ALGEBRA: ALGEBRA Basic Concepts
Sums and Products: Sums and Products Sums r+r+r+s+s =3r+2s d+d – ( a+a+a+a ) = 2d – 4a Products 8 x b x b x a x a x a = 8a 3 b 2 k+k – 3 x d x d x d = 2k– 3d 3
ALGEBRAIC NOTATION: ALGEBRAIC NOTATION Rules: We leave out the “x” signs between any multiplied quantities E.g : a x b is written as ab We write numbers in front of letters: E.g : b x 3 is written as 3b We write the letters in alphabetical order: E.g : b x a is written as ab More Examples: t x 6s = 6st 4 x k+m x 3 = 4k +3m 3x( r+s )= 3( r+s )
Language of algebra: Language of algebra 4y 2 - 6x + 2xy – 5 + x 2 Is this an equation or an expression? How many terms does it contain? State the constant tern State the coefficient of X – the coefficient is -6 X 2 - the coefficient is 1
substitution: substitution Substituting the variable represented by a letter with the given number If we substitute negative numbers we have to place it in BRACKETS Examples if a= -2 and b=4 then 5a + 3b = 5 x (-2) +3 x 4 = -10 +12 = 2 b. For a = 2, b = -1 and c = 3 evaluate: 3a - 2b = 3 x 2 – 2 x (-1) = 6+2 = 8 c 2 +b = 3 2 + (-1) = 9 – 1 = 8
PowerPoint Presentation: By using substitution answer the following questions: ( i ) Work out the value of 2a + ay when a = 5 and y = –3 ( ii) Work out the value of 5t ² - 7 when t=4 Work out the value of 5 x + 1 when x = –3 (iv) Work out the value of D when: D = ut + 2 kt If u = 5 t = 1.2 k = –2 Page 65 ex 2E Questions 1, 3 and 5
Collecting like terms: Collecting like terms Like terms are algebraic terms which contain the same variables to the same indices 2xy and 4xy are like terms 3x 2 and 4x are NOT like terms
PowerPoint Presentation: Simplify ( a ) 3 g + 5 g ( b ) 3x + y - x + 2y (c) 4a + 9b – 3a – 5b ( d ) 3p + q – 2p – 2q (e) 2w – 4v –3w + 2v (f) 3x² - 2x + x² + x
Product and quotient simplification: Product and quotient simplification Simplify: 2 × 5 = 10 4 x 3 2 = 12 3 6 x 2 = 30 4