Algebra

1. Semester 1 Final Exam Review Algebra

2. Agenda • Vission/Mision • Classroom Norms • Where should you be? • Linear Combination • Applications • Questions

3. Vision and Mission • Vision: Through a combination of research-based, individualized, and specialized curriculum and instruction in the home; online conferencing with a certified teacher; and access to a community of experts in science and technology, our students will emerge as confident leaders of the digital age. • Mission: The mission of the Michigan Virtual Charter Academy is to provide an innovative, intensive academic preparation that inspires and educates students to achieve the highest levels of academic knowledge and skills. Michigan Virtual Charter Academy embraces a collaborative partnership between teachers and parents in order to empower students to reach extraordinary heights. Extraordinary results require extraordinary efforts! Through commitment, hard work, consistency, and responsibility, every student will meet the challenge of mastering high expectations.

4. *Have something ready to take notes with *Stay appropriate and on topic in chat *Complete the Setup Wizard before every class *Participate!!! *If you come in late, just roll with it and figure out where we are. Classroom Norms

5. Semester Final Exam • Must take the exam on the assigned day. • 2 parts to the test (just like your unit tests) • 15 multiple-choice questions • 3 multi-part questions on teacher-scored test • If you know how to do everything on this review you will do great on the final!

6. What algebraic property does this statement show?3+(-7)=(-7)+3 • Associative • Commutative • Closure • symmetric

7. What algebraic property does this statement show?3+(-7)=(-7)+3 • Associative • Commutative • Closure • symmetric

8. Solve: 3x-5=7x-21 • 2 • 3 • 4 • 5

9. Solve: 3x-5=7x-21 • 2 • 3 • 4 • 5 3x-5=7x-21 add 5 to both sides 3x=7x-16 subtract 7x from both sides -4x=-16 divide both sides by -4 x=4

10. Solve: |x|+4=7 • -3, +3 • 3 • 11 • -11, +11

11. Solve: |x|+4=7 • -3, +3 • 3 • 11 • -11, +11 |x|+4=7 subtract 4 from both sides |x|=3 take out absolute value sign x=-3, 3

12. Combine like terms to simplify: 7x+3y-2+6x-1+2y • x+1+5y • 13x+2y -3 • X+2y-3 • 13x+5y-3

13. Combine like terms to simplify: 7x+3y-2+6x-1+2y • x+1+5y • 13x+2y -3 • X+2y-3 • 13x+5y-3 7x+3y-2+6x-1+2y 13x+5y-3

14. Which equation can be used to solve the following word problem: Emilio has 3 more nickels than dimes, and the total value of his coins is $1.15. How many nickels does he have? Let n represent the number of nickels. • .10n+.05n+3=$1.15 • .10n+.05(n+3)=$1.15 • .10(n+3)+.05n=$1.15 • .10(n-3)+.05n=$1.15

15. Which equation can be used to solve the following word problem: Emilio has 3 more nickels than dimes, and the total value of his coins is $1.15. How many nickels does he have? Let n represent the number of nickels. • .10n+.05n+3=$1.15 • .10n+.05(n+3)=$1.15 • .10(n+3)+.05n=$1.15 • .10(n-3)+.05n=$1.15 n= nickels n-3=dimes .10(n-3)+.05n=$1.15

16. Evaluate the expression when a=5 and b=-2: |a|-b • 3 • 7 • -7 • -3

17. Evaluate the expression when a=5 and b=-2: |a|-b • 3 • 7 • -7 • -3 |a|-b |5|-(-2) 5-(-2) 5+2 7

18. Select the pair of equations whose graphs are perpendicular. • 5x-8y=9 and 12x-5y=7 • x+6y=8 and y=2x-8 • y=2x-7 and x+2y=3 • 2y=-3x+5 and 2x+3y=4

19. Select the pair of equations whose graphs are perpendicular. • 5x-8y=9 and 12x-5y=7 • x+6y=8 and y=2x-8 • y=2x-7 and x+2y=3 • 2y=-3x+5 and 2x+3y=4 See next slide for solution

20. 5x-8y=9 and 12x-5y=7 -8y=-5x+9 -5y=-12x+7 y=5/8x-9/8 y=12/5x-7/5 x+6y=8 and y=2x-8 6y=-x+8 y=-1/6x+8/6 y=2x-7 and x+2y=3 2y=-x+3 y=-1/2x+3 2y=-3x+5 and 2x+3y=4

21. Write an equation in slope-intercept form for the line passing through (-2,8) and (3,4).

22. Write in equation in slope-intercept form for the line passing through (-2,8) and (3,4).m = (8-4)/(-2-3) = 4/-5y-(4)=-4/5(x-3)y-4=-4/5x+12/5y=-4/5x+12/5+4y=-4/5x+32/5

23. Given the linear equation 2x+y=6, find the slope of its graph.

24. Given the linear equation 2x+y=6, find the slope of its graph.2x+y=6 y=-2x+6m=-2

25. Given the linear equation 3y=5x-4, find the y-intercept.

26. Given the linear equation 3y=5x-4, find the y-intercept.3y=5x-43y/3=5x/3-4/3y=5/3x-4/3y-intercept is -4/3

27. Solve the system of equations:3x+3y=-6 and x+3y=0

28. Solve the system of equations:3x+3y=-6 and x+3y=03x+3y=-6-x-3y=02x =-6x=-3(-3)+3y=03y=3y=1

29. Solve for x: 6 = 5 x-4 2

30. Solve for x: 6 = 5 x-4 2(6)(2)=(5)(x-4)12=5x-2032=5x32/5=x6 2/5=x

31. The length of a rectangle is 5 mm longer than its width. Its perimeter is more than 30 mm. Let w equal the width of the rectangle. Write an expression for the length in terms of the width.Use expressions for the length and width to write an inequality for the perimeter, on the basis of the given information. Solve the inequality, clearly indicating the width of the rectangle.

32. a) Let w = width of the rectangle. Let (w + 5) = length of the rectangle.b) Substitute these expressions into the formula for the perimeter of a rectangle. Perimeter = 2w + 2(w + 5) The perimeter is more than 30 mm, so the inequality is 2w + 2(w + 5) > 30.c) Solve for w.2w+2(w+5)>302w+2w+10>304w+10>304w>20w>5The width of the rectangle is greater than 5 mm.

33. Suppose you pay $45.00 for an electronic game that has been discounted 15%. What is the original price of the electronic game to the nearest cent?

34. If the game is discounted 15%, then the price you pay for the game is 85% of the original price. Use this information to set up a percent proportion. Reduce fractions to lowest terms before solving for x.45/x=85/10045/x=17/20(45)(20)=(17)x900=17xx=52.94The original price is $52.94.

35. Seth and George both worked hard over the summer. Together, they earned a total of $425. George earned $25 more than Seth. How much did each of them earn?

36. Let s be the money Seth earned and g be the money George earned.g + s = 425g = 25 + sSubstitute for g in the first equation.g + s = 425  (25 + s) + s = 42525 + 2s = 4252s = 400s = 200Substitute 200 for s in the equation to solve for g.g = 25 + (200) = 225Seth earned $200 and George earned $225.

37. Semester Final Exam • Must take the exam on the assigned day. • 2 parts to the test (just like your unit tests) • 15 multiple-choice questions • 3 multi-part questions on teacher-scored test • If you know how to do everything on this review you will do great on the final!