|
|
Exam-Style Questions.Problems adapted from questions set for previous Mathematics exams. |
1. | GCSE Higher |
Use algebra to prove that \(0.3\dot1\dot8 \times 0.\dot8\) is equal to \( \frac{28}{99} \).
2. | GCSE Higher |
m and n are positive whole numbers with m > n
m2 – n2 = (m + n)(m – n)
If m2 – n2 is a prime number prove that m and n are consecutive numbers.
3. | GCSE Higher |
Express as a single fraction and simplify your answer.
$$\frac{p-1}{q-1}-\frac pq$$Using your answer to part (a), prove that if \(p\) and \(q\) are positive integers and \(p \lt q\), then
$$\frac{p-1}{q-1}-\frac pq\lt 0$$4. | GCSE Higher |
(a) Prove that the product of two consecutive whole numbers is always even.
(b) Prove, by giving a counter example, that the sum of four consecutive integers is not always divisible by 4.
5. | GCSE Higher |
The number \(T\) can be expressed as \(T = 4k + 3\) where \(k\) is a positive integer.
(a) Show that \(T^2\) is always an odd number.
\(T\) and \(U\) are consecutive odd numbers where \(U > T\).
(b) Write down an expression for \(U\), in terms of \(k\).
(c) Show that \(U^2 - T^2\) is always a multiple of 16.
6. | IB Analysis and Approaches |
Consider two consecutive positive even numbers, \(2n\) and \(2n + 2\).
Show that the difference of their squares is equal to twice their sum.
If you would like space on the right of the question to write out the solution try this Thinning Feature. It will collapse the text into the left half of your screen but large diagrams will remain unchanged.
The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.
The solutions to the questions on this website are only available to those who have a Transum Subscription.
Exam-Style Questions Main Page
To search the entire Transum website use the search box in the grey area below.
Do you have any comments about these exam-style questions? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.
