Algebra 1st Semester Exam Review PDF

TO BE WELL PREPARED FOR THE HONORS ALGEBRA 1st SEMESTER EXAM: Complete this review packet. Check your answers on Canvas. Review all 1st semester test and quiz problems. For #1-4: Simplify completely. 45 127...

TO BE WELL PREPARED FOR THE HONORS ALGEBRA 1st SEMESTER EXAM: Complete this review packet. Check your answers on Canvas. Review all 1st semester test and quiz problems. For #1-4: Simplify completely. 45 127 3[15 3(4)] 1. {2[6 + 7(9)] 3} – 6 ____________ 2. 3 1 ____________ 640 3 9(2) 216 63 33 2,56897536646 6 40 34 1341111 9 3. 31– (8 – 2)8 3 + (1 + 3) ____________ 4. 4(3)2 (4 32 )3 3 49 ____________ 31 6187 3 4 4.9 14 973 3 36 3 353 36 3953 36 13 For #5-7: Write a variable expression (not equation) for: Ijf 5. 5 less than the product of –3 and 6. the total dollar value of d dimes, q the difference of x and y quarters, and h half dollars ____________________________ lodt ________________________ 25qtjs.E 7. the quotient when the sum of a number m and five is divided by the sum of five and the square of m BII.or Stm5 __________________________________ For #8-12: Write a mathematical sentence for each word sentence. Do not solve. 8. The square of a number n is no more than 9. The total dollar value of x dollars and half the cube of the same number. q quarters is at most $125.50. PIER n'Enz _______________________________ _________________________________ 10. Jo is p years old. Her age seven years 11. A late fee for a library book is $2 plus ago was one-fifth her age twenty-one 15 cents per day (d) and the total fee years from now. is $3.20. p 7 46 ______________________________ 21 Sd 2 3.20 _________________________________ 12. The average of three scores is at least 90. The scores are 85, 91, and x. 85 95 290 ___________________________________  For #13-19, solve each equation, if possible. Use the proper steps of balance. (HINT: The answer could be  or “all real numbers.”) 13. 10y – 36 = 6(y – 6) + 6y y = ________ 14. 8(a + 7) – 13a = 32 – 5a a = ________ 3 6 Y 15. (p + 2) = 12 p = ________ 16.  t = ________ t  2 0.2t  4 1 2 4 1 2 17. d d d = ________ 18. w3  w5 w = ________ 3 3 9 2 3 19. 5x – 3(x + 8) = –2(12 – x) x = ________ 20. If 4x – 3 = –5, then what is the value of –2x + 11? ________ For #21-23, solve each formula in terms of the given variable. yz 1 21.5 x  5 Ffor y 22. 2x – y = 9 for y 23. V  r 2 hBfor  3 3 SEESIZE IYL y Éax 9 1 BEFIT  =______________________ 5 2 y = _________________ y = _________________ 2 9 BET Solve each inequality (if possible) and graph the solution on a number line. Write your solution using interval notation. If there is no solution, write  and leave the graph empty. 1 24.2  3h  3  8 2 193,0 _________________ (interval notation) 2 34 3216 qgg 3h 19 42193 25. a) x ≤ –2 or x ≤ 8 78 _____________________ (interval notation) 8 t suigtion C b) x ≤ –2 or x ≥ 8 m 2 U 8P _____________________ (interval notation) 2 Eos E oTubitta 8 8 0 2 512x > 0 E 26. 5 x  40 and _________ 4857811ha but there'EnoNOVERLAP (NO interval notation- why??) of Flaiprrow XL XC 100 and X 0 5000 Of  27. 8(a + 5) > –(20 – 3a) (Answer in interval notation) _______________ 89 407 20 39 sa 28. 4 ≤ –2(a + 9) < 11 60 a iz (Answer in interval notation) 14 5 11 ________________ II ÉÉÉÉ E nzas n.s s.it's 95099 129. 3 y  17  20 and 13  4 y  7 (Answer in interval notation) 1,5 ______________ 3423 LIP 921 and AND YES graphoverlap wog For #30-32, solve each inequality and graph the solution on a number line. Write your solution using interval notation. Set up a compound (AND or OR) statement first. (HINT: “Great-OR; Less thAN-D”) OR 30. 2n  4  6 2n MAR (COMPOUND) ______________ 2n _______ ______________ 4 6 40 of X 2 215 OR 242 13015,0 (Answer in interval notation) __________________ 1 31.  n  1  2 2 00 ÉTELAND Intl (COMPOUND) ______________ _____ ______________ 2 6 the 1 2 14203 (Answer FLIP 2 in interval notation) __________________ Ffp 2 N2 2 AND 2 NEG 2,6 K ratfink 32. – 4 ISOLATE THE ABSOLUTE VALUE FIRST: Intl │_______│≥ _____ Fei F ÉÉ (COMPOUND) ______________ oR antis 1 ______ ______________ do 8 Fat kn 0 2 z O 012114 EFL's I 610 U 4,6 (Answer in interval notation) __________________ or nay OR 33. SOLVE: │x + 7│+5 = 10 ISOLATE THE ABSOLUTE VALUE FIRST: │_______│= _____ s s Xt Smosh.gg Epoints 4 7 4 7 5 _______ ______________ (COMPOUND) ______________ OR 5 12 99 902 X 2 OR X (No interval notation is needed for an equation.) ANSWER(S): { _____ 2 } 12 , ______  Mffte iiIIF Egos Atyeo O O Add  ginned fpBÉd Boise Froggy 1 My  Solve the system of equations using the substitution method. 107 38. 3x + 4y = 12 e to okay y = –2x + 10 8122ha É F g or 38 p 5.6 1.27 Solve each system of equations using elimination. 7C 32 39. 4x + 5y = 15 t 388 12x – 8y = 22 t sb 1 or 2k 11 or 2.5 1 toff Solve each system of equations using substitution or elimination. (HINT: Convert to standard form or slope intercept form first.) I 4(x + y) = 8(y – 4) 40. 4 84 32 4 49 32 2(x – 1) = y – 15 44 2 2 13 2 72 2 9 15 4 5,3 4 2 37 26 125,2331 SOLUTION off 44 20 X 5 Find the range R of each function when the domain D = {–2, 0, 2.5, 6} 15 5,3 41. f(g) = –3g – 7 25 14.5 7 1 R = {________________________} 42. Write an equation in function notation f(x) for each relation. fx 3 66 fyj.tk a. ____________________ b. ____________________ tbpIb 3 3 gemstm MI Yz  45. Find the slope as a fraction in simplest form. a) (–1,5), (–3, –1) m = _______ b) (1, –½) ( 2¾, –¼) m = _______ FEI 4 33 41(–4, r) has5,1 1and 44 4 h 46. Find the value of r so that the line through (2, –3) a slope of. 1 6 4 3 63 1 12 251 o r = _________ 2 47. Write the slope-intercept and standard form equations of the line whose slope is 2 an And whose y-intercept is 9. Mtb 9 bag 4 2 9 Slope-intercept Form Equation: _____________________ 2179 Ax FormByeEquation: _____________________ I 2 4 19 I Standard 2 9 9 46. Write the slope-intercept and standard form equations of the line that passes through (–1, –7) and (1, 3). Use Pt slope m first 3 7 4 5 4 5 2 Slope-intercept Form Equation: _____________________ app c y 3 51 1 5 5 5 9 2 Standard Form Equation: _____________________ g 3 5 2 5 9 42 1 4 48. Write y – 4 = – (x + 6) in standard form. 26 47632 972 AXtBy C 24 8 3 18 Standard 3 29 10 Form Equation: _____________________ 3 29 10 49. Write the slope-intercept form of an equation of the line that passes through (–2, 0) and is parallel to the graph of y = –3x. 3 mof 11 line 3 stope pM pt 521 yen y 0 31 Slope-intercept 4 3 6 Form Equation: _____________________ 4 3 6 50. Write the standard form of an equation of the line that passes through (–2, 0) and is perpendicular to the graph of y = –3x. me 3 mof 1 line tb Pfo ig xÉ2 C _____________________ Ax BYEquation: 3 y 6 2373 Standard Form x 34 2 39 4 2 14 397 2 1 For #51-53, determine whether each relation is a function. Answer yes or no. yes 51. {(1, 5), (2, 4), (3, 5), (4, 9)} ________ Nolitesfalline 52. x = –2 ____________ 513 no 53. {(5, 1), (4,2), (5, 3), (9, 4)} ________ 54. If f (n) = 6 – 2n4, find f (–1). ffl 6 26 1 4 f (–1) = __________________ 2 55. If f(x) = –x , find f (2/3). 6 261 49 f (2/3) = _________________ 23 1435  Evaluate each absolute value expression if a = –4, b = 3, and c = 9. 53. 2⎪a – b⎥ + ⎪c⎥ 23 ANSWER: ________________ 211 4 31 191 2 71 9 2 7 9 23 54. c – b⎪3 – a⎥ 12 ANSWER: ________________ 9 3 13 1 471 9 3 71 9 21 12 For #58-66: Define your variables, write an equation or inequality, solve, and answer the final question using appropriate unit labels. 58. A magazine is on sale for 15% off the original price. If the original price of the magazine is $4.60, what is the discounted price? FINAL ANSWER: ________________ 59. How many pounds of peanuts costing $3.00 a pound should be mixed with 4 pounds of cashews costing $4.50 a pound to obtain a mixture costing $3.50 a pound? Pounds pound total Peanuts 3 3 Cashews 4.50 MIX X 4 3.50 3,5 14 3 18 3.5 14 4 5K x 45 48 8 8 FINAL ANSWER: __________ pounds of peanuts 60. How much pure acid must be added to 7 gallons of a 40% acid solution to produce a 70% acid solution? gallons acid gallonsof acid 100 Pure acid I 40 acid 4 4 2.8 70 acid Xt 7 7 4.9 2.8 7 4.9 Equation:_____________________________ 34 21 3 7 21 7 FINAL ANSWER: __________ gallons of PURE (100%) acid X 7 61. Find four consecutive even integers such that the sum of the first three is four less than the fourth integer. DEFINE: 4 8 st 2 Let x = the 1 even int.; ___________ = 2 nd even int; 406 ___________ = 3 rd 6 even int.; __________ = 4 th even int. 4 2 4 4 EQUATION: ______________________________ 6 4 3 6 2 2 L 2 ____, FINAL ANSWERS: ____, 2 and ____ 0 ____, 4 62. In 2010, there were approximately 275 students in the Delaware High School band. In 2015, that number increased to 308. What is the percent of increase in the number of students in the band? DEFINE: Let x = ___________ increase 275k 3300 EQUATION:_____________________________ 0 tet 12 offer increase FINAL ANSWER: _________________ chqgna.is 63. The cost for 7 dance lessons is $82. The cost for 11 lessons is $122. Use point-slope form to write and solve a linear equation in two variables (x and y) to find the cost of 4 lessons. Let x = # of lessons y = Cost ($) The 2 points are (7, _______) and (11,______). no F Find m here: m = _________ M 82 1o x POINT-SLOPE equation (use 2 variables): ________________________________ y D X 4 1 070m SOLVE: 52 FINAL ANSWER: _________________ 4 21514 52 64. The start-up cost to join eTunes music is $7.95 plus $0.95 per song downloaded. farate Write a linear equation in two variables (x and y) in slope-intercept form. If Will spent $26, how many songs did he download? 95 x = # of songs; y = Cost ($) m = ________; b=__________ 7.95 amount starting 7.95 SLOPE-INTERCEPT equation (use 2 variables): ________________________________ 95 SOLVE: 4 is I iq 19songs FINAL ANSWER: _________________ 65. Joleen is a sales representative in a clothing store. Each week, she earns $300, plus a commission equal to 4% of her total sales. This week, her goal is to earn at least $520. What must her total sales be to achieve her goal? DEFINE: Let x = Joleen’s total sales ($). 3007.04 Write and solve an INEQUALITY here: ________________________________ 520 04 2220 25500 Her total sales must FINAL ANSWER: _____________________________ be AT LEAST 5500 66. Two trains are traveling in between Detroit, Michigan and Los Angeles, California on the same track. The track is 3,600 km long. Train A is traveling east from L.A. to Detroit at a rate of 80 kph. Train B is traveling west from Detroit to L.A. at 100 kph. Write and solve an equation to answer the question below. Define your variables in the table below. (HINT: rt = d) Trains r timotton d Train A (L.A. to Detroit) 80 80 x 100 Train B (Detroit to L.A.) Y look 80 1004 3600 EQUATION: _________________________ 1806 3600 4 20 20hr5 a. How long will it take for the two trains to meet? ____________ 80 b. How far did Train A travel? _______________ 1600 100 207 km B 207 c. How far did Train A travel? _______________ 2000 Km For #67 and 68: Define your variables, write a SYSTEM OF 2 EQUATIONS, solve, and answer the final question using appropriate unit labels. 67. At a baseball game, Tom bought 5 hot dogs and 3 bags of chips for $14.82. Scott bought 7 hot dogs and 6 bags of chips for $22.89. Find the cost of each hot dog and bag of chips. SOLVE BY ELIMINATION DEFINE: SYSTEM: OR SUBSTITUTION: hotdogs 2 _____________________ x________________ 5 39 44.8275240444392 22.89 9 g chips _________________ 7 64 _____________________ 512.257 34 14.82 3 5675 11.25 34FINAL14.82 4 2.25 3.57 2.25hot dog and ___________/ ANSWER: _________/ 1.19 bag of chips 39 68. Gabe has 60 coins consisting of quarters and dimes. The combined value of the quarters and dimes is $9.45. How many quarters and dimes does Gabe have? SOLVE BY ELIMINATION DEFINE: SYSTEM: OR SUBSTITUTION: x quarters ________________ 4 4 60 _____________________ 4 60 4 4 60 23 37 dimes 125 104 9.45 ye _________________ _____________________ 25 10 60 47 945154245 check 25 600 104 945 23quarters 5.75 FINAL ANSWER: Gabe has _______ 37 dimes. 23 quarters and _______ 3 dimes É 5 Simplify each expression completely. Assume that no variable or denominator equals zero. 69. 11 5 (xz) _______________ 70. ta'd _______________ 343 xz 4316 9246 71. 4m _______________ 72. 04a4b6 _______________ ftp fm 1.21 ge 73. (3a )(–2 6a3d6 ) _______________ 74. a _______________ yay 75. (–15x ) s _______________ 76. Éd _______________ 43 64 33,2 Find each sum or difference. 77. (3 – 2p + 3) + ( – 7p + 7) 78. (8 Exes – 4x – 3) – (–2x – + 5) 2 4p 9 10 _______________ 9 2 8 _______________ Find each product. Write your final answers in standard form. don'tforget to Fol 4h42m 79. (2n – 4)(2n + 5) ________________20 9h24m 116 80. (3n 4)2 _______________ 4h4 on 8h 20 3h 4 3h 4 2 9h2 12h 12h 16 25 81. (5x + 7) (5x –7) __________ 49 2 335 5 2 82. (2x – 1)( – x + 2) _______________ 25 2 35 35 49 42 2 83. Name the property that each equation illustrates. TIE attest EFFETE Be sure to include (+) or (x) when appropriate. 3 4 a. 4 3 inv inv 1 __________ f. assoc a(bc) = (ab)c __________ assoc a = 20(b + a) b. 20(a + b) a __________ comt invinv g. 3 + (-3) = 0 __________ c. 1a = a __________ idea ident d. ab + c = ba + c __________ com i. zero h. 3(0) = 0 __________ zero ident 3 + 0 = 3 __________ com a + ac __________ ident e. a(b + c) = ab dis dis j. assoc (20 + a) + b = 20 + (a + b) __________ assoc I com inv 84. Graph this piecewise function: HINT: Find the endpoints of each piece and an extra point to help you graph. Write these points on the blanks provided. glosedggoints It ORE 0,3 2,4 4,5 408 4 8 8 8 horizontal no x pointsright and then find: 2141 f(-4) = ________ 8 f(2) = ________ 2 3 4 oooo 8 f(7) = ________ 85. Solve the system below by graphing. Give one point in solution set and show that it checks in both linear inequalities. 2x + 3y > 12 –6x + 12y < 12 o 8,2 Solution point: __________ Check in the 1st inequality here: 2 8 312 12 16 6 7 12 Check in the 2nd inequality here: 6 81 12 2 212 48 24 24 E 12