Algebra 1 2 Semester 2 Final Review Pick

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

1. ) Solve a graph the inequality: 5 x + 2 < 3(x-1) • 5 x + 2 < 3 x-3 • 5 x-3 x + 2 < 3 x-3 x-3 • 2 x + 2 < -3 • 2 x + 2 -2 < -3 -2 • 2 x < -5 • x < -5/2 2 nd Semester Review

2. ) Graph 5 < x < 7 • 5 < x < 7 • (A) Closed Dot Open Dot 2 nd Semester Review

3. ) Solve -10 < 2 x + 8 < 6 • -10 -8 < 2 x + 8 -8 < 6 -8 • -18 < 2 x < -2 • -18/2 < 2 x/2 < -2/2 • -9 < x < -1 2 nd Semester Review

4. ) Solve |x+1| > 2 2 nd Semester Review x+1 < -2 x+1 > 2 • x+1 < -2 • x+1 > 2 • x+1 -1 < -2 -1 • x+1 -1 > 2 -1 • x < -3 • x > 1 x < -3 or x > 1 Remember: < is and , > is or

5. ) Graph |x - 1| < 4 x-1<4 x - 1 > -4 • x - 1 < 4 • x - 1 > -4 • x - 1+1 < 4+1 • x -1+1 > -4+1 • x < 5 • x > -3 -3 < x < 5 2 nd Semester Review

6. ) Graph 2 x - y > -2 • 2 x -y > -2 x -2 • -y/-1 > (-2 x -2)/-1 • y < 2 x + 2 Graph it 2 nd Semester Review

6. ) Graph y < 2 x + 2 Sketch y = 2 x + 2 Now pick a point on one side of the dotted line (0, 0) 2 nd Semester Review

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

6. ) Graph y > 2 x + 2 y= 2 x + 2 ) C ( 2 nd Semester Review

7. ) Solve by linear combination 2 x+4 y = 2 3 x-4 y = -7 • 2 x+4 y = 2 • 2(-1)+4 y = 2 • -2 + 4 y = 2 • 2 x+4 y = 2 3 x-4 y = -7 • 5 x = -5 • 5 x/5 = -5/5 • -2+2+4 y=2+2 • x = -1 • 4 y = 4 (A) (-1, 1) • y = 4/4 = 1 2 nd Semester Review

8. ) Determine if the system has no solutions, one solutions, or many solutions. • -2 x + 8 y = 36 3 x -12 y = 49 • 3(-2 x + 8 y = 36) 2(3 x -12 y = 49) • -6 x + 24 y = 108 6 x - 24 y = 98 2 nd Semester Review

8. ) Determine if the system has no solutions, one solutions, or many solutions. • -6 x + 24 y = 108 6 x - 24 y = 98 • 0 = 206 (A) False No Solution 2 nd Semester Review

9. ) Determine the solution to the system of inequalities y < x -3 3 x + y < -4 • y < x -3 3 x + y < -4 • 3 x -3 x + y < -3 x -4 • y < -3 x -4 2 nd Semester Review

9. ) Determine the solution to the system of inequalities • y < x -3 y < -3 x -4 • Graph • Pick a point y < x -3 3 x + y < -4 2 nd Semester Review

y < x -3 y < -3 x -4 Now pick a point on one side of both lines - (0, 0) 2 nd Semester Review

Test a Point 2 nd Semester Review • Take the point (0, 0) and plug in the values in y < x -3 • y < x - 3 • 0 < (0) -3 • 0 < -3 Since it’s False,

y < x -3 y < -3 x -4 2 nd Semester Review

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

y < x -3 y < -3 x -4 2 nd Semester Review

10. ) Simplify 3 9 • 6 3 6 • 9 6 • (6 • 6) • (6 • 6 • 6) • (B) 12 6 2 nd Semester Review

11. ) Simplify 4 7 • (4 ) 4 7 (4 ) 4 4 4 4 • (4 )(4 )(4 )(4 ) • (B) 28 4 2 nd Semester Review

12. ) Simplify the product (4 gh 4)2(gh)4 4 2 4 • (4 gh ) (gh) 2 2 8 • 4 g h 4 4 g h • 6 12 • (C) 16 g h 2 nd Semester Review

-3 13. ) Simplify the product c -3 • c • 9 c 3 • 1/c 9 c 6 • c (C) • 9 c 9 3 c /c • = • c • c • c c • c 2 nd Semester Review

14. ) Rewrite using -3 positive exponents 4 -3 3 • 4 = 1/64 (C) 2 nd Semester Review

15. ) Multiply 3 • 2 3 2 • 3 • 0 5 • 3 • = • 8 • 3 • 1 • 24 (C) 2 nd Semester Review

16. ) Rewrite using positive exponents -1 -2 7 A /B -1 -2 • 7 A /B 2 1 • 7 B /A (D) 2 nd Semester Review

17. ) Which is equivalent 9 3 to 3 /3 9 3 • 3 /3 = 9 -3 3 = 6 3 • (C) 2 nd Semester Review

18. ) Simplify 7 5 4 6 (-20 x y )/(-5 x y ) 7 5 • (-20 x y ) 4 6 (-5 x y ) 3 • 4 x /y = (B) 2 nd Semester Review

19. ) What’s the perimeter of the triangle. 2 2 2 • a + b = c 2 2 2 • 3 + 4 = c 2 • 9 + 16 = c 2 • 25 = c • 5 = c 2 nd Semester Review

20. ) Solve 2 • 25 x 2 25 x -4=0 -4+4=0+4 2 • 25 x = 4 2 • 25 x /25 = 4/25 2 • x = 4/25 • x = ± 2/5 (D) 2 nd Semester Review

21. ) Graph y = 2 x +3 2 nd Semester Review

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

22. ) Solve by the Quadratic 2 formula: x -x -2 = 0 • x = 1 1+8 2 • x = 1 9 = 1 2 2 3 2 nd Semester Review

22. ) Solve by the Quadratic 2 formula: x -x -2 = 0 • x = 1+3 & 1 -3 2 2 • x = 4 & -2 = 2 2 • X = 2 & -1 2 nd Semester Review

23. ) Simplify: (3 v 4 - 4) - (8 v - 5) + (8 v 4 + 2 v) • 3 v 4 - 8 v + 5 + 8 v 4 + 2 v 4 4 • 3 v + 8 v - 8 v + 2 v - 4 + 5 4 • 11 v - 6 v + 1 (A) 2 nd Semester Review

24. ) Multiply (x+1)(x-9) • (x+1)(x-9) foil 2 • x -9 x + x - 9 2 • x -8 x - 9 2 nd Semester Review

25. ) Multiply (3 c+7)(3 c-7) • (3 c+7)(3 c-7) foil 2 • 9 c -21 c + 21 c - 49 2 • 9 c - 49 2 nd Semester Review

26. ) Multiply (x+2)(x 2 +2 x + 5) 2 • (x + 2)(x + 2 x + 5) • x 3 + 2 x 2 + 5 x + 2 x 2 + 4 x + 10 3 2 2 • x + 2 x + 5 x + 4 x + 10 3 • x + 2 4 x + 9 x + 10 2 nd Semester Review

27. ) Multiply using the Vertical format 2 • 6 y + 2 y + 6 y -8 3 6 y 2 2 y + + 6 y 2 - 48 y - 16 y - 48 6 y 3 - 46 y 2 - 10 y - 48 2 nd Semester Review

2 x 28. ) Factor - 5 x + 6 2 • x - 5 x + 6 • (x - 3)(x - 2) (C) 2 • x - 2 x -3 x + 6 2 • x - 5 x + 6 2 nd Semester Review

2 2 x 29. ) Factor + 3 x - 9 2 • 2 x + 3 x - 9 • (2 x -3)(x + 3) (D) 2 • 2 x + 6 x -3 x - 9 2 • 2 x + 3 x - 9 2 nd Semester Review

30. ) Factor 2 • x - 5 x - 6 2 x - 5 x - 6 • (x -6)(x + 1) (C) 2 • x + 1 x - 6 2 • x - 5 x - 6 2 nd Semester Review

31. ) Solve 2 • x 2 x + 2 x - 15 = 0 • (x - 3)(x + 5) = 0 • x - 3 = 0 & x + 5 = 0 • x = 3 & x = -5 (A) 2 nd Semester Review

32. ) Solve g/2 = 2/8 • G = 2 2 8 • 8 g = 4 • g = 1/2 (D) 2 nd Semester Review

33. ) Solve 5/(x+1) = 4/1 • 5 = 4 x+1 1 • 4 x + 4 = 5 • 4 x = 1 • x = 1/4 (A) 2 nd Semester Review

34. ) Solve 6/(x+2) = (x+1)/x • 6 = x+1 x+2 x • 6 x = (x + 2) (x + 1) • 6 x = 2 x + 3 x + 2 • 6 x - 6 x = 2 x Next Page + 3 x - 6 x + 2 2 nd Semester Review

34. ) Solve 6/(x+2) = (x+1)/x • 0 = - 3 x + 2 • 0 = (x -1)(x - 2) • x - 1 = 0 & x - 2 = 0 • x = 1 & x = 2 (B) 2 x 2 nd Semester Review

35. ) What % of 20 is 5? • is % of • 5 = • . 01 • 20 • 5 =. 2 x ? • 5/. 2 =. 2 x/. 2 • 25 = x (D) 2 nd Semester Review

36. ) 10% of 80 is what #? • is % of ? • = 10 • . 01 • 80 • x = 8 (C) 2 nd Semester Review

37. ) A bus travels 300 miles on 12 gallons of gas. How many gallons will it need to travel 400 miles? • 300/12 = 400/ x • 300 x = 4800 • 300 x/300 = 4800/300 • x = 16 (A) 2 nd Semester Review

38. ) Eight balls numbered from 1 to 8 are placed in an urn. If one ball is selected at random, find the probability that it is an even-numbered ball • 4/8 = 1/2 ( D) 2 nd Semester Review

39. ) Which of the following is a function? • A. ) {(-2, 7), (7, -3), (-2, -1)} • B. ) {(-2, 7), (-3, -1), (-3, -2), (-1, -3)} • C. ) {(-2, 7), (7, -2), (-1, -1)} • D. ) {(-2, 7, -3, -1)} 2 nd Semester Review

40. ) Find f(-3) given f(x) = -3 x - 4 • f(-3) = -3(-3) - 4 • f(-3) = 9 - 4 • f(-3) = 5 (D) 2 nd Semester Review

41. ) Decide whether the graph represents y as a function of x 2 nd Semester Review

42. ) Find the slope of f(-3) = -2, f(3) = 2 • (-3, -2) and (3, 2) • (x 1, y 1) and (x 2, y 2) • m = y 2 - y 1 = 2 - -2 x 2 - x 1 3 - -3 • m = 4/6 = 2/3 (B) 2 nd Semester Review

43. ) Find the equation of f(-1) = 5, f(-3) = -1 • (-1, 5) and (-3, -1) • (x 1, y 1) and (x 2, y 2) • m = y 2 - y 1 = -1 - 5 x 2 - x 1 -3 - -1 • m = -6/-2 = 3 2 nd Semester Review

43. ) Find the equation of f(-1) = 5, f(-3) = -1 • m = -6/-2 = 3 & y =mx + b • 5 = 3(-1) + b • 5 = -3 + b • 8 = b • y = 3 x + 8 (C) 2 nd Semester Review

44. ) Draw a Box&Whisker Plot for: 33, 28, 14, 27, 36, 32, 20 • 14, 20, 27, 28, 32, 33, 36 Median 1 st Quartile Median 2 nd Quartile Median 3 rd Quartile 2 nd Semester Review