CHEMISTRY 047 STUDY PACKAGE

Transcription

1 CHEMISTRY 047 STUDY PACKAGE Tis maerial is inended as a review of skills you once learned. PREPARING TO WRITE THE ASSESSMENT VIU/CAP/D:\Users\carpenem\AppDaa\Local\Microsof\Windows\Temporary Inerne Files\Conen.Oulook\JTXREBLD\Cemisry 047 (add Scienific Noaion).doc/Marc 7 00

2

3 SOLVING FORMULAE (PART A) INTRODUCTION A formula is an equaion wi leers. Solving a formula involves manipulaing i, so a a paricular leer is "isolaed" in e formula. Te ecniques used in manipulaing formulae are similar o ose previously discussed in solving equaions. FORMULAE WITH ONE TERM ON EACH SIDE Wen solving a formula, firs locae e leer a you are asked o solve for. Ten, "isolae" e leer in e same way as solving equaions. x () x () ax b c b x ac, solve for x x 0 Solve F Fr v m mv, for m r Solve a b c d b d a c, for d bc a d If Force (F) equals mass (m) imes acceleraion (a), wa is e mass? Te volume (v) of a cylinder equals pi ( π) imes e radius squared imes e eig. Wa is e eig? F ma v π r F v m a r Te mass equals e force divided by e acceleraion. Te eig equals e volume divided by e produc of π and e radius squared.

4 FORMULAE WITH BRACKETS Wen solving a formula, a bracke can be oug of as one uni. Noe a e bracke (a + b) beaves in an idenical manner o e leer x in e examples below. A A x x, for A (a + b), for A A or (a b) a b Wen solving for a leer wic is inside a bracke, solve for (or isolae) e bracke firs. Ten a erm wic is added will be subraced on e oer side of e equaion. A (a b), for a A A a b A b b a or a (V V V + V V S ) S, for V S V or V S V Solve: EXERCISE I V W. a) A lw, for w b) I, for V c) E R I, for I d) I pr, for e) E mc, for m f) A r, for A 4 r, for π ) F mv g) V, for r i) V r, for r a c w j), for x k) A b d, for b l), for d x w d kmm m) F r, for k n) E e R r, for e r. a) A (a b), for b) A (c d), for d c) C (F ), for F d) s 9 e) s (V V ), for V f) s (V V ), for H m(, for H )

5 RULES FOR WORKING WITH POSITIVE AND NEGATIVE NUMBERS 4 Tink of combining numbers raer an adding or subracing em. RULE I: If e signs are e same, add e numbers, and use e same sign. RULE II: If e signs are differen, ignore e signs, subrac e smaller number from e larger and use e larger number s sign. Examples a) + Te signs are differen, so subrac e numbers ( ) and use e sign of e larger ( ) + b) 9 Again, e signs are differen, so subrac e numbers (9 7) and use e sign of e larger (e 9 wic is negaive) 9 7 c) Te signs are e same (bo negaive), so add e numbers ( + ) and use e same sign ( ) d) ( ) Use e rules for muliplicaion: negaive imes negaive is a posiive, so ( ) + 8 e) ( 6) + 6 RULE III: Wen muliplying or dividing, if e signs are e same, e answer is posiive. RULE IV: Wen muliplying or dividing, if e signs are differen, e answer is negaive.

6 Examples a) ( ) ( ) Te signs are e same, so e answer is posiive. b) ( ) (4) Te signs are differen, so e answer is negaive. c) ( ) () ( 6) () () () 6 ( ) ( 6) () d) 0 or ( 0) (0) Te signs are differen, 0 so e answer is negaive. e) 8 9 or ( 8) ( 9) 9 Te signs are e same, so e answer is posiive. EXERCISE II (4) ( 6) or (4) x ( 6). () ( 8) or () x ( 8). ( 0) ( ) or ( 0) x ( ). (4) ( ) ( 0) ( ) 9. ( 0) 0. (7) ( ). () (8). ( 4) ( 6) ( 7). ( 48) (8) 6. ( 6 ) ( 4) or x 4

7 . or x 7 7. (.4) (.7) or (.4) x (.7) (.6) ( 4.8) (.) (.) ( 4.) 8. (.6) (.8) (.) ( 4.) (4.68) (.) (4.) (.4) (.) (.4) (.) ( 0.)

8 SUBSTITUTION Leers are ofen used o represen numbers for general calculaions. For example, if you borrow $000 (Principal P) a % ineres (rae r) for years (ime ), you could calculae e amoun owed a e end of wo years by using e general formula below. Amoun owed Principal + Principal x rae x ime P + Pr (000) + (000) (0.) () Amoun owed is $40 Noe:. Wen subsiuing, always sore e number in a bracke.. Cange % o a decimal 7 EXAMPLES USING SUBSTITUTION In e following examples, numbers are subsiued (wi brackes). Ten e order of operaion (B.E.M.A.) is compleed. Evaluae xy x y, if x and y 4 xy x y ( ) (4) ( ) (4) ( ) (4) (+) (4) 8 0 Evaluae e surface area (A) of a ball, if A 4 r wen r and.4 A 4 r 4 (.4) () 4 (.4) () 4 EXERCISE III. Evaluae e following: a) ( ) ( ) + () ( ) b) ( )( )() ( )( ) c) ( )( 6) ( 8) 4 d) ( + 4 ) () (+) e) ( )( ) (4 6) f) ( ) () + ( ) () g) ( ) ( ) 8 ) ( ) ( + 9) ( ). Subsiue and evaluae e following: a) Amoun owed P + Pr, if P $00, r 9%, and years b) Amoun owed if P $000, r %, and year c) xy xz, if x, y, and z

9 ANSWERS 8 I Answers (Formula Solving) A W I E. a) w b) V IR c) I d) e) m l E pr c f) A r V g) 4r A k) b l) d A. a) a b f) sm ( ) H dw w ) r m) mv i) F Fr m m V r k n) e j) x re R r A 9 s b) c d c) C F d) V V a c s V V e) II Answers (Working wi Posiive and Negaive Numbers) III Answers (Subsiuion). a) 4 b) c) 9 d) 7 e) f) g) 4 7 ) 9. a) $ 7.00 b) $ 7.00 c) + 4

10 9 SCIENTIFIC NOTATION SCIENTIFIC NOTATION WITH LARGE NUMBERS A large number can be convered ino a one-digi number imes e number 0 o a power. Tis process convers e number ino Scienific Noaion. Noe e lis of exponens for e base 0 o e rig ,000 0,000 00,000,000,000 x,000,000,00. x,000 x 0 6. x 0,000,000 SCIENTIFIC NOTATION WITH SMALL NUMBERS A small number (i.e. a decimal less an ) can also be convered o a one-digi number imes e number 0 o a negaive power. Noe e lis of negaive exponens for e base 0 o e rig..000 x.000 x x.0 4. x CONVERTING TO AND FROM SCIENTIFIC NOTATION Wen convering a number ino scienific noaion, move e decimal place o creae a one-digi number. Muliply is one-digi number by e appropriae power of x 0 0,000,000.0 x x x 0 4 Wen convering from scienific noaion ino a number, move e decimal poin e appropriae number of places o e rig (for large numbers) or o e lef (for small numbers).. x 0 0. x 0 8 0,000,000. x x 0. USING SCIENTIFIC NOTATION Wen using scienific noaion, your answer mus ave a one-digi number. In e following examples, numbers are convered ino proper scienific noaion (i.e. wi a one-digi number). x 0. x 0 x 0. x 0 4. x 0 - x 0-4. x 0 4. x 0

11 SCIENTIFIC NOTATION AND THE THREE RULES OF EXPONENTS Wen using scienific noaion, noe e following: Answers mus be in proper scienific noaion (i.e. a one-digi number). Negaive powers of 0 are no convered ino posiive powers. Fracions mus be convered o decimals. RULE I : Wen muliplying wi e same base, add powers. (.0 x 0 4 ) (.0 x 0 7 ) 6.0 x 0. x 0 4 x.0 x 0 7. x 0. x 0 RULE II : Wen dividing wi e same base, subrac powers. 0 9 x 0 x 0 4. x x x x 0 RULE III : Wen a bracke is aken o a power, muliply powers. 6. x 0 (.0 x 0 ).0 x 0 6 ( x 0 4 ) x x 0 6 x 0. x 0 0 EXERCISE. Conver o Scienific Noaion: b) c) a) 6000 d).00 e).0006 f) ,000 6,700,000. Conver o numbers: a).6 x 0 4 b) x 0 6 c). x 0 d) x 0 e).68 x 0 4 f).0 x 0. Conver o proper scienific noaion (i.e. a one-digi number): a) x 0 4 b) x 0 c). x 0 6 d). x 0 4. Simplify e following and wrie your answer in proper scienific noaion: a) (. x 0 4 ) (.0 x 0 ) b) (.0 x 0 4 ) (.0 x 0 ) c) (6. x 0 ) (.0 x 0 ).0 x 0 f) 9.0 x x 0 d) 4.0 x x 0 e) 6.0 x 0 g) ( x 0 4 ) ) (.0 x 0 ) i) (.0 x 0 )

12 ANSWERS. a) 6 x 0 b). x 0 c).67 x 0 7 d) x 0 - e) 6. x 0-4 f) x 0-6. a) 6,000 b) c) 0 d).00 e) f) 0.. a). x 0 b). x 0 - c) x 0 d). x a) 4. x 0-7 b). x 0 0 c).4 x 0-4 d) x 0 8 e) x 0 g) 8 x 0 ). x 0 - i) 4.0 x 0 4 f). 0 7