HCI AM Topical Revision Worksheet 1 (Indices & Surds))

Page | 1 Hwa Chong Institution Integrated Programme/mainstream Secondary Three Mathematics Name: _________________________________ ( ) Class: _________ Date: _____________ Surds & Indices, Equations involving Indices & Surds AM Revision Practice 1 1 Express ( ) 1 21225 5 35 n n n + − − in the form ( )5na , where a is a constant, and state the value of a. [3] 2 Solve the equation 2 7 2 1.x x x+ − = − [4] 3 Without using tables or calculators, evaluate 10 ,x given that 2 1 1 32 5 2x x x− + += . [3] 4 Given that ( ) 25 5 125 yx = and ( ) 2 181 3 27 xy − = , find the values of x and y. [4] 5 By using appropriate substitution, or otherwise, solve the equation ( ) 1116 12(4 ) 64 4 1 4 .x x x x +−− = + − [4] 6 A rectangular block has a square base. The length of each side of the base is ( )23+ cm and the volume of the block is (2 3 3 2)+ cm 3. Find, without the use of a calculator, (a) the area of the base, [2] (b) the height of the block in the form ( )23ab + cm, where a and b are integers. [3] 7 Without using a calculator, find the value of m such that 6 108 9 2 62712 243 2 m + −  = . [4] Be consistent in your practice!!

Page | 2 Solutions to AM Revision Practice 2 1 ( ) 1 21225 5 35 n n n + − − ( ) ( ) ( ) ( ) 1 22 2 221 2 55 5 35 55 5 35 155 5 35 245 5 3 8 55 nn n nn n n n n n  + + − = − =  −= = = 2 2 7 2 1x x x+ − = − ( )( ) 22 2 2 2 7 2 2 1 7 2 1 2 7 2 1 4 4 0 4 2 6 0 2 3 0 2 3 1 31 (rej) or 2 x x x x xx x x x xx xx xx xx + − = − + − = − − = − + = − − = − − = − + =− = you forgot to reject again??!! 3 2 1 1 32 5 2x x x− + += 2 1 3 1 4 2 5 1 2 5 5 1 1610 5 x x x xx x − − − + − =   = = 4 ( ) 25 5 125 yx = ( ) 12 32 2 4 2 3 55 23 2 4 6....(1) 181 3 27 33 4 2 3.....(2) 2(1) (2) 8 2 4 2 12 3 12 9 3 4 364 4 3 xy xy xy yx xy xy x y x y x x y + − −− = += += = = − =− + + + − = − = =  = −  = 3 ,34xy==

Page | 3 5 ( ) 1116 12(4 ) 64 4 1 4x x x x +−− = + − 2 44 12(4 4) 64 1 4 4 x x x x −  = + −  Let 4xy= ( )( ) 2 2 48 16 64 0 63 64 0 64 1 0 64 or 1 (n.a) 4 64 3 x y y y y yy yy yy x − − − + = − − = − + = = =− = = Gotcha! reject 1y=− 6 (a) Area of base ( ) 2 23=+ 2 2 6 3 5 2 6 = + + =+ (b) Height 2 3 3 2 5 2 6 += + ( ) 2 3 3 2 5 2 6 5 2 6 5 2 6 10 3 4 18 15 2 6 12 25 4 6 10 3 12 2 15 2 12 3 3 2 2 3 3, 2ab +−= +− − + −= − =−+− =− = =− 7 6 12 + 108 27 − 9 243      2 2 = m 6 6 12 6 3 9 243 262712 12 243 243 m + −  = 4 3 2 3 3 81 262 9 27 213 3 3 2 693 m m  + −  =  + −  = 8 3 2 69 8 669 8 9 m m m = = = healthy and positive results??!!!