DSC1520 RevisionPack.

Study Unit 1 : Mathematical preliminaries Chapter 1 : Sections 1.1 – 1.6 1. Basics • Numbers: different type of numbers – Natural, Real, etc. Also called constants • Basic operations o + (add); 2 + 3 = 5 o – (subtract); 3 – 2 = 1 o x (multiply); also •; 3 x 2 = 3•2 = 6 o ÷ (division) also / or fraction ( 1 2 = 1 divide by 2); 6÷3=6/3= 6 3 =2 Remember: 1 x anything = anything 1 x 8 = 8 0 x anything = 0 0 x 4 = 0 1 + anything = one more than anything 1+345=346 0 + anything = anything 0+34=34 anything ÷ 0 = not allowed 12 ÷ 0 = not allowed 0 ÷ anything = 0 0÷7=0 Page 2 of 167 • Brackets ( ) : group operations together (3+4)–3 = 7 – 3 = 4 • Order of operation: BODMAS Brackets; Of; Divide; Multiply; Add; Subtract 40 – 4 x (5 + 8) + 20 = 40 – 4 x (13) + 20 = 40–52+20 = 8 • Variables: used for unknown or generalisation of things: place holder: use alphabetic characters for example X or A or Y. Can take on different values 3x + 2y +7g + x 3x is known as a term with coefficient 3 and variable x Remember : the last term x has a coefficient value of 1 in front of it namely 1x o Operations on variables or unknown:  + and – : only if same variable, then + or – coefficients and variable stays the same 3x + 4x + 3 = (3 + 4)x + 3 = 7x + 3 5x – x – 6 = (5 – 1)x – 6 = 4x – 6 Page 3 of 167  x and ÷ : only if same variable, then x and ÷ coefficient and unknowns 3a x 4a = (3x4) (a x a) = 12a 2 = 2 xx x = 2x • Laws of operations o Commutative law : order  a + b = b + a 3+4=4+3=7  a x b = b x a 3×4=4×3=12  a – b ≠ b – a 4–3=1 ≠ 3–4=–1  a ÷ b ≠ b ÷ a 4÷2=2 ≠ 2÷4=0,5 o Associative law: ( )  (a + b) + c = a + (b + c) (3+4)+2=7+2=9 3+(4+2)=3+6=9  (a x b) x c = a x (b x c) (3×4)×2=12×2=24 3×(4×2)=3×8=24  (a – b) – c ≠ a – (b – c) (3–4)–2=–1–2=–3 3– (4–2)=3–2=1  (a ÷ b) ÷ c ≠ a ÷ (b ÷ c) (12÷2)÷2=6÷2=3 12÷(2÷2)=12÷1=12