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Key Stage 2 is the legal term for the four years of schooling in maintained schools in England and Wales normally known as Year 3, Year 4, Year 5 and Year 6, when the pupils are aged between 7 and 11 years.
KS1 SATs, Phonics and Reading Check (taken in Year 1 but may be retaken, if the required standard isn't reached, in Year 2) 2 7-11 4 3–6 SATs, eleven plus exam (generally only for Grammar school entry) 3 11-14 3 7–9 12+ and 13+ (generally only for Grammar school entry) formerly SATs (until 2017) 4 14-16 2 10–11 GCSEs: 5 16-18 2 12–13
Dividing the numerator and denominator of a fraction by the same non-zero number yields an equivalent fraction: if the numerator and the denominator of a fraction are both divisible by a number (called a factor) greater than 1, then the fraction can be reduced to an equivalent fraction with a smaller numerator and a smaller denominator.
The term is defined in The Education (Northern Ireland) Order 2006 as "key stage 3 is the period beginning at the same time as the next school year after the end of key stage 2 and ending at the same time as the school year in which the majority of pupils in his class complete three school years in that key stage". [6]
The first GCSE exams were sat in 1988. [6] They replaced the former CSE and O-Level qualifications, uniting the two qualifications to allow access to the full range of grades for more pupils. However the exam papers of the GCSE sometimes had a choice of questions, designed for the more able and the less able candidates.
Graph of the fractional part of real numbers The fractional part or decimal part [ 1 ] of a non‐negative real number x {\displaystyle x} is the excess beyond that number's integer part . The latter is defined as the largest integer not greater than x , called floor of x or ⌊ x ⌋ {\displaystyle \lfloor x\rfloor } .
Continued fractions can also be applied to problems in number theory, and are especially useful in the study of Diophantine equations. In the late eighteenth century Lagrange used continued fractions to construct the general solution of Pell's equation, thus answering a question that had fascinated mathematicians for more than a thousand years. [9]
Many of the calculations throughout Fibonacci's book involve numbers represented as Egyptian fractions, and one section of this book [11] provides a list of methods for conversion of vulgar fractions to Egyptian fractions. If the number is not already a unit fraction, the first method in this list is to attempt to split the numerator into a sum ...