PAPER 1 - TOPICS

Numbers

1. Natural numbers This is the set of positive whole numbers: N = {1,2,3,4,5,…} 2. Integers This is the set of positive whole Z numbers, negative whole numbers and the number zero: = {…,-3,- 2,-1,0,1,2,3…} 3. Rational numbers A rational number (i.e. a fraction) is a number of the form where a and b are both integers, with b ≠ 0. In other words, a rational number is a ratio of two integers.

Example: 4. Irrational numbers These are all real numbers with the exception of rational numbers: R \ Q. In simple terms, irrational numbers are numbers that go on forever, i.e. they cannot be written on the page. Examples: 5. Real numbers This is the set of all numbers including decimals and fractions: R={-∞≤x≤∞} Other important concepts 6. Prime numbers These are numbers that have only 2 factors; the number itself and 1.

Prime numbers: {2,3,5,7,11,13,17,19,…} 7. Lowest common multiple (LCM) Example: The LCM of 5 and 7 is 35 as it is the lowest number that both 5 and 7 divide into evenly. 8. Highest common factor (HCF) Example: The HCF of 9 and 7 is 63 as 63 is the highest number that divides into both 9 and 7 evenly. 9. Absolute value (modulus) of a number: |Number| = positive value of that number. ∈ 10. Scientific notation: a ×10 n , where n Nand1≤ a <10. 11. Percentage error 12. Significant figures To round off a number to a given number of significant figures, change the number into scientific notation (i.e. a × 10n) first. The number of digits in ‘a’ corresponds to the specified number of significant figures. 13. Distance, speed and time Distance = Speed x Time;