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Algebra 1-2 Semester 2 Final Review

Algebra 1-2 Semester 2 Final Review. Pick up your Final Review Form B Packet. 2nd Semester Review. 1.) Solve & graph the inequality: 4x-3 < 2(x+2). 4x - 3 < 2x + 4 4x -2x - 3 < 2x -2x + 4 2x - 3 < 4 2x - 3 +3 < 4 +3 2x < 7 x < 7/2. (A). -4. -2. 0. 2. 4.

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Algebra 1-2 Semester 2 Final Review

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  1. Algebra 1-2Semester 2 Final Review • Pick up your Final Review Form B Packet 2nd Semester Review

  2. 1.) Solve & graph the inequality: 4x-3 < 2(x+2) • 4x - 3 < 2x + 4 • 4x -2x - 3 < 2x -2x + 4 • 2x - 3 < 4 • 2x - 3+3 < 4+3 • 2x < 7 • x < 7/2 (A) -4 -2 0 2 4 2nd Semester Review

  3. 2.) Graph -4 < x < 3 • -4 < x < 3 • (C) -2 0 2 4 6 8 Closed Dot Open Dot 2nd Semester Review

  4. 3.) Solve -6 < -2x + 6 < 8 • -6 < -2x + 6 < 8 • -6 -6 < -2x + 6 -6 < 8 -6 • -12 < -2x < 2 • -12/-2 < -2x/-2 < 2/-2 • 6 > x > -1 (B) 2nd Semester Review

  5. 4.) Solve |x+1| > 6 2nd Semester Review x+1 < -6 x+1 > 6 • x+1 > 6 • x+1-1 > 6-1 • x > 5 • x+1 < -6 • x+1-1 < -6-1 • x < -7 x < -7 or x > 5 (A) Remember: < is and , > is or

  6. 5.) Graph |x - 2| < 2 x - 2 < 2 x - 2 > -2 • x - 2 > -2 • x -2+2> -2+2 • x > 0 • x - 2 < 2 • x - 2+2< 2+2 • x < 4 0 < x < 4 (B) -4 -2 0 2 4 6 2nd Semester Review

  7. 6.) Graph 4x - 3y < -12 • 4x -3y < -12 • 4x - 4x -3y < -4x -12 • -3y < -4x -12 • -3y/-3 < (-4x -12)/-3 • y > 4/3x + 4 Graph it 2nd Semester Review

  8. 6.) Graph 4x - 3y < -12 Sketch y = 4/3x + 4 Y Now pick a point on one side of the dotted line -(0,0) X 2nd Semester Review

  9. Test a Point 2nd Semester Review • Take the point (0,0) and plug in the values in y > 4/3x + 4 • y > 4/3x + 4 • 0 > 4/3(0) + 4 • 0 > 4 False Since it’s False, Shade the opposite side of (0,0).

  10. 6.) Graph 4x - 3y < -12 (C) Y X 2nd Semester Review

  11. 4x-2y = 163x+2y = 5 7.) Solve by linear combination • 3x+2y = 5 • 3(3)+2y = 5 • 9 + 2y = 5 • 9-9+2y=5-9 • 2y = -4 • y = -4/2= -2 • 4x-2y = 163x+2y = 5 • 7x = 21 • 7x/7 = 21/7 • x = 3 (B) (3,-2) 2nd Semester Review

  12. 8.) Determine if the systemhas no solutions, one solutions, or many solutions. • 3x + y = 14 6x + 2y = 28 • -2(3x + y = 14) • -6x - 2y = -28 6x + 2y = 28 2nd Semester Review

  13. 8.) Determine if the systemhas no solutions, one solutions, or many solutions. • -6x - 2y = -28 6x + 2y = 28 • 0 = 0 (D) True Many Solutions 2nd Semester Review

  14. y > x + 13x + y < 5 9.) Determine the solution to the system of inequalities • y > x + 13x + y < 5 • 3x -3x + y < -3x + 5 • y < -3x + 5 2nd Semester Review

  15. y > x + 13x + y < 5 9.) Determine the solution to the system of inequalities • y > x + 1y < -3x + 5 • Graph • Pick a point 2nd Semester Review

  16. (9) y > x + 1y < -3x + 5 Y Now pick a point on one side of both lines - (0,0) X 2nd Semester Review

  17. Test a Point 2nd Semester Review • Take the point (0,0) and plug in the values in y > x + 1 • y > x + 1 • 0 < (0) + 1 • 0 < 1 True Since it’s True, Shade the (0,0) side.

  18. (9) y > x + 1y < -3x + 5 Y X 2nd Semester Review

  19. Test a Point 2nd Semester Review • Take the point (0,0) and plug in the values in y < -3x + 5 • y < -3x + 5 • 0 < -3(0) + 5 • 0 < 5 True Since it’s True, Shade the (0,0) side.

  20. (9) y > x + 1y < -3x + 5 Y X 2nd Semester Review

  21. 10.) Simplify 43 • 42 • 43 • 42 • (4•4•4) • (4•4) • (A) 45 2nd Semester Review

  22. 11.) Simplify (32)9 • (32)9 (32)(32)(32)(32)(32)(32)(32)(32)(32) • (D) 318 2nd Semester Review

  23. 12.) Simplify the product (2fg6)4(fg)5 • (2fg6)4(fg)5 • 24f4g24 • f5g5 • (A) 16f9g29 2nd Semester Review

  24. 13.) Simplify the product a7 • a-4 • a7 • a-4 • a7 • 1/a4 = a7/a4 • a•a•a•a•a•a•a a•a•a•a • a3 (D) 2nd Semester Review

  25. 14.) Rewrite using positive exponents 5-1 • 5-1 = 1/51 = 1/5 (A) 2nd Semester Review

  26. 15.) Multiply 30 • 4 • 22 • 30 • 4 • 22 = • 1 • 4 • 4 • 16 (C) 2nd Semester Review

  27. 16.) Rewrite using positive exponents 6ab2c-3 • 6ab2c-3 • 6ab2/c3 (B) 2nd Semester Review

  28. 17.) Which is equivalent to 515/55 • 515/55 = 515-5 = 510 • (A) 2nd Semester Review

  29. 18.) Simplify (18x7y4)/(-9x3y5) • (18x7y4)(-9x3y5) = • -2x4/y (D) 2nd Semester Review

  30. 19.) What’s the perimeter of the triangle. 2nd Semester Review • a2 + b2 = c2 • 152 + 82 = c2 • 225 + 64 = c2 • 289 = c2 • 17 = c 17 15 (A) 8 Perimeter = 15+8+17=40

  31. 20.) Solve 36x2 - 49 = 0 • 36x2 - 49 + 49 = 0 + 49 • 36x2 = 49 • 36x2/36 = 49/36 • x2 = 49/36 • x = 49/36 • x = ± 7/6 (A) 2nd Semester Review

  32. 21.) Graph y = x2 - 2 2nd Semester Review

  33. 22.) Solve by the Quadratic formula: x2 -x -3 = 0 • x = -b b2 - 4ac 2a • x = --1 (-1)2 - 4(1)(-3) 2(1) 2nd Semester Review

  34. 22.) Solve by the Quadratic formula: x2 -x -2 = 0 • x = 1 1 + 12 2 • x = 1 13 = 2 (D) 2nd Semester Review

  35. 23.) Simplify: (5e3 + 5) - (4e2 + 1)+ (2e3 + 5e2) • 5e3 + 5 -4e2 - 1 + 2e3 + 5e2 • 5e3 + 2e3 - 4e2+ 5e2 + 5 - 1 • 7e3 + e2 + 4 (B) 2nd Semester Review

  36. 24.) Multiply (x-4)(x+2) • (x-4)(x+2) foil • x2 +2x - 4x - 8 • x2 -2x - 8 (C) 2nd Semester Review

  37. 25.) Multiply (4u+9)(4u-9) • (4u+9)(4u-9) foil • 16u2 -36u + 36u - 81 • 16u2 - 81 (A) 2nd Semester Review

  38. 26.) Multiply (x+1)(x2 - x - 2) • (x + 1)(x2 - x - 2) • x3 -x2 -2x + x2 -x -2 • x3 -x2 + x2 -2x -x -2 • x3 - 3x - 2 (C) 2nd Semester Review

  39. 27.) Multiply using the Vertical format • 2y2 + 7y + 2 y - 6 (C) 2y3 + 7y2 + 2y - 12y2 - 42y - 12 2y3 - 5y2 - 40y - 12 2nd Semester Review

  40. 28.) Factor x2 - 16 • x2 - 16 • (x )(x ) • (x - 4)(x + 4) (A) • x2 - 4x + 4x - 16 • x2 - 16 2nd Semester Review

  41. 29.) Factor x2 - 2x - 24 • x2 - 2x - 24 • (x )(x ) • (x - 6)(x + 4) (B) • x2 + 4x - 6x - 24 • x2 - 2x - 24 2nd Semester Review

  42. 30.) Factor x2 - 49 • x2 - 49 • (x )(x ) • (x - 7)(x + 7) (D) • x2 + 7x - 7x - 49 • x2 - 49 2nd Semester Review

  43. 31.) Solve x2 + 3x - 10 = 0 • x2 + 3x - 10 = 0 • (x - 2)(x + 5) = 0 • x - 2 = 0 & x + 5 = 0 • x = 2 & x = -5 (B) 2nd Semester Review

  44. 32.) Solve c/3 = 5/45 2nd Semester Review • c = 53 45 • 45c = 15 • 45c/45 = 15/45 • c = 15/45 = 1/3 (A)

  45. 33.) Solve (x-1)/3 = (x+5)/(x-1) 2nd Semester Review • x-1 = x+5 3 x-1 • (x-1)(x-1) = 3(x+5) • x2 - 2x + 1= 3x + 15 • x2-2x-3x+1= 3x-3x+15 Next Page

  46. 33.) Solve (x-1)/3 = (x+5)/(x-1) • x2-2x-3x+1= 3x-3x+15 • x2- 5x + 1 -15 = 15 -15 • x2- 5x - 14 = 0 • (x -7)(x + 2) = 0 • x - 7 = 0 & x + 2 = 0 • x = 7 & x = -2 (B) 2nd Semester Review

  47. 34.) Solve x/(2x-1) = 5/3 2nd Semester Review • x = 52x-1 3 • 3x = 10x - 5 • -7x = -5 • x = -5/-7 = 5/7 (C)

  48. 35.) What % of 4 is 1? • is % of ? • 1 = • .01 • 4 x • 1 = .04x • 1/.04 = .04x/.04 • 25 = x (A) 2nd Semester Review

  49. 36.) 90% of 40 is what #? • is % of ? • = 90 • .01 • 40 x • x = 36 (D) 2nd Semester Review

  50. 37.) A van travels 48 miles on 4 gallons of gas. How many gallons will it need to travel 120 miles? • 48/4 = 120/ x • 48x = 480 • 48x/48 = 480/48 • x = 10 (C) 2nd Semester Review

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