lgeba Substitution in algeba Remembe... In an algebaic expession, lettes ae used as substitutes fo numbes. Example Find the value of the following expessions if s =. a) s + + = = s + + = = Example Find the value of the following expessions if a = and b =. a) (a + ( + ) = = (b + a) (a + ( + ) ( + ) = ( + ) ( + ) = = Find the value of the following expessions if x =. x a) + x = x + = c) = d) x + + x = e) + x = f ) x + x + = Find the value of the following expessions if c = and d =. a) c d + = + (d c) = c) d + c + = d) (d + c) (d c) = = e) c d f ) (c d) + d c = Find the value of the following expessions if u =, k = and t =. a) (t ) + (u + k) = k (t k) + u = c) (k + u) + (t u) = d) (u + k) (t k) = e) (t u) + (k + t) = f ) k (u t) (u k) = _text.indb // :
Find the value of the following expessions if x =, y = and z =. a) + z = + z = c) (y z) x = z d) z x + y = e) (z y) (y x) + = x f ) z + (y x) (y + x) = y x z The lettes c and d stand fo two whole numbes. a) Which two numbes could c and d stand fo if cd =? What if cd = and c d =? Look at you answes to pat a) to find c and d. c) cd = and c d = What is the value of c and d? The lettes x and y stand fo two whole numbes. a) x = y and x + y = What is the value of x and y? x = y and x + y = What is the value of x and y? Ty this a a = b What is h? b = c g = h c = d f = g W d.. table = e + e = f a) Choose a -digit numbe. This numbe is a. Feed it into the flowchat. What numbe is h? c) Ty this with othe -digit numbes. What do you notice? Why? d) What would happen if a was a -digit numbe? _text.indb // :
Simplifying algebaic expessions Lettes can be used to stand fo an unknown numbe. s with aithmetic, in algeba, do the division fist then the multiplication, then addition, then the subtaction. Example Simplify a a + a + a a Example Simplify s a a + a + a a = a + a + a a a = a a = a s Example Simplify n c c n c c = n = n = s = s = s = s Simplify each of the following expessions. a) z z + z + z p + p p p + p c) v v + v v v d) c b c + b e) f u f + f u f ) x + x w + x + w g) t + t h) d + g g + d g i) k + d + d d k j) e + e h h e k) u + s s s + u l) y a + y y + a m) c v c + g + v n) h s + h t + s o) q + q t z + z p) g c g c + d q) s t t + h s ) j + j d d s) b + h + h b h + g t) u u + j + j f u u) + + t y y Each of the following algebaic expessions has been simplified. Wite two diffeent expessions involving addition and subtaction fo each befoe they wee simplified. a) y a c) t d) x + y e) e d _text.indb // :
Simplify each of the following expessions. a) m a c) w d) t e) c f ) k g) b c h) z y i) h j) u k k) t l) f m) n g n) s o) q p) h q) d e ) s) b p t) z n u) y j j g e b n z d s u u j y f Each of the following algebaic expessions has been simplified. Wite two diffeent expessions involving multiplication and division fo each befoe they wee simplified. a) g c c) d d) t e) a Ty this Choose of the expessions you simplified in questions and and check you answes by substituting numbes fo lettes. Example Ty the expession and you answe. If z = a) z z + z + z z + + = = = _text.indb // :
Equations Equations have symbols o lettes to epesent unknown numbes. When you find the value of the lette you have solved the equation. Example + g = g = So g = To check: + = Example a + = a = = So a = a = To check: + = Example a = a = (To find out what a stands fo we multiply both sides by.) a = To check: a = = Wite the value of each lette. a) c = c= + f = f = c) s = s= d) y + = y = e) t = t= f ) m = m= g) k = k= h) + j = j= i) n = n= j) g = g= Wok out the value of each lette. Show all you woking. a) z =. g t = c). = s d) = e). = k f ) = a g) z =. h) f =. i). = j). = h k).n = l). = d j _text.indb // :
Wok out the value of each lette. a) x + = x= a = a= c) y = y= d) c + = c= e) z = z= f ) + b = b= Solve these equations. Show all you woking. a) d + = h + = c) d +. =. d) +. = e + e) s = +. f ). =. + p. g) b. = h) d = i). +. =. + y Ty this Change these into equations. Solve the equation to find the missing numbes. a) I think of a numbe and multiply it by. I then subtact. The answe is. I think of a numbe and multiply it by. I then add. The answe is. c) I double a numbe and then add. The answe is. d) I think of a numbe and divide it by. I then subtact. The answe is. e) I double a numbe, add and then subtact.. The answe is.. _text.indb // :
Pattens and sequences You can often find the patten o ule in a sequence by looking at the diffeence between the numbes. What is the next numbe in this sequence? Each numbe is less than the pevious one, so the next numbe is. The ule is subtact. fomula (plual fomulae) uses lettes o wods to give a ule. What is the ule fo this sequence of numbes? n? Look at the elationship between the pais of numbes. =. So fo n, the fomula is n. You can use this to find any numbe in the patten. What is the th numbe? = Wite the next two numbes and the ule fo each sequence. a) c) d)..... e)..... f ).... Wite the patten o ule fo each sequence. Wite Yes o No fo each question. a) Will be in this sequence? Will be in this sequence? c) Will be in this sequence? d) Will be in this sequence? e) Will be in this sequence? _text.indb // :
Choose the coect ule fo these sequences. a) n? n? n? n? c) d) n n n n + n + n + n + n n n n n n n n n Fo each of the sequences above, what is the value of if is? Ty this Shape numbe (S) Maths fo the Middle East P Numbe of ods (R) aw_.. The fomula fo this is R = S + a) How many ods will be used fo the th shape? How many ods will be used fo the th shape? c) Which shape numbe will use ods? d) What is the fomula fo this sequence of ods? Maths fo the Middle East P aw_.. _text.indb // :
Functions and elationships The ule fo a sequence is: multiply by and then subtact. x In Out The function can be shown as = Maths fo the Middle East P aw_.. This is the table of esults showing the sequence. Copy and complete a table of esults fo each function. a) = + c) = d) = e) = f) = + g) = h) = + i) = j) + = k) + = l) + = = Wite the function and complete each table of esults. a) c) d) _text.indb // :
e) g) f) h) ssessment Wite the value of each lette in these equations. a) + z = z= g = g= c) n = n= d) h = h= e) + c = c= f ) x + = x= Wite the ule and the next two numbes in each sequence. a) c) d) e) f ) a) What is the function fo this sequence? = What is the value of if is equal to? _text.indb // :