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14580AK_FM.pgs
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Answer Key
ALGEBRA 2 and TRIGONOMETRY
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9 8. 9. 10. 11. 12. 13. Enrichment Activity 2-5: Investigating Ratios and Growth Rate in Leaves Students answers will all differ as they have different size leaves. If the length to width ratios are very similar, students should conclude that the rate of growth in their tree or bush is constant. If the length to width ratios vary a lot, they should conclude that the growth rate for their tree or bush is not constant. Students should be assessed on the following characteristics: a. the accuracy of their measurement b. the construction of their data table and scatter plot c. the accuracy of their computations with the calculator d. their knowledge of ratio and average e. the neatness of their work f. their ability to follow directions g. how well they work with others if the activity is done as a group h. their ability to reach a conclusion Enrichment Activity 1-6: Factoring the Sum and Difference of Two Cubes 1. 2. 3. 4. 5. 6. a3 2 b3 5 a3 2 a2b 1 a2b 2 ab2 1 ab2 2 b3 5 a2( a 2 b) 1 ab ( a 2 b) 1 b2( a 2 b) 5 ( a 2 b)( a2 1 ab 1 b2) (2x 1 y)(4x2 2 2xy 1 y2) (x 2 2y)(x2 1 2xy 1 4y2) (5 2 3d)(25 1 15d 1 9d2) (4x 1 3y)(16x2 2 12xy 1 9y2) a4 2 b4 5 a4 2 a3b 1 a3b 2 a2b2 1 a2b2 2*…show more content…*

1 3 11. 4 14. 16 3 b 5. s 2 b 5 a 1 2 1 c 2 b 5 a 1 b 2 2b 1 c 2 15. 4 !3 12. 1 2 5c 1 a 2 b 2 b 6. s 2 a 5 a 1 2 1 c 2 a 1 5 a 2 2a 2 b 1 c Enrichment Activity 13-4: Solving Trigonometric Inequalities p p 1. p # x , p or 54 # x , 32 4 2 p 2. p , x , 32 2 5c 2 a 1 b 2 2 7. 1 2 cos C 5 ab ? c 1 a 2 b ? c 2 a 1 b 2 2 2 5 ab ( s 2 b)( s 2 a) p 3. p # x # 32 2 p 4. p , x , p or 76 , x , 2p 6 p 5. a. p, 54 4 b. Graph y 5 sin x and y 5 cos x and identify intervals where the graph of sin x is below the graph of cos x. The solution is 0 # x , p or 4 5p 4 , x , 2p. 8. ( 1 1 cos C)( 1 2 cos C) 2 5 A ab B s( s 2 a)( s 2 b)(s 2 c) 2 2 1 2 cos2 C 5 A ab B s( s 2 a)( s 2 b)(s 2 c) 2 2 sin2 C 5 A ab B s( s 2 a)( s 2 b)(s 2 c) 2 2 sin C 5 ab !s(s 2 a)( s 2 b)( s 2 c) (Reject negative root since the sine of any angle of any triangle is always positive.) p c. p # x # 54 4 6. 7. 8. p # x # 74 p p , x , 56 or 76 , x , 11p 6 p 0 , x # p or p , x # 34 or p 4 2 p p or 32 , x # 74 p 4 p 6 9. Area 5 1ab sin C 2 2 5 1ab ? ab !s(s 2 a)( s 2 b)( s 2 c) 2 p , x # 54 5 !s( s 2 a)(s 2 b)( s 2

9 8. 9. 10. 11. 12. 13. Enrichment Activity 2-5: Investigating Ratios and Growth Rate in Leaves Students answers will all differ as they have different size leaves. If the length to width ratios are very similar, students should conclude that the rate of growth in their tree or bush is constant. If the length to width ratios vary a lot, they should conclude that the growth rate for their tree or bush is not constant. Students should be assessed on the following characteristics: a. the accuracy of their measurement b. the construction of their data table and scatter plot c. the accuracy of their computations with the calculator d. their knowledge of ratio and average e. the neatness of their work f. their ability to follow directions g. how well they work with others if the activity is done as a group h. their ability to reach a conclusion Enrichment Activity 1-6: Factoring the Sum and Difference of Two Cubes 1. 2. 3. 4. 5. 6. a3 2 b3 5 a3 2 a2b 1 a2b 2 ab2 1 ab2 2 b3 5 a2( a 2 b) 1 ab ( a 2 b) 1 b2( a 2 b) 5 ( a 2 b)( a2 1 ab 1 b2) (2x 1 y)(4x2 2 2xy 1 y2) (x 2 2y)(x2 1 2xy 1 4y2) (5 2 3d)(25 1 15d 1 9d2) (4x 1 3y)(16x2 2 12xy 1 9y2) a4 2 b4 5 a4 2 a3b 1 a3b 2 a2b2 1 a2b2 2

1 3 11. 4 14. 16 3 b 5. s 2 b 5 a 1 2 1 c 2 b 5 a 1 b 2 2b 1 c 2 15. 4 !3 12. 1 2 5c 1 a 2 b 2 b 6. s 2 a 5 a 1 2 1 c 2 a 1 5 a 2 2a 2 b 1 c Enrichment Activity 13-4: Solving Trigonometric Inequalities p p 1. p # x , p or 54 # x , 32 4 2 p 2. p , x , 32 2 5c 2 a 1 b 2 2 7. 1 2 cos C 5 ab ? c 1 a 2 b ? c 2 a 1 b 2 2 2 5 ab ( s 2 b)( s 2 a) p 3. p # x # 32 2 p 4. p , x , p or 76 , x , 2p 6 p 5. a. p, 54 4 b. Graph y 5 sin x and y 5 cos x and identify intervals where the graph of sin x is below the graph of cos x. The solution is 0 # x , p or 4 5p 4 , x , 2p. 8. ( 1 1 cos C)( 1 2 cos C) 2 5 A ab B s( s 2 a)( s 2 b)(s 2 c) 2 2 1 2 cos2 C 5 A ab B s( s 2 a)( s 2 b)(s 2 c) 2 2 sin2 C 5 A ab B s( s 2 a)( s 2 b)(s 2 c) 2 2 sin C 5 ab !s(s 2 a)( s 2 b)( s 2 c) (Reject negative root since the sine of any angle of any triangle is always positive.) p c. p # x # 54 4 6. 7. 8. p # x # 74 p p , x , 56 or 76 , x , 11p 6 p 0 , x # p or p , x # 34 or p 4 2 p p or 32 , x # 74 p 4 p 6 9. Area 5 1ab sin C 2 2 5 1ab ? ab !s(s 2 a)( s 2 b)( s 2 c) 2 p , x # 54 5 !s( s 2 a)(s 2 b)( s 2

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