Saved Question Sets
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Basic mathematical proof (show me that...)
5 Questions
Generated: 15/10/2025 10:32
each question should be worded as, for example, 'show me that 3x + 4 = 19 has a solution of x = 5' and make them suitable for year 8 students.
Q1:
Show me that the equation 2x + 3 = 11 has a solution of x = 4
Q2:
Show me that the sum of three consecutive even numbers starting from 4 is equal to 18
Q3:
Show me that a triangle with sides measuring 6 cm, 8 cm, and 10 cm is a right-angled triangle
+ 2 more question(s)
Dividing Fractions
5 Questions
Generated: 15/10/2025 11:03
3 pure calculations, and 2 worded questions in context.
Q1:
Calculate: ¾ ÷ ½
Q2:
Work out: 2⅓ ÷ ⅚
Q3:
Find the value of: (¾ ÷ ⅔) ÷ ½
+ 2 more question(s)
Multiplying fractions
5 Questions
Generated: 15/10/2025 11:26
3 calculations, followed by 2 worded questions in context.
Q1:
Calculate the following: 2/3 × 4/5
Q2:
Work out 1 1/4 × 2/3, giving your answer in its simplest form
Q3:
Find the value of (3/8 × 4/9) ÷ 1/6
+ 2 more question(s)
Proof by counterexample
5 Questions
Generated: 15/10/2025 14:59
Q1:
A student claims: 'All prime numbers are odd.' Provide a counterexample to disprove this statement.
Q2:
Disprove the following statement by finding a counterexample: 'For all integers n, n² + n + 41 is a prime number.'
Q3:
Consider the statement: 'If a number is divisible by 6, then it is divisible by 12.' Find a counterexample to show this statement is false.
+ 2 more question(s)
Always, Sometimes, Never
5 Questions
Generated: 15/10/2025 15:01
Mathematical statements that are always true, sometimes true or never true.
Q1:
For each statement below, decide whether it is ALWAYS true, SOMETIMES true, or NEVER true:
(a) The sum of two even numbers is even
(b) The product of...
Q2:
Classify each statement as ALWAYS, SOMETIMES or NEVER true. Justify your reasoning with examples or counterexamples:
(a) The angles in a triangle add...
Q3:
Determine whether each statement is ALWAYS, SOMETIMES or NEVER true. Show your working where appropriate:
(a) If you add two prime numbers, the resul...
+ 2 more question(s)
True or false
5 Questions
Generated: 15/10/2025 15:03
Q1:
True or false: All prime numbers are odd numbers.
Q2:
True or false: The square root of 16 is both 4 and -4.
Q3:
True or false: In any triangle, the sum of two sides is always greater than the third side.
+ 2 more question(s)
Prime factors
5 Questions
Generated: 16/10/2025 15:17
worded questions involving prime factors, lcm, hcf.
Q1:
Find the prime factorisation of 84. Express your answer in index form.
Q2:
Two numbers have prime factorisations 2² × 3 × 5 and 2 × 3² × 7. Calculate:
(a) the highest common factor (HCF) of these two numbers
(b) the low...
Q3:
A school is organising a sports day and needs to divide students into equal teams. There are 108 Year 7 students and 84 Year 8 students. What is the l...
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Find the median
4 Questions
Generated: 29/10/2025 15:33
Q1:
Find the median of the following set of numbers: 12, 7, 15, 9, 11, 14, 8
Q2:
The heights (in cm) of 9 students in a class are: 142, 138, 145, 152, 139, 148, 141, 147, 150. Calculate the median height of these students.
Q3:
A survey recorded the number of books read by 12 students during a month: 3, 5, 2, 7, 4, 6, 8, 3, 5, 4, 6, 9. If one more student is added to the surv...
+ 1 more question(s)