2 + 16n + 10
- 8n^2 + 12n + 10
- 8n^2 + 16n + 8
- 8n^2 + 16n + 10
-
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)
-
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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