Precalculus Skill Builders Vol 1 Solutions

More documents

Recommendations

Info

11. Kathleen is 6 feet tall. Her shadow is 3 feet long. At the same time of day, a tree casts a shadow that is 21 feet long. How tall is the tree? [ 42 feet ] 12. Kyle is 1.5 meters tall and casts a shadow 4 meters long. A flagpole casts a shadow that is 30 meters long. How tall is the flagpole? [ 11.25 meters ] 13. Lisa’s dog is 2.5 feet tall and casts a shadow that is 4 feet long. A fire hydrant casts a shadow that is 6 feet long. How tall is the fire hydrant? [ 3.75 feet ] 14. Fernando is constructing a scale model of his father’s yacht. The actual yacht has a sail that is 25 feet tall and the base of the sail is 15 feet long. If the model’s sail is 14 inches tall, how long is its base? [ 8.4 inches ] 15. Cameron is building a scale model of his sailboat. The right-triangular sail of the actual boat has a base that is 12 feet long. The height of the actual sail is 20 feet long. The base of the model’s sail is 8 inches long. How long is the hypotenuse of the model’s sail? (The hypotenuse is different from the height!) [ 8 34 3 ] 16. List all of the similar triangles that are in the figure at right. [ ∆ABC, ∆APB, ∆CPB ] Pre-Calculus with Trigonometry
9. Factoring Standard Forms Rules for Factoring Difference of Two Squares: a 2 ! b 2 = (a + b)(a ! b) Sum of Two Cubes: a 3 + b 3 = (a + b)(a 2 ! ab + b 2 ) Difference of Two Cubes: a 3 ! b 3 = (a ! b)(a 2 + ab + b 2 ) Special Products (a + b) 2 = a 2 + 2ab + b 2 (a ! b) 2 = a 2 ! 2ab + b 2 (a + b) 3 = a 3 + 3a 2 b + 3ab 2 + b 3 (a ! b) 3 = a 3 ! 3a 2 b + 3ab 2 ! b 3 Factor each of the following expressions. 1. x 2 ! 12x + 36 [ (x ! 6) 2 ] 3. 9a 2 + 24a + 16 [ (3a + 4) 2 ] 5. (x + y) 2 ! 4(x + y) + 4 [ (x + y ! 2) 2 ] 7. b 2 ! 16 [ (b ! 4)(b + 4) ] 9. 4x 2 ! 1 [ (2x ! 1)(2x + 1) ] 11. s 6 ! t 6 [ (s 3 ! t 3 )(s 3 + t 3 ) ] 13. a 3 ! b 3 [ (a ! b)(a 2 + ab + b 2 ) ] 2. z 2 ! 6z + 9 [ (z ! 3) 2 ] 4. 16x 2 + 40xy + 25y 2 [ (4x + 5y) 2 ] 6. 4(a ! b) 2 ! 8(a ! b) + 4 [ 4(a ! b ! 1) 2 ] 8. 7x 4 ! 7 [ 7 x + 1 ( ) (x ! 1)(x 2 + 1) ] 10. (a ! b) 2 ! (a + b) 2 [ !4ab ] 12. x 3 + 1 [ (x + 1)(x 2 ! x + 1) ] 14. 8 p 3 + 27q 3 [ (2p + 3q)(4p 2 ! 6pq + 9q 2 ) ] <strong>Skill</strong> <strong>Builders</strong>
Page 1 and 2: Skill Builders (Extra Practice) Vol
Page 3 and 4: 2. Laws of Exponents Example: Solut
Page 5 and 6: 4. Properties of Lines Given the po
Page 7 and 8: 5. Multiplying Binomials Example: M
Page 9 and 10: 9. Find the exact area of the follo
Page 11 and 12: Example: Rationalize 45 . Solution:
Page 13: 5. Find the length of x. [ x = 21 5
Page 17 and 18: 11. Algebraic Fractions Facts about
Page 19 and 20: 12. Solving Quadratics Solve the qu
Page 21 and 22: 13. Inequalities Example 1: Solve:
Page 23: Graph the solution. 11. x ! 2y < 4

Precalculus Skill Builders Vol 1 Solutions

Create successful ePaper yourself

Delete template?

Save as template?