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 -2x - 3 < 2x -2x + 4 2x - 3 < 4 2x - 3+3 < 4+3 2x < 7 x < 7/2 (A) -4 -2 2 4 2nd Semester Review

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

3.) Solve -6 < -2x + 6 < 8 -6 < -2x + 6 < 8 (B) 2nd Semester Review

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

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

4x -3y < -12 4x - 4x -3y < -4x -12 -3y < -4x -12 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

Now pick a point on one side of the dotted line -(0,0) 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

Since it’s False, Shade the opposite side of (0,0). 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).

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

7.) Solve by linear combination 4x-2y = 16 3x+2y = 5 4x-2y = 16 3x+2y = 5 7x = 21 7x/7 = 21/7 x = 3 3x+2y = 5 3(3)+2y = 5 9 + 2y = 5 9-9+2y=5-9 2y = -4 y = -4/2= -2 (B) (3,-2) 2nd Semester Review

3x + y = 14 6x + 2y = 28 -2(3x + y = 14) -6x - 2y = -28 6x + 2y = 28 8.) Determine if the system has 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

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

9.) Determine the solution to the system of inequalities y > x + 1 3x + y < 5 y > x + 1 3x + y < 5 3x -3x + y < -3x + 5 y < -3x + 5 2nd Semester Review

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

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

Since it’s True, Shade the (0,0) side. 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.

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

Since it’s True, Shade the (0,0) side. 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.

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

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

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

12.) Simplify the product (2fg6)4(fg)5 (A) 16f9g29 2nd Semester Review

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

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

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

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

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

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

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

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

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

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

22.) Solve by the Quadratic formula: x2 -x -2 = 0 2nd Semester Review

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

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

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

(x + 1)(x2 - x - 2) x3 - 3x - 2 x3 -x2 -2x + x2 -x -2 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

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

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

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

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

x2 + 3x - 10 = 0 (x - 2)(x + 5) = 0 x - 2 = 0 & x + 5 = 0 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

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

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

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

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

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

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

37. ) A van travels 48 miles on 4 gallons of gas 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

38. ) Ten balls numbered from 1 to 10 are placed in an urn 38.) Ten balls numbered from 1 to 10 are placed in an urn. If one ball is selected at random, find the probability that it is number 10. 1/10 ( D) 2nd Semester Review

39.) Which of the following is a function? B.) {(6, -4), (-4, 0), (6, 3)} C.) {(6, -4), (-4, 6), (3, 3)} D.) {(6, -4), (0, 3), (0,6), (3, 0)} 2nd Semester Review

40.) Find f(-1) given f(x) = 4x - 2 f(-1) = -6 (C) 2nd Semester Review

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

42.) Find the slope of f(-3) = 2, f(5) = -2 (-3, 2) and (5, -2) (x1, y1) and (x2, y2) m = y2 - y1 = -2 - 2 x2 - x1 5 - -3 m = -4/8 = -1/2 (C) 2nd Semester Review

43.) Find the equation of f(-3) = -9, f(3) = 3 (-3, -9) and (3, 3) (x1, y1) and (x2, y2) m = y2 - y1 = 3 - -9 x2 - x1 3 - -3 m = 12/6 = 2 2nd Semester Review

43.) Find the equation of f(-3) = -9, f(3) = 3 m = 12/6 = 2 & y = mx + b 3 = 2(3) + b 3 = 6 + b -3 = b y = 2x - 3 (B) 2nd Semester Review

44.) Draw a Box&Whisker Plot for: 29, 23, 6, 22, 33, 28, 13 6, 13, 22, 23, 28, 29, 33 Median 1st Quartile Median 2nd Quartile Median 3rd Quartile 2nd Semester Review

44.) Draw a Box&Whisker Plot for: 29, 23, 6, 22, 33, 28, 13 6, 13, 22, 23, 28, 29, 33 (A) 6 13 23 29 33 2nd Semester Review

45.) What is the mean of: 17, 20, 6, 24, 28, 25, 23, 1 17, 20, 6, 24, 28, 25, 23, 1 144 144/8 = 18 (C) 2nd Semester Review

46.) What is the median of: 10, 10, 22, 22, 22, 9, 1, 4, 21, 11, 22 1, 4, 9, 10, 10, 11, 21, 22, 22, 22, 22 Median (A) 2nd Semester Review

47.) Name the mode or modes of: 9,8,11,27,17,25,10,27,7,16,17 7,8,9,10,11,16,17,17,25,27,27 (D) Modes Modes 2nd Semester Review

120 = 2•2•2•3•5 = 2 30 = 48.) Simplify 60 • 2 60 • 2 = (B) 60 • 2 = 120 = 2•2•2•3•5 = 2 30 = (B) 2nd Semester Review

3•3•6 + 5•5•6 3 6 + 5 6 8 6 49.) Simplify 54 + 150 54 + 150 (B) 54 + 150 3•3•6 + 5•5•6 2nd Semester Review 3 6 + 5 6 8 6 (B)

50.) Simplify 3 (4 + 6) 4 3 + 18 = 4 3 + 2•3•3 = 4 3 + 3 2 (B) 4 3 + 18 = 4 3 + 2•3•3 = 4 3 + 3 2 (B) 2nd Semester Review