Precalculus Skill Builders Vol 1 Solutions

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1. Find the equation of the line that is parallel to the line y = 3x + 9 and passes through the point (–4, 3). Write your answer in point-slope form. [ y ! 3 = 3(x + 4) ] 2. Find the equation of the line that is parallel to the line y = 2x + 8 and passes through the point (–4, 3). Write your answer in slope-intercept form. [ y = 2x + 11 ] 3. Find the equation of the line that is parallel to the line y = !6x ! 8 and passes through the point (8, 3). Write your answer in point-slope form. [ y ! 3 = !6(x ! 8) ] 4. Find the equation of the line that is parallel to the line y = !5x ! 9 and passes through the point (7, 1). Write your answer in slope-intercept form. [ y = !5x + 36 ] 5. Find the equation of the line that contains the points (1, 7) and (–5, –3). Write your answer in slope-intercept form. [ y = 5 3 x + 16 3 ] 6. Find the equation of the line that contains the points (–5, –10) and (9, 6). Write your answer in slope-intercept form. [ y = 8 7 x ! 30 7 ] 7. Find the equation of the line that contains the points (–1, 4) and (–5, –4). Write your answer in point-slope form. [ y ! 4 = 2(x + 1) or y + 4 = 2(x + 5) ] 8. Find the equation of the line that contains the points (5, 2) and (8, 11). Write your answer in point-slope form. [ y ! 2 = 3(x ! 5) or y ! 11 = 3(x ! 8) ] 9. Find the equation of the line that is perpendicular to the line y = 7x + 1 and passes through the point (3, –1). Write your answer in point-slope form. [ y + 1 = ! 1 7 (x ! 3) ] 10. Find the equation of the line that is perpendicular to the line y = 6x + 2 and passes through the point (3, 7). Write your answer in slope-intercept form. [ y = ! 1 6 x + 15 2 ] 11. Find the equation of the line that is perpendicular to the line y = !9x ! 8 and passes through the point (1,6). Write your answer in slope-intercept form. [ y = 1 9 x + 53 9 ] 12. Find the equation of the line that is perpendicular to the line y = 2x + 5 and passes through the point (–6, –7). Write your answer in slope-intercept form. [ y = ! 1 2 x ! 10 ] 13. Find the distance between the points (–3, –5) and (5, 4). [ 145 ] 14. Find the distance between the points (–1, 6) and (3, –4). [ 2 29 ] 15. Find the distance between the points (4, 3) and (18, 14). [ 317 ] 16. Find the distance between the points (0, 7) and (4, 16). [ 97 ] Pre-Calculus with Trigonometry
5. Multiplying Binomials Example: Multiply (x + 2)(x ! 5) . Each term in the first binomial is distributed over the second binomial, as shown below. Solution: (x + 2)(x ! 5) = x(x ! 5) + 2(x ! 5) = x 2 ! 5x + 2x ! 10 = x 2 ! 3x ! 10 Multiply the following binomials. 1. (x + 3)(x ! 6) [ x 2 ! 3x ! 18 ] 3. (b 2 – 3)(b + 5) [ b 3 + 5b 2 – 3b – 15 ] 5. (p 11 – p 10 )(p 10 – p 9 ) [ p 21 – 2p 20 + p 19 ] 7. (5h 4 + 1)(6h – 2) [ 30h 5 – 10h 4 + 6h – 2 ] 9. (x + 3)(x + 6)(x – 7) [ x 3 + 2x 2 – 45x – 126 ] 11. (m 99 + m 98 )(m 97 – m 96 ) [ m 196 – m 194 ] 13. (100 j 100 – j)(9 j 2 + 1) { } ] [ 900 j 102 + 100 j 100 – 9 j 3 – j 15. (c 2 x + d 3 y)(2x + c 2 d) [ 2c 2 x 2 + 2d 3 xy + c 4 dx + c 2 d 4 y ] 2. (a 3 + 1)(a 2 – 4) [ a 5 – 4a 3 + a 2 – 4 ] 4. (z 3 + 1)(z 2 – 1) [ z 5 – z 3 + z 2 – 1 ] 6. (q 4 + 4)(q 3 + 3) [ q 7 + 3q 4 + 4q 3 + 12 ] 8. (d 5 – d 4 )(d 6 + 1) [ d 11 – d 10 + d 5 – d 4 ] 10. (x 2 + 3)(x – 2)(x + 1) [ x 4 – x 3 + x 2 – 3x – 6 ] 12. (6n 4 + 3n 3 )(6n 3 + 3n 2 ) [ 36n 7 + 36n 6 + 9n 5 ] 14. (2!k 5 + 5k 4 )(!k + 3) [ 2! 2 k 6 + 11! k 5 + 15k 4 ] 16. ( f 3 y 3 + g 2 x 2 )( fy + gx) [ f 4 y 4 + f 3 gxy 3 + fg 2 x 2 y + g 3 x 3 ] <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: 4. Properties of Lines Given the po
Page 9 and 10: 9. Find the exact area of the follo
Page 11 and 12: Example: Rationalize 45 . Solution:
Page 13 and 14: 5. Find the length of x. [ x = 21 5
Page 15 and 16: 9. Factoring Standard Forms Rules f
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

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