Math Review Part C Advanced Level (Up to end of MAT 05) A scientific calculator is allowed. Answers provided in the final section.
Math Review Part C Advanced Level
Advanced Level Algebra ALGEBRAIC EXPRESSIONS Simplif the following algebraic epressions b combining like terms. 5 +. 5 7( ).. (6+ ) ( 9) A summar of the Laws of Eponents is given below. 0 = = ( where 0) n = n = + m n m n m n = m n ( ) = m n mn Using the above laws, complete the following simplifications.. ( )(5 )( ) 5. 6 7 0 6. a b 8ab Math Review Part C Advanced Level
LINEAR EQUATIONS AND INEQUALITIES Solve each of the following linear equations. 7. 5+ 7= 8 8. 5 ( + ) = 9. + 5 = 0. 0.+.9 = 0.7. Solve each of the following inequalities.. 8. 5 +. < + 8 Math Review Part C Advanced Level
Write an algebraic equation or inequalit to represent each problem. Then solve the problem using our equation or inequalit. Be sure to identif the variable.. The sum of two consecutive odd integers is 56. Find the integers. Let the st number = Let the nd number = + 5. Ms. Jones earns a base salar of $880 per month, plus $ for each product that she sells. During November she earned a total of $5680. How man products did she sell? 6. Tickets for a local concert sold for $5 and $8. Jim collected $99 on the sale of 80 tickets. How man of each tpe did he sell? 7. You have $0,000 to invest. You invest part of this at 6% interest and the rest at 8%. What is the most ou can invest at 6% to earn at least $0 interest? Math Review Part C Advanced Level
GRAPHING OF LINEAR EQUATIONS AND INEQUALITIES Graph each of the following. 8. = 9 8 7 6 5 0-9 -8-7 -6-5 - - - - 0 5 6 7 8 9 - - - -5-6 -7-8 -9 9. + = 6 9 8 7 6 5 0-9 -8-7 -6-5 - - - - 0 5 6 7 8 9 - - - -5-6 -7-8 -9 Math Review Part C Advanced Level 5
0. > 6+ 9 8 7 6 5 0-9 -8-7 -6-5 - - - - 0 5 6 7 8 9 - - - -5-6 -7-8 -9 Math Review Part C Advanced Level 5
SYSTEMS OF EQUATIONS A solution of a sstem of equations in two variables is an ordered pair of numbers that makes both equations true. Solve the following sstems of equations.. + = =. = 7 = 8. 5+ = 7 5+ = FACTORING POLYNOMIALS Factor each of the following.. + 0+ 5 5. 6. 5 + 7 7. 8 + 5 Math Review Part C Advanced Level 6
RATIONAL EXPRESSIONS AND EQUATIONS Simplif. 8. 5+ 0 + 6 5 9. 9 + + + 0. + 7. a a a+ a Solve each equation.. + = 5 5. = +. 50 50 = Math Review Part C Advanced Level 7
Solve each problem using an algebraic equation. 5. A tank can be filled in 8 hours b pipe A alone and in hours b pip B alone. How long will it take to fill the tank if both pipes are in operation? 6. The speed of a river is 5 km per hour. A boat travels 7 km upstream in the same time as it takes to travel 6 km downstream. What would be the speed of the boat in still water? RADICAL EXPRESSIONS AND EQUATIONS Simplif b combining like radical terms. 7. 5 5+ 5 8. 5 + 5 9. 5 5 9 9 Math Review Part C Advanced Level 8
Multipl and simplif the following. 0. 5(+ 5). ( )( + ). ( 5 )( 5 ) + Simplif.. 6. 8 5. 8 8 ( ) Solve each equation. 6. 7= 7. + = 8. 5 = + Math Review Part C Advanced Level 9
QUADRATIC EQUATIONS The quadratic formula below is important; be sure to remember it. ± = a b b ac Solve each of the following quadratic equations. 9. 6+ 9= 0 50. 5= 0 5. + 5 6= 0 5. + = Math Review Part C Advanced Level 0
Graph each of the following questions. 5. = + ( ) 9 8 7 6 5 0-9 -8-7 -6-5 - - - - 0 5 6 7 8 9 - - - -5-6 -7-8 -9 5. = + ( ) 9 8 7 6 5 0-9 -8-7 -6-5 - - - - 0 5 6 7 8 9 - - - -5-6 -7-8 -9 Math Review Part C Advanced Level
FUNCTIONS Given f( ) = and g ( ) = +, find the following. 55. f ( ) 56. g 57. ( f + g)( ) Math Review Part C Advanced Level
Advanced Level Trigonometr TRIGONOMETRIC RATIOS The trigonometric ratios are: opposite sin = hpotenuse adjacent cos = hpotenuse opposite tan = adjacent The Law of Sines is: a = b = c sin A sin B sin C The Law of Cosines is: = + c a b abcosc Use the above information or a scientific calculator to answer the following questions. 58. Find the measure of ACB A 5 B C Math Review Part C Advanced Level
59. Find the length of EF EF = E F 5 D 60. Solve the DEF b finding the measure of each of those sides and angles whose quanitt is not given and is represented onl b letter. D F = f = d = f 5 E d F Math Review Part C Advanced Level
6. Solve the ABC b finding the measure of each of those sides and angles represented onl b letter. A b C b = A = C = 0 B Math Review Part C Advanced Level 5
Math Review Part C Advanced Level 6
Answers Part C Algebraic Epressions.. 7 9. + 8. 9 5 5. 0 0 or 6. 8a b Linear Equations and Inequalities 7. = 5 8. = 6 9. 0 = 7 0. =.. 8.. <. n+ n+ = 56 The numbers are 7 and 9 5. 880 + n = 5680 Number of products sold is 50 6. 5n+ 8(80 n) = 99 7 tickets at $5 and tickets at $8 7. 6% n+ 8%(0000 n) 0 $8,000 ma. Math Review Part C Advanced Level 7
Graphing of Linear Equations and Inequalities 8. = - - 9 8 7 6 5 0-9 -8-7 -6-5 - - - - 0 5 6 7 8 9 - - - -5-6 -7-8 -9 9. + = 6 0.5 0 9 8 7 6 5 0-9 -8-7 -6-5 - - - - 0 5 6 7 8 9 - - - -5-6 -7-8 -9 Math Review Part C Advanced Level 8
0. > 6+ 5 0 - - - - 9 8 7 6 5 0-9 -8-7 -6-5 - - - - 0 5 6 7 8 9 - - - -5-6 -7-8 -9 Sstem of Equations. (,). (5,). (,) Factoring Polnomials. ( + 5)( + 5) or ( + 5) 5. ( ) = ( + )( ) 6. (+ )(5 ) 7. (+ 5)( 0+ 5) Math Review Part C Advanced Level 9
Rational Epressions and Equations 8. 9. 0. 9 +. a + aa ( + ). = 6. =. = 5. + = time is 8 t 6. 7 6 = r 5 r+ 5 9 9 0 or 9 hours and 5 minutes. speed is.8 km per hour Radical Epressions and Equations 7. 6 7 5 8. 5 9. 0. 5 + 5. =. 0.. 5. 6. = 00 7. = or 5 8. = Quadratic Equations 9. = 50. = ± 6 or.5 and.5 5. = and 5. 7 ± 85 = or 8. and. Math Review Part C Advanced Level 0
5. ( ) = + 0 6 - - - - 9 8 7 6 5 0-9 -8-7 -6-5 - - - - 0 5 6 7 8 9 - - - -5-6 -7-8 -9 5. = + ( ) 0 - - -7 9 8 7 6 5 0-9 -8-7 -6-5 - - - - 0 5 6 7 8 9 - - - -5-6 -7-8 -9 Math Review Part C Advanced Level
Functions 55. 56. 57. + + Trigonometric Ratios 58. the measure of BCA = 6.9 59. the measure of EF =.7 (units) 60. F = 80 (80 + 0 ) = 60 d 5 = sin 0 sin80 d =. f 5 = sin 60 sin80 f =. 6. b = + 0 0 cos 70 b =.75.75 = sin A sin 70 A = 6. C = 80 (70 + 6. ) = 7.6 Math Review Part C Advanced Level
Table of Trigonometric Ratios Angle tan sin cos Angle tan sin cos 0.07 0.07.000 6.06 0.79 0.695 0.05 0.05 0.999 7.07 0.7 0.68 0.05 0.05 0.999 8. 0.7 0.669 0.070 0.070 0.998 9.50 0.755 0.656 5 0.087 0.087 0.996 50.9 0.766 0.6 6 0.05 0.05 0.995 5.5 0.777 0.69 7 0. 0. 0.99 5.80 0.788 0.66 8 0. 0.9 0.990 5.7 0.799 0.60 9 0.58 0.56 0.988 5.76 0.809 0.588 0 0.76 0.7 0.985 55.8 0.89 0.57 0.9 0.9 0.98 56.8 0.89 0.559 0. 0.08 0.978 57.50 0.89 0.55 0. 0.5 0.97 58.600 0.88 0.50 0.9 0. 0.970 59.66 0.857 0.55 5 0.68 0.59 0.966 60.7 0.866 0.500 6 0.87 0.76 0.96 6.80 0.875 0.85 7 0.06 0.9 0.956 6.88 0.88 0.69 8 0.5 0.09 0.95 6.96 0.89 0.5 9 0. 0.6 0.96 6.050 0.899 0.8 0 0.6 0. 0.90 65.5 0.906 0. 0.8 0.58 0.9 66.6 0.9 0.07 0.0 0.75 0.97 67.56 0.9 0.9 0. 0.9 0.9 68.75 0.97 0.75 0.5 0.07 0.9 69.605 0.9 0.58 5 0.66 0. 0.906 70.78 0.90 0. 6 0.88 0.8 0.899 7.90 0.96 0.6 7 0.50 0.5 0.89 7.078 0.95 0.09 8 0.5 0.69 0.88 7.7 0.956 0.9 9 0.55 0.85 0.875 7.87 0.96 0.76 0 0.577 0.500 0.866 75.7 0.966 0.59 0.60 0.55 0.857 76.0 0.970 0. 0.65 0.50 0.88 77. 0.97 0.5 0.69 0.55 0.89 78.705 0.978 0.08 0.675 0.559 0.89 79 5.5 0.98 0.9 5 0.700 0.57 0.89 80 5.67 0.985 0.7 6 0.77 0.588 0.809 8 6. 0.988 0.56 7 0.75 0.60 0.799 8 7.5 0.990 0.9 8 0.78 0.66 0.788 8 8. 0.99 0. 9 0.80 0.69 0.777 8 9.5 0.995 0.05 0 0.89 0.6 0.766 85.0 0.996 0.087 0.869 0.656 0.755 86.0 0.998 0.070 0.900 0.669 0.7 87 9.08 0.999 0.05 0.9 0.68 0.7 88 8.66 0.999 0.05 0.966 0.695 0.79 89 57.90.000 0.07 5.000 0.707 0.707 Math Review Part C Advanced Level
Math Review Part C Advanced Level
Table of Squares & Square Roots n n n n n n.000 5 60 7.. 5 70 7. 9.7 5 809 7.80 6.000 5 96 7.8 5 5.6 55 05 7.6 6 6.9 56 6 7.8 7 9.66 57 9 7.550 8 6.88 58 6 7.66 9 8.000 59 8 7.68 0 00.6 60 600 7.76.7 6 7 7.80.6 6 8 7.87 69.606 6 969 7.97 96.7 6 096 8.000 5 5.87 65 5 8.06 6 56.000 66 56 8. 7 89. 67 89 8.85 8. 68 6 8.6 9 6.59 69 76 8.07 0 00.7 70 900 8.67.58 7 50 8.6 8.690 7 58 8.85 59.796 7 59 8.5 576.899 7 576 8.60 5 65 5.000 75 565 8.660 6 676 5.099 76 5776 8.78 7 79 5.96 77 599 8.775 8 78 5.9 78 608 8.8 9 8 5.85 79 6 8.888 0 900 5.77 80 600 8.9 96 5.568 8 656 9.000 0 5.657 8 67 9.055 089 5.75 8 6889 9.0 56 5.8 8 7056 9.65 5 5 5.96 85 75 9.0 6 96 6.000 86 796 9.7 7 69 6.08 87 7569 9.7 8 6.6 88 77 9.8 9 5 6.5 89 79 9. 0 600 6.5 90 800 9.87 68 6.0 9 88 9.59 76 6.8 9 86 9.59 89 6.557 9 869 9.6 96 6.6 9 886 9.695 5 05 6.708 95 905 9.77 6 6 6.78 96 96 9.798 7 09 6.856 97 909 9.89 8 0 6.98 98 960 9.899 9 0 7.000 99 980 9.950 50 500 7.07 00 0000 0.000 Math Review Part C Advanced Level 5
Math Review Part C Advanced Level 6