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Exam-Style Questions.Problems adapted from questions set for previous Mathematics exams. |
1. | GCSE Higher |
Prove algebraically that \(0.2\dot6\) can be written as \( \dfrac{4}{15}\)
2. | GCSE Higher |
Use algebra to prove that \(0.3\dot1\dot8 \times 0.\dot8\) is equal to \( \frac{28}{99} \).
3. | GCSE Higher |
(a) Prove that the recurring decimal \(0.\dot2 \dot1\) has the value \(\frac{7}{33}\)
(b) The value of \(x\) is given as:
$$x=\frac{1}{5^{120}\times2^{123}}$$Show that, when \(x\) is written as a terminating decimal, there are 120 zeros after the decimal point.
(c) The reciprocal of any prime number \(p\) (where \(p\) is neither 2 nor 5) when written as a decimal, is always a recurring decimal.
A theorem in mathematics states:
The period of a recurring decimal is the least value of \(n\) for which \(p\) is a factor of \(10^n – 1\)
Marilou tests this theorem for the reciprocal of eleven.
She uses her calculator to show that 11 is a factor of \(10^2 – 1\) then makes this statement:
"The period of the recurring decimal is 2 because 11 is a factor of \(10^2-1\). This shows the theorem to be true in this case."
Explain why Marilou's statement is incomplete.
4. | GCSE Higher |
(a) Use algebra to show that the recurring decimal \(0.\dot2 \dot4\) can be written as \( \frac{8}{33}\).
(b) Find the fraction, in its lowest terms, equal to the recurring decimal \(0.5 \dot2 \dot4\).
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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.
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