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IS '167B:,%@,.Z-67B:,%@},.'# A- APb#+2Q)3,*0*0# Al6-?:<, A v 6- 0Q A }A" AP A  0 A 6-6-?:,$ 6-&"6-?:,$ @& A }4~SB&6-?:A d,7<,0~Q A`%6-A:7<+B:,&,%,,%6-8<, " AV AX+6}8<,-8<,& 8<, +68<,- 6-&6-7<,0~R A  "6-?:, @  6- A } 0 A6-?:A d,"$5 6-?:,-@E"--68<,-1 5 ,-@-}$68<,-( , * 6-6-6-6-!6-'6-*$ 4)4~ET6-* "6-?:,$4 6-?:, @}>AdAUR"F:Ad,"AU" AP\6.>:?:A!,,$;'?:A!<<@# AG6-?:,V6-?:A!E,Z6-?:<@$,#6-?:<<<,)6.3 A<6-?:,K6-?:A!E,Z6-?:A}!E,$G6-?:<,)6.NUMBER CORRECT = =67B:,,.=:8<,,G AM6-?:<@,/6.NUMBER INCORREC}T = C67B:,,.=:8<,,M AM6-?:<@,/6.NUMBER UNANSWERED = C67B:,,.=:8<,,M A6-?:A }R,$6-6-@'6-@36-@?6-@K6-@W6-@c6-@o6-@|6-6}@6-W6-A!f6-A!g'6-A!d36-BH2?6-BQK6-W6-J 6.A6.B6.} *6.>:@0,26.C:6.DB6.EJ6.FG 6.M6.P6.R=6.ӠŠҠϠG6.~SC}6. W6-A!'6-A!0'6-A!B3-A!3?-A!6K6-A!HW6-A!T76-?:A!!,@%}-6-?:A d,7 A D:ALGEBR.BASANF1F2F3FLINTTLTXSCSKTMCPERWRSRTSRSSCPXYYLNX1Signed Numbers~A signed number is positive + (ornegative - ) from 0.Addition~To add signed numbers that are alike in}sign& add and keep the same sign.` Add~ -5 +7` + -3 + +6` -- ---` } -8 +13~RAIf the signs are unlike& subtract anduse the sign of the largest absolutevalue.` Add~ -8` } + +3` --` -5~RASubtraction~Change the sign of the bottom numberand follow the same rules }as inaddition.` Subtract~ +7` - -3` ---` +10` Subtract~`(+3}) - (+5) = (+3) + (-5) = -2~RAMultiplication~To multiply two numbers with the samesign& the answer is positive (+).` } Multiply~ (+3)(+7) = +21` (-4)(-3) = +12To multiply two numbers with differentsigns& the answer is ne}gative (-).` Multiply~ (-5)(+4) = -20` (+4)(-6) = -24~RADivision~The same rules apply as inmulti}plication.` Divide~ +6` -- = +3` +2` -8` -- = -2` } +4~RALinear Equations~Order Of OperationsRules~1. Remove fractions and decimals bymultiplication.2. }Remove parenthesis bymultiplication.3. Combine similar terms on each sideof the equation.4. Collect unknowns on one sid}e of theequation and constants on the otherside.Note~ When a term crosses the equalsign it changes its sign.~RA5. Divi}de both sides by thecoefficient.Note~ Use the same number as thecoefficient& not the opposite sign.Example~ 7y + 3 = 3y} + 19` 4y + 3 = 19` 4y = 16` y = 4 Ans.~RAExample~ 3/4 y + 2 = 2/3 y + 3Multipl}y by 12~ 9y + 24 = 8y + 36` y + 24 = 36` y = 12 Ans.Example~ 5/9 x + 2 = }7/2 x - 3Multiply by 18~ 10x + 36 = 63x - 54` 10x = 63x - 90` -53x = -90` } x = 1.7 Ans.~RALiteral Equations~1. Have more than one variable.2. Follow same rules as numericaleq}uations.Example~ ax + b = c + dSolve for x~ ax c + d - b` -- = ---------` a a` } c + d - b` x = --------- Ans.` a~RASystems Of Linear Equations1. Eliminate one} unknown by linearcombination.Example~ Solve for x~` 4x - 2y = 2` 5x - 2y = 14Multiply by -1~}` -1(5x - 2y = 14)` 4x - 2y = 2` -5x + 2y = -14` --------------` } -x = -12` x = 12 Ans.~RAQuadratic Equations~1. Generally have 2 roots.2. Get all equal to 0.}3. Solve by factoring.` 2Example~ x + 7x + 12 = 0` (x + 4)(x + 3) = 0` x = -4 or} -3 Ans.~RA` 2Example~ x - 16 = 0` 2` x = 16` x = + or - 4} Ans.~RA4. If you cannot solve by factoring&use the quadratic formula.` _______` / 2`} x = -b +/- \/ b -4ac` -----------------` 2a~RA` 2Example~ x - 2x - 1 = 0` } ___________` 2 +/- \/4 -4(1)(-1)` -------------------` 2` _` 2} +/- \/8` = ---------` 2` _` = +/- \/2 Ans.~RARadical EquationsWhen solving equati}ons with radicals&put the radical alone on one side& thensquare both sides to remove theradical. You must check your answe}r(s).In some cases one or more answers mustbe rejected.` _Example~ \/y = -6` y = 36 Ans.` } _____Example~ \/y + 5 = 7` y + 5 = 49` y = 44 Ans.~RAExample~` _ } _ _` 4\/2 + 3\/2 = 7\/2 Ans.Note~ Only like radicals can be added;for example~` _ }_` \/2 cannot be added to 2\/3.~RANote~ Radicals are simplified byremoving any perfect square factors.` ___ } ___Example~ \/578 + \/450 = ?` ___ ___` \/289x2 + \/225x2 = ?` _ _ _` 17\}/2 + 15\/2 = 32\/2 Ans.~RAIn simplifying radicals that contain asum or difference in the radical sign;first add or subtra}ct and then take thesquare root.~RA` _________` Example~ / 2 2` / y + }y` / -- --` \/ 9 16` ___________` / 2 2` } / 16y + 9y` / ----------- =` \/ 144` ____` } / 2` / 25y 5y` / ---- = -- Ans.` \/ 144 12~RAReducing Algebraic Fract}ions~1. To reduce algebraic fractions÷ the numerator and denominator bythe same factor. Do NOT cancel terms.` } 2` 2y - 8yExample~ Reduce~ ---------` 4 3` 4y -16y` } 2y (y-4) 1` -------- = --- Ans.` 3 2` 4y (y-4) } 2y~RA` 2 5`Example~ Find the sum~ - + -` C y(The lowest common denomin}ator is Cy)~` 2 y 5 C` - x - + - x -` C y y C` 2y 5C` } = -- + --` Cy Cy` 2y + 5C` = ------- Ans.` Cy~RAExample~ } Multiply~` Find the product~` 3 3` a b` -- x --` 2 2` } b a` 3` a x b` = -- --` 2 1` b` a b` }= - x - = ab Ans.` 1 1~RAComplex algebraic fractions aresimplified just as in arithmetic.Multiply each term }of the complexfraction by the common denominator.` 1 1` - + -` a bExample}~ -----` ab` b + a` ----- Ans.` 2 2` a} b` Multiply each term by ab~Note~ DO NOT CANCEL TERMS.~ET~ETAddition~To add signed numbers that are alike inI~Q1. (+5) + (-9) =(a) -4 (b) -5 (c) 0 (d) +4 (e) -1~RCA1. (a) -4 Ans.` +5` + -9` ----` -4 Ans.~RA~Q}2. (-3) + (-6) =(a) -3 (b) -9 (c) 1 (d) -6 (e) 0~RCB2. (b) -9 Ans.Note~ When adding two numbers with likesigns& ad}d and keep the same sign.` -3` + -6` -----` -9 Ans.~RA~Q3. (+3) - (-7) =(a) 4 (b) -4 (c) 10 (d) 0 (e) 5}~RCC3. (c) 10 Ans.` +3` - -7` ----` +10 Ans.~RA~Q4. (+12) - (-6) =(a) 15 (b) 18 (c) 6 (d) -18 (e) 4~RC}B4. (b) 18 Ans.Note~ Change the sign of the bottomnumber and follow the addition rule.` +12` - - 6` -----` +}18 Ans.~RA~Q5. (-5)(-3) =(a) -8 (b) 5 (c) 0 (d) 15(e) -15~RCD5. (d) 15 Ans.Note~ Negative times negative equals} apositive.` -5` x -3` ----` 15~RA~Q6. (-7)(+1/3)(-9) =(a) 22 (b) 11 (c) -21 (d) 0 (e) 21~RCE6. (e) }21 Ans.Note~ Multiply one at a time.` (-7) x (+1/3) = (+7/3)` (-7/3) x (-9) = 21 Ans.~RA~Q7. (-8)(+5)/(-2) =}(a) 20 (b) 10 (c) -4 (d) -20 (e) 0~RCA7. (a) 20 Ans.Note~ Do multiplication first& thendivision.` -8` x +5` } ----` -40` -40/-2 = 20 Ans.~RA~Q8. Solve for y~ 4y + 3 = 9(a) 2/3 (b) 2 (c) 3/2 (d) 1/2(e) 1~RCC8. (c) 3/2} Ans.Note~ Subtract 3 from both sides& thendivide by 4.` 4y 6` -- = -` 4 4` y = 3/2 Ans.Note~ Isolat}e the variable on one sideby adding or subtracting& then dividethe coefficient in front of thevariable to both sides.~RA}~Q` K K9. Solve for K~ - + - = 1` 5 6(a) 30/11 (b) 3 (c) 20/11 (d) 0(e) 24/11~RCA}9. (a) 30/11 Ans.Note~ Find the common denominator (30)&then multiply both sides by thatnumber. Next& solve for the vari}able.` 30(K/5) + 30(K/6) = 30` 6K + 5K = 30` 11K = 30` K = 30/11 Ans.~RA}~Q10. Solve for y~ ay = by + c(a) c/(b - a) (b) (a - b)/c(c) ab/c (d) ab (e) c/(a - b)~RCE10. (e) c/(a - b) Ans.}Note~ Move all terms with y to oneside& and solve for y.` ay = by + c` -by = -by` ay - by = c`y(a - b) c}`-------- = -----` (a - b) a - b` c` y = ----- Ans.` a - b~RA~Q11. If k + y = 8m and k} - y = 6n& thenk is?(a) 4m + 3n (b) 7m + n (c) 2m + 3n(d) m + n (e) 4m + n~RCA11. (a) 4m + 3n Ans.Note~ Eliminate} one unknown; solve forthe other& then substitute.` k + y = 8m` k - y = 6n` 2k + 0y = 8m+6n` 2k 8m 6n`} -- = -- + --` 2 2 2` k = 4m + 3n Ans.~RA~Q12. If 8y = 3y + 15& then 4y + 5 =(a) 2 (b) 17 (c) 18} (d) 5 (e) 1~RCB12. (b) 17 Ans.` 8y = 3y + 15` -3y = -3y` 5y 15` -- = 0y + --` 5y 5y}` y = 3Therefore~` 4y + 5 =` 4(3) + 5 =` 12 + 5 = 17 Ans.~RA~Q13. What is the value of A in~` } 2` y = x + Ax - 5` when y = 19 and x = 3(a) -2 (b) -3 (c) 5 (d) 1 (e) 3~RCC13. (c) 5 Ans.` 2}` 19 = (3) + A(3) -5` 19 = 9 + 3A -5` 19 = 4 + 3A` -4 -4` 15 3A` -- = --` 3 3` 5 = A Ans.Note~ First sub}stitute the numbers forthe variables& then solve.~RA~Q14. If .69y = 2.07& then y =(a) 1 (b) 2 (c) 6 (d) 3 (e) .03~}RCD14. (d) 3 Ans.Multiply by 100 to get rid of thedecimal& then solve for the unknown.` 100(.69y) = 100(2.07) }` 69y 207` --- = ---` 69 69` y = 3 Ans.~RA~Q1 }5. If 5ky + 8 = 9ky&` then ky =(a) 2 (b) 3 (c) 8 (d) 4 (e) 1~RCA15. (a) 2 Ans.` 5ky + 8 = 9ky` - }5ky -5ky` 8 4ky` - = ---` 4 4` 2 = ky Ans.Note~ Treat ky as } one variable thensolve for it.~RA~Q16. Solve for y~` 2` y + 18 = 9y(a) 2 or 6 (b) 1 or 6 (c) 6(d) 6 or 3 } (e) -9~RCD16. (d) 6 or 3 Ans.` 2` y + 18 = 9y` -9y -9y` 2` y - 9y + 18 = 0(y - 6)(y - 3) = 0`} y = 6 or 3 Ans.Note~ Move everything to one side toget the equation equal to zero& thentreat it as a Quadrati}c Equation andfactor. Be careful to arrange thevariables in order of descending powersbefore factoring.~RA~Q` } 217. Solve for y~ 5y = 80(a) +/-2 (b) +/-4 (c) +/-8(d) +/-12 (e) +/-6~RCB17. (b) +/-4 Ans.` 2` }5y - 80 = 0` 2` 5(y - 16) = 0` 2` y - 16 = 0(y + 4)(y - 4) = 0` y = +/-4 Ans.~RA}~Q` 218. Solve for y~ 7y = 5y(a) 0 (b) 0 or 1/2 (c) 0 or 5/7(d) 1 or 2 (e) -1 or -2~RCC18. (c)} 0 or 5/7 Ans.` 2` 7y = 5y` -5y -5y` 2` 7y - 5y = 0` y(7y - 5) = 0` y = }0 or 5/7 Ans.Note~ Move everything to one side ofthe equation and factor out what is incommon& then solve.~RA~Q19. Sol}ve for y~` _____` / 2` \/ y + 8 - 2 = y(a) 2 (b) 4 (c) 0 (d) 10 (e) 1~RCE19. (e) 1 An}s.Note~ Move everything that does notbelong to the square root to the otherside; square both sides& then treat itas a qu}adratic equation.~RA19.` _____` / 2` \/ y + 8 = y + 2` 2 2` } y + 8 = (y + 2)` 2 2` y + 8 = y + 4y + 4` 8 = 4y + 4` -4 -} 4` 4 = 4y` y = 1 Ans.~RA~Q` __ __20. Find the sum of \/80 and }\/45.` _ _ __(a) 7\/5 (b) 7\/2 (c) 7\/10(d) 0 (e) 5~RCA` _20. (a) 7\/5 Ans.}` __ __ _ _` \/80 = \/16\/5 = 4\/5` +` __ _ _ _` \/45 = \/9\/5 = 3\/5` _ } _ _` 4\/5 + 3\/5 = 7\/5 Ans.Note~ Break the square roots down untilfully simplified& then add. (Only addth}e coefficient and keep the squareroot the same.)~RA~Q21. Find the difference between` __ __\/98 and \/32.` }_ _ _(a) 3\/4 (b) 3\/2 (c) 3\/1` _(d) 1 (e) 5\/3~RCB` _21. (b) 3\/2 Ans.` } __ __ _ _` \/98 = \/49\/2 = 7\/2` -` __ __ _ _` \/32 = \/16\/2 = 4\/2`  } _` = 3\/2 Ans.Note~ Follow the same format - as inthe previous example& but subtract like!}roots.~RA~Q22. Find the product of` ___ __\/32y and \/2y.(a) 64y (b) 4y (c) 1 (d) 8y (e) 2y~RCD22. (d) 8"}y Ans.` ____` ___ __ / 2\/32y x \/2y = \/ 64y = 8y Ans.Note~ Multiply what is in the squarer#}oots - then break it down.~RA~Q` ___23. Solve~ 1/y = \/.49(a) 5/7 (b) 2/7 (c) 10/7 (d) 0(e) 1~$}RCC23. (c) 10/7 Ans.Note~ Take the square root and thensolve for it.` 1/y = .7` .7y = 1`10(.7y) = (1)10` %} 7y = 10` y = 10/7 Ans.~RA~Q` 324. If y = 2.86 find (2.86) to thenearest hundredth?&}(a) 23.39 (b) 26.39 (c) 23 (d) 3.39(e) 1~RCA24. (a) 23.39 Ans.Note~ Raise it to the third power& thenround it off t'}o the nearest hundredth.(2.86) (2.86)= 8.18(8.18) (2.86)= 23.39~RA~Q25. Find the square root of 23409.(a) 15 (b) 5(} (c) 93 (d) 90(e) 153~RCE25. (e) 153 Ans.A quick way to identify the correctanswer is to take the __square root of)}the last digit. The \/9 = 3& leavingchoices (c) and (d) aspossibilities. 93 squared = 8649;whereas 153 squared = 23409.~R*}A~Q26. Find the square root of 15775.36?(a) 125.6 (b) 124.3 (c) 100(d) 26.3 (e) 24.3~RCA26. (a) 125.6 Ans. The squ+}are root ofthe last two digits is .6. The onlypossible answer among the choices is(a) 125.6.~RA~Q` __ ,} __27. Divide 6\/80 by 3\/20.(a) 2 (b) 4 (c) 8 (d) 1 (e) 16~RCB27. (b) 4 Ans.Note~ Simplify each root then divide-}.` ______ _` 6\/16 x 5 6 x 4\/5` ---@@@@@- = -------@` 3\/4 x 5 3 x 2\/5` _` .} 24\/5` ---@- = 4 Ans.` 6\/5~RA~Q` _______` / 2 2` / y + y2/}8. Find / -- -` \/ 16 9(a) 1/2y (b) 4y/12 (c) 5y/12 (d) 6y(e) 8y~RCC28. (c) 5y/12 Ans.Note~ C0}ombine what is inside the squareroot& then take the square root ofthat.` __________ ____` / 2 2 1} / 2` / 9y + 16y / 25y` / ---------- = / ----` \/ 144 \/ 144` 5y/12 A2}ns.~RA~Q29. n/7 + 3n/2 =(a) 23n/14 (b) 24n/2 (c) 20(d) 12n/7 (e) 0~RCA29. (a) 23n/14 Ans.Note~ Find the common 3}denominator&convert each fraction to thatdenominator& then add.` 2n 21n 23n` -- + --- = --- Ans.` 14 14 4} 14~RA~Q30. Combine into a single fraction~` 1 + a/b(a) ba/b (b) ab/b (c) a/b(d) (b + a)/b (e) 1~RCD30. (d5}) (b + a)/b Ans.Note~ b/b = 1` b/b + a/b =` (b + a)/b Ans.~RA~Q` k + y y + k31. Divide ----- by6} -----` k - y y - k(a) 1 (b) 2 (c) -1 (d) 0 (e) -11~RCC31. (c) -1 Ans.Note~ When dividing by a fracti7}on youmultiply by the reciprocal of thedivisor.`k + y y - k y - k`----- x ----- = -----`k - y y + k k - y` 8} -1(-y + k)` = --------` (k - y)` -1(k - y)` = 9} -------` (k - y)` = -1 Ans.~RA~Q` 1 - 1/y32. Simplify~ -------` :} a/y(a) (y - 1)/a (b) -1 (c) y-1(d) (a - 1)/y (e) (1 - a)/y~RCA32. (a) (y - 1)/a Ans.Note~ To simplify a ;}complex fractionmultiply by the common denominator.` 1 - 1/y y` = ------- x -` a/y y` y - 1<}` = ----- Ans.` a~RA~Q` 2 333. (2k /y) =` 6 5` 8k 2k=}(a) --- (b) bk/y (c) ---` 3 3` y y` 2 5(d) 6k /3y (e) 6k /y>}~RCA` 6` 8k33. (a) --- Ans.` 3` yNote~ When a power is raised to anotherexponent& ?}find the product of theexponents.` a b ab` Rule (x ) = x .~RA~Q` 1 1` @} - - -` k y34. Simplify~ -----` 4(a) (y - k)/2ky (b) (y - k)/4ky(c) y - k (d) 2yA} - k (e) y - k~RCB34. (b) (y - k)/4ky Ans.` 1 1` = - - -` k y (ky)` ----- x ----` 4 B} (ky)` y - k` = ----- Ans.` 4kyNote~ To simplify a complex fraction&multiply by the common denominatorC}.~RA~Q` 235. If (k - y) = 49 and ky = 4` 2 2` find k + y(a) 56 (b) 50 (c) 25 (d) 12 (D}e) 57~RCE35. (e) 57 Ans.` 2 2 2` (k - y) = k - 2ky + y = 49` 2 2` = E}k - 2(4) + y = 49` 2 2` k - 8 + y = 49` 2 2` k + y = 57 Ans.~ET~ET = v~Q` 2 4` - - -1. Simplify~ k y` -----` 3` 8y - 12k !G} 2y - 4k(a) -------- (b) -------` ky 3ky` 4k - 2y 8k - 2y 3ky(c) ------- (d) ------- (e)!H} -------` 3ky 3ky 2y - 4k~RCB~Q` _______` / 2 2` / y + y2. / - -!I}` \/ 25 144(a) -60y/13 (b) 60y/13 (c) -13y/60(d) 13y/60 (e) 17y/-60~RCD~Q` 23. If (k - y) = 15 an!J}d ky = 9&` 2 2` find~ k + y(a) 33 (b) 43 (c) 23 (d) 13 (e) 53~RCA~Q` 2 !K} 24. If (a + b) = 36 and a - b = 108&find a - b.(a) 4 (b) 5 (c) 6 (d) 10 (e) 3~RCE~Q5. (-7)(-4) =(a) -24 (b)!L} -28 (c) 28 (d) 1/-28(e) 1/28~RCC~Q6. (-5)(1/6)(-7) =(a) 35/6 (b) -35/6 (c) 6/35(d) -6/35 (e) 36/6~RCA~Q7. (!M}-9)(3)/(2) =(a) 2/27 (b) -2/27 (c) 27/2(d) -27/2 (e) 14~RCD~Q8. If 6y = 3y + 12& then 4y + 8 =(a) -63 (b) -36 (!N}c) 63 (d) 24(e) 12~RCD~Q9. If .42y = 1.26& then y =(a) .3 (b) .30 (c) .33 (d) 3.3(e) 3~RCE~Q10. If 9ky - 16 =!O} 5ky& then ky =(a) 1/4 (b) -1/4 (c) 1/2 (d) -4(e) 4~RCE~Q11. Find the sum of y/9 and 2y/4.(a) 3y/36 (b) 3y/13 (!P}c) 11y/18(d) 1 (e) 11/18y~RCC~Q12. Rewrite as a single fraction.` k` 1 + -` y` k - 1 y + k !Q} y - k(a) ----- (b) ----- (c) -----` y y k` 1 - k 1 + k(d) ----- (e) -----` y !R} y~RCB~Q` 4` 2 - -` y13. Simplify~ -----` !S} k` -` y` 2y - k 4 - 2k -2y + 4(a) ------ (b) ------ (c) -------`!T} 4 y k` 2y + 4 2y - 4(d) ------ (e) ------` k k~RCE~Q` !U} 214. Solve for y~ 3y = -4y(a) 0& 4/3 (b) 0& 3/4 (c) 0& -3/4(d) -4/3 (e) 0& -4/3~RCE~Q15. Solve for y` !V} ______` / 2` \/ y + 3 - 3 = y(a) -2 (b) -1 (c) 1/3 (d) -1/3(e) 9~RCB~Q` __ !W} __16. Find the sum of \/50 and \/32.` _ _ __(a) 5\/3 (b) 4\/3 (c) \/18` _ _(d) 9\!X}/2 (e) 7\/2~RCD~Q` _______` / 2 217. Value of \/ a + b =` _ _!Y}(a) 0 (b) > 0 (c) \/a + \/b(d) a + b (e) ab~RCB~Q` 218. y + 16y + 64 is divisible by~(a) y + 16 (b) y + 64 (!Z}c) y + 8(d) y + 4 (e) y + 32~RCC~Q` 219. Solve for y~ 3y = 75(a) +/- 5 (b) -5 (c) 5 (d) 1/5![}(e) -1/5~RCA~Q20. Find the difference between` ___ ___`\/243 and \/108.` _ _ _(a) -3\/3 !\} (b) 2\/3 (c) -2\/3` _ _(d) 3\/3 (e) \/3~RCD~Q21. Find the product of` __ __\/54 and \/12.` !]}_ _ _(a) -\/2 (b) \/2 (c) 16\/2` _ _(d) -18\/2 (e) 18\/2~RCE~Q` 1 !^} y + 122. Find y if~ 2 - - = -----` y y(a) 0 (b) 1 (c) 2 (d) 3 (e) 4~RCC~Q` !_}223. Solve for y~ y - 7y - 8 = 0(a) 8&-1 (b) -8&1 (c) 6&3 (d) 5&5(e) 8&1~RCA~Q` 224. Solve for!`} y~ y + 16 = 10y(a) 8&2 (b) -8&-2 (c) -8&2 (d) 8&-2(e) 7&8~RCA~Q25. The sum of +5 and -19 is =(a) 20 (b) 14 (!a}c) -14 (d) -4 (e) 0~RCC~Q26. The sum of -3 and -6 is =(a) 9 (b) 3 (c) -9 (d) 18 (e) -3~RCC~Q27. The difference !b}between 3 and -17is~(a) 20 (b) -10 (c) 4 (d) -4 (e) 11~RCA~Q28. The difference between 20 and -5is~(a) 15 (b) 2!c}5 (c) -25 (d) -15(e) 10~RCB~Q29. Solve for y~ 12y - 5 = 19(a) 10 (b) -8 (c) 5 (d) -2 (e) 2~RCE~Q30. Solve fo!d}r a~ ka = -ya + d` k + y k - y d(a) ----- (b) ----- (c) -----` d d k + y` d !e} y - k(d) ----- (e) -----` k - y d~RCC~Q` 1 ___31. If - = \/.36& then y =` y(a) .6 (b) !f}.36 (c) 3/5 (d) 5/3(e) 3.6~RCD~Q` 332. y = 5.48& find (5.48) to thenearest 100th.(a) 30.03!g} (b) 164.54 (c) 901.81(d) 4941.91 (e) 2708.71~RCB~Q33. Find the square root of 80389156.(a) 4665 (b) 689 (c) 8966!q}.|?b7PRNTS SYSB>D0 B?AUTORUN SYSB'RDOS SYSByAUTORUN BAKB?|ALGEBR BASB3BAA BXBBB B%FBCC BtAA BAB (d) 9463(e) 7662~RCC~Q` ___ __34. Divide \/108 by \/75.` _ _ _(a) 6\/3 (b) 5\!r}/3 (c) 2\/3` _ _(d) -2\/3 (e) 6/5~RCE~ET~ETCopyright ARROW INSTRUCTIONAL SYSTEMS` July 198!s}3 (c) 2\/3` _ _(d) -2\/3 (e) 6/5~RCE~ET~ETCopyright ARROW INSTRUCTIONAL SYSTEMS` July 198 Welcome to the MATH MODULE of theHAYDEN SCORE IMPROVEMENT SYSTEM FORTHE SAT& one of three modules designedto help you rai%u}se your SAT scores.This Algebra Section is an effectivetool to begin your preparation for theMathematical section of the S%v}cholasticAptitude Tests. The system is easy tooperate so that you can concentrate onits content. All of the informationyo%w}u need to answer questions appearson the screen& as do instructions formoving from one part of the program toanother. More%x} detailed informationfollows in the User's Guide.~RAThis ALGEBRA SECTION providesinstruction and practice in solvingthe %y}entire range of algebra problemsof the types found on the SAT~ linearand literal equations& systems oflinear equations& qu%z}adratic andradical equations& and reducingalgebraic fractions.Other areas in the Mathematicalsection of the SAT are Geom%{}etry& andQuantitative Comparisons and WordProblems; two separate sections inthis Math Module provide reviewmaterial in th%|}ese areas.~RAMENUSThe MAIN MENU lets you move easilyfrom one section of the program toanother. Simply press the keycor%}}responding to the letter next tothe section you wish to see.~RASelecting }B. Algebra} from the MainMenu displays a DETAIL%~} MENU whichoffers you the following options~A. Definitions& Analysis and` StrategiesB. Examples With TutormodeC. Examp%}les Without Tutormode~RADEFINITIONS& ANALYSIS AND STRATEGIESshould be reviewed before going on tothe examples. It provide%}s usefulstrategies for tackling the kinds ofquestions the subject covers. First&background information on eachquestion ty%}pe is presented& thenmethods for answering these questions&including valuable tricks andshortcuts& are demonstrated.~RAE%}XAMPLES WITH TUTORMODE is the core ofthe Hayden System. This option givesyou a detailed& step-by-stepexplanation of how to%} arrive at thecorrect answer. By reviewing andpracticing& you develop more efficientproblem-solving techniques.~RAEXAMPL%}ES WITHOUT TUTORMODE providesquick drill and practice in areaswhere you are already strong so thatyou can improve speed an%}d accuracy. Ifyou answer incorrectly& you are shownthe correct answer& but no detailedexplanation is provided. At the end %}ofthe section& the computer tallies thenumber of questions answered correctlyand incorrectly& providing anindication of h%}ow well you havemastered the material.~RAFUNCTION KEYSA function key is a key which has aspecific effect on the program%}'soperation each time it is pressed.Whenever a menu is on your screen thefollowing function keys areoperational~` M%} (Main Menu)` Q (Quit)Pressing }M} always brings you back tothe MAIN MENU. Pressing }Q} causes thecomputer to ask if %}you really want toquit. If you answer }Y}& you end theprogram. If you answer }N}& youcontinue where you left off.~RAWhil%}e text is on the screen pressing}R} restarts the section (erasing anyprevious answers that you may haveentered)& pressing %}}M} takes you tothe last menu displayed and pressing}Q} enables you to quit.~RAThe left-arrow key lets you pagebackwards%} through the text one screenat a time until the first screen ofthe section is reached. When aquestion appears on the scree%}n& yourprevious answer& if any& is shown. Youcan replace that answer by enteringanother one& or you can leave youranswer %}undisturbed by pressing theleft-arrow again.~RAPressing the letter }O} leaves thecurrent question temporarilyunanswered %}and displays the nextquestion. At the end of the sectionyou have a chance to review all theunanswered questions.~ET~ET$} The HAYDEN SCORE IMPROVEMENT SYSTEM FOR THE SAT is organized into three modules. It includes both simulated SAT exams an)}d complete reviews of the areas typically covered by the Verbal and Mathematical sections of the SAT. In addition to this )}Math Module& the following modules are available: ~RA The PRACTICE TESTS MODULE includes an Analysis of the SAT& a Pre-Te)}st and two Practice Tests. The ANALYSIS OF THE SAT gives you insight into the workings of the actual exam -- its organi)}zation and scoring& plus test-taking strategies and tips for raising your scores. ~RA The PRE-TEST is a diagnostic/presc)}riptive tool for determining your strengths and weaknesses in the areas typically covered by the Mathematical and Verbal )}sections of the SAT. It is a two-hour test consisting of a mix of Math and Verbal questions similar to that on an actual S)}AT. After you complete the test your computer will provide scores in each of sixteen subjects which contribute to your Mat)}h and Verbal scores. This profile of your performance indicates which additional modules in the Hayden System will be use)}ful in your preparation. ~RA The PRACTICE TESTS are two-hour simulated exams with complete Mathematical and Verbal sectio)}ns timed and formatted to be representative of the latest SATs and scored on the SAT scale. After reviewing your weak are)}as& take these Practice Tests and see how your performance would measure up on the actual exam. ~RA The VERBAL MODULE pro)}vides tutorials& drill and analysis in the verbal areas normally covered on the SAT. The VOCABULARY SECTION provides a )}thorough review of antonyms& analogies and sentence completions& as well as an on-screen dictionary with 1000 words. ~RA )}The READING COMPREHENSION SECTION offers strategies and practice in responding to questions about the material just read.)} Working with passages drawn from the most up-to-date sources in a variety of fields will help you improve your ability t)}o determine main ideas& to recognize logical implications and to extract factual information from what you read. ~RA Eac)}h topic in a given section can be approached in three ways~ `acquiring background with `DEFINITIONS& ANALYSIS AND STRATE)}GIES `gaining practice and instruction with `EXAMPLES WITH TUTORMODE `drilling with `EXAMPLES WITHOUT TUTORMODE ~ET )}~ET `gaining practice and instruction with `EXAMPLES WITH TUTORMODE `drilling with `EXAMPLES WITHOUT TUTORMODE ~ET (