Secondary H Unit Lesson Worksheet Simplify: mm + 2 mm 2 4 mm+6 mm + 2 mm 2 mm 20 mm+4 5 2 9+20 2 0+25 4 +2 2 + 2 8 2 6 5. 2 yy 2 + yy 6. +2 + 5 2 2 2 0 Lesson 6 Worksheet List all asymptotes, holes and intercepts and graph the function yy = 2 + 6 yy = 2 2 ( 2) 2 yy = 2 4 yy = 2(2 2 ) 2 + 2 Lesson 7 Worksheet Solve: + = +2 2 + = 7 2 + 5+6 +2 + = mm+2 mm 6 Review Worksheet Simplify: 5 7 2 2 6 2 6 4 + 5+6 2 2 5 2 4 2 + 2 2 9 5 2 + +
List all asymptotes, holes and intercepts and draw the graph 5. yy = ( )2 2 6. yy = 2 2 7. yy = 2 4 2 8. Solve: + 2 = + 2 + 2 2 Secondary H Unit AAAAAAAAAAAA KKKKKK 9., 0.,,5 4 2 a. The expression is not the ratio of two + polynomials. b. The expression is the ratio of two polynomials. 5 a. factors are opposites, = ( ) b. factors are not opposites, 2 yy can be rewritten as yy + 2, so the two expressions are the same 7. 7zz+2 zz, zz, 9. 4aa 2 2aa, aa 0, 2 2 2ss+ ss 2, ss 0 2 mm+4, mm 4,7 mm 7 +2 28. The student canceled terms instead of factors. 2 2 6 5tt 6 22 5 25 4 5. kk + kk 2 6. 4 (+7)(2+) 7. aa2 4aa+4 aa 8. 2 9. They are not the same, you show why. 2 tt + 2 cc+ cc 25. tt 5 7tt 2 0 25 26. 5 27. 2 28. 5 The student forgot to write the divisor as its reciprocal before canceling. aa2 2aa (aa+2) 6. +2 4(+7) 4 2aa2 7aaaa 6bb 2 (5aa+bb)(2aa bb)
6. 7mm 47 (mm+2)(mm 7) 77. aa 2 + aa 2 (aa+)(aa+5) 88. 4tt2 + 5tt+5 tt 2 (tt+) 9a. rr +.7rr b. 7 7rr c..8 hrs. 0. 7 22 yy+22 6bb+5 0 24bb rr 6a. The product would be a common denominator, each expression is a factor of their product. b. the product of the denominators wil only be the LCD if those denominators have no common factors. 7. The student added the denominators instead of using the LCD. 8. The answer will not always be in simplest form; the numerator may contain a factor of the LCD. 20. yy2 +2yy+2 yy+ 2 0+5 +2 25. 2tt+ 2tt 29. 82 + 0. 8 5 ( 5) 2( 5) 5. 4 + 6. yy 8 7. yy+4 2yy 8. 4cc+ cc+ Worksheet 5mm 4 (mm 2)(mm+2) mm 0 (mm 5)(mm+4) 4+5 ( 4)( 5)( 5) 8+20 ( 4)(+4)( 2) 5. yy 6. + 4 8. Inverse, yy = 6 9. Direct, vv = 5uu p varies directly with q, r, and t and inversely with s. 6. FF = kkkk 7. zz = 5 20 ; zz = dd 2 yy 9 9. zz = 4 ; zz = 9
6 (Part ) pts. of discont. none, x-int: (0, 0), (-2, 0), y-int: (0, 0) pts. of discont. x = 2, x =, x-int: none, y-int: (0, ) VA: = 2, = VA: x = -, hole: (2, 5 ) 5. HA: y = 0 6. HA: y = 4 0. VA: x = -4, HA: y = 0, hole: (-5, -), x-int: none, y-int: (0, 4 ) VA: x = 9, HA: y =, hole: (-2, 2 ), x-int: (0,0), y-int: (0, 0) VA: x = -, HA: y = 0, x-int: (, 0), y-int: (0, -) VA: x =, HA: y =, hole: (2, ), x-int: (-, 0), y-int: (0, -) 5 VA: x = -5, HA: y =, x-int: (, 0), y-int: (0, 5 ) 5. VA: x = -2, x = -, HA: y = 0, x-int: (, 0), y-int: (0, 2 ) 6. VA: x =, HA: y = 0, hole: (-, -), x-int: none, y-int: (0, -2) 7. VA: x = -, x =, HA: y =, x-int: none, y-int: (0, -) 6 (Part 2) Check all graphs on your calculator and ask your teacher if you have questions 8. VA: x = 4, HA: y =, x-int (0,0), y-int (0,0) 29. VA: x = 5, HA: y = 2, x-int: (, 0), y-int: (0, ) 2 5 0. VA: none, HA: none, hole: (-, 0), x-int none, y-int: (0, ) VA: x = -, x = 5 20, HA: y = 2, x-int: (5, 0), (-5, 0), y-int: (0, ) 2 7. VA: x = -2, x = 2, HA: y = 0, hole: (0, -), x-int: none, y-int: none
6 Worksheet VA: x = -, HA: y =, hole: (2, 5 ), x-int: (-, 0), y-int: (0, ) VA: x = 2, HA: y = 0, x-int: none, y-int: (0, 4 ) VA: x = -2, x = 2, HA: y = 0, x-int: (, 0), y-int: (0, 4 ) VA: x = 0, x = -2, HA: y = 2, x-int: (, 0), (-, 0), y-int: none 7 6. x = 5 7. a = - 8. n = -2 0. The LCD was not found; the correct answer is = 6 9 EE = mmvv2 2 E=mcc 2 5. F = ma 6. cc = ± aa 2 bb 2 7. TT = ±2ππ ll gg 25a. LL = 24RR 24rr TT 26. x = 27. no solution 28. no solution k = -4 no solution y = 6 x =, 2 5. x = - 7 Worksheet x = 4, - x = 7 m = -2, Unit Chapter Review + 5 2, 0 + 2aa 2, mm, x - 5 (aa+), a, aa 5. 2ss+ 2ss, ss 2, ss 4 6. 2, cc 4 8. 2 ( 2) 9. aa2 + 2aa 8 (aa 2 )(aa+2) 0. 2 + 2 + 5 8 + 24+7 28 2 +7 20 (+2)( 4) 52 +2+27 ( )(2+) 5. 8,40 59rr 6. 2 7. yy = 72
8. yy = 6 9. zz = 7 4 ; zz = 56 20. zz = 4 yy ; zz = 2 29. VVVV: = 2, HHHH: yy = 0 ; hoooooo aaaa (, ), x-int: none, y-int: (0, ) (check graph on calc) 2 x = nnnn ssssssssssssssss 5. = 2, 9 Review Worksheet 5 2 4+4 2( )(+2) 2 8 0 (5+6)( 2) +2 9 5 + For #5 7 check the graph on your calculator 5. VA: x = -, HA: y =, hole (, 0), x-int: none, y-int: (0, -) 6. VA: x = 0, x =, HA: y =, x-int: (, 0), (-, 0), y-int: none 7. VA: x = -2, x = 2, HA: y = -, x-int: (0, 0), y-int: (0, 0) 8. x = 2 Section 7 (Labs) Page 26: yy = 6, yy = 5. 6 = 6. (-, -2), (4, ) 7. No extraneous solutions 2 2 8., 9 9. (,); 4, 0. (0, 2); (, ) (0, ) 4 8 4 Page 222: < < oooo > 2 < < 2 oooo > <, oooo 2 < < 2, oooo > 5. < < oooo > 6. < < 0 oooo > 7. < < 2 0rr >