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Unit A
Prime numbers Multiples, Factors and Prime Numbers LCM and HCF Rounding Numbers Ratios Metric and Imperial Units Sequences Finding the nth term Making Formulas from words Basic Algebra Solving Equations Rearranging Formulas Drawing Triangles Loci and Construction Pythagoras theorem and bearings Trigonometry 3D Pythagoras and trigonometry Coordinates Sampling Methods Mean, Median, Mode and Range
Multiples, Factors and Prime Numbers
FACTORS The factors of a number are all the numbers which go into the number exactly, with no remainder. For example the factors of 6 are 1, 2, 3 and 6. Remember that 1 and the number itself are always factors of any number, and these two factors are called trivial factors because they are obvious. PRIME NUMBERS A prime number has no factors except 1 and itself, for example, 2, 3, 5 and 7 are all prime numbers. A prime number must have two factors, 1 and itself, so 1 is not a prime number. The prime numbers less than 60 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53 and 59 - it is helpful to be able to recognise them. MULTIPLES A multiple of a number is any number that it goes into, for example 6, 12, 18, 24, 30 and 36 are all multiples of 6. Any number is of course a multiple of itself since it goes into itself once. The multiples of a number are therefore the numbers that make up its “times table”.
Prime Numbers
1) Prime Numbers don't divide by anthing. For example: The only numbers that multiply to give 7 are 1 x 7 The only numbers that multiply to give 31 are 1 x 31 The only way to get any prime number is 1 x itself. 2) They end in 1,3,7 or 9. 1) 1 is not a prime number. 2) The first four prime numbers are 2, 3, 5 and 7. 3) Prime numbers end in 1, 3, 7 or 9. (2 and 5 are the only exception for this rule.) 4) But not all numbers ending in 1, 3, 7 or 9 are primes.
LMC and HCF
HCF The highest common factor (HCF) of two whole numbers is the largest whole number which is a factor of both. Consider the numbers 12 and 15: The factors of 12 are : 1, 2, 3, 4, 6, 12. The factors of 15 are : 1, 3, 5, 15. 1 and 3 are the only common factors (numbers which are factors of both 12 and 15). Therefore, the highest common factor of 12 and 15 is 3. LMC The lowest common multiple (LCM) of two whole numbers is the smallest whole number which is a multiple of both. Consider the numbers 12 and 15 again: The multiples of 12 are : 12, 24, 36, 48, 60, 72, 84, .... The multiples of 15 are : 15, 30, 45, 60, 75, 90, .... 60 is a common multiple (a multiple of both 12 and 15), and there are no lower common multiples. Therefore, the lowest common multiple of 12 and 15 is 60.
Loci And Construction
In mathematics they usually mean one of two things when they talk about a locus: 1. The path traced out by a moving object. 2. All the points that satisfy some conditions