Final Exam Review

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1 MATH 9 ~~Final Exam Review~~ Unit #1: Square Roots and Surface Area NAME: DATE: CLASS: is a perfect square. What does this mean? 2. Find all of the perfect squares between 1 and Complete the following table. Only complete the 3 rd and 4 th column if the number is a perfect square. Number Perfect Square (y/n) Square Root (if yes) Check (Work backwards to show that it is a perfect square) 4. Calculate the square root of the following. You may use a calculator, and round to 2 decimal places. a) b) 11.10

2 5. The calculations in question 4 yielded approximate values, and not exact values. Explain what this means. 6. Using benchmarks, estimate the square root of the following. You may not use a calculator. a) 8 b) 2 c) 20 d) 32 e) 47 f) Jamie say that 16 =8. Did Jamie make an error? If so, identify how Jamie made that error. 8. A square has an area of cm 2. a. What is the side length of the square? b. What is the perimeter of the square?

3 9. A square space is divided into four sections. Sections A and B are also squares. Section A has an area of 16 m 2, while Section B has an area of 9 m 2. Determine the combined area of the remaining space in the auditorium. 10. Calculate the unknown side length of the triangle in each case: a) b) c) d) 11. Leon's bedroom is rectangular. The length of one wall of Leon's bedroom is 3 metres. The length from one corner of the bedroom to the diagonally opposite corner is 5 metres. What is the length of the other wall?

4 12. Vincent lives right in the middle of the city where the houses are very close together. He wants to paint a window sill on the second floor of his house. This window sill is 3.5 meters above the ground. There is 2 meters between his house and his neighbour s house, and the window is on the side of the house. Vincent has a 5-meter ladder. a. Draw a diagram to model the situation. b. If he places the ladder at the height of the window sill, how far away from his house would the base of the ladder need to reach? c. If he places the ladder as far away from his house as he can, how far up his house will the ladder reach? d. Is this ladder suitable for this job? 13. In your own words, explain what surface area is.

5 14. Draw a fully labelled net for each of the following: m a) m b) c) d)

6 15. Solve for the surface area of the above given four figures: a) b) c) d)

7 16. Determine the surface area of the following composite shapes: a. b. The cylinder has a length of 3.5m and a diameter of 0.5m. c.

17. Calculate the surface area of the birdhouse given below. The entrance to the bird house has a diameter of 3 cm. The perch is a cylinder with a length of 7 cm and a diameter of 1 cm.

8 17. Calculate the surface area of the birdhouse given below. The entrance to the bird house has a diameter of 3 cm. The perch is a cylinder with a length of 7 cm and a diameter of 1 cm. All other side lengths are given on the diagram. b. Mary wants to paint the bird house. Paint costs $6.00 per can and each can will cover an area of 500 cm 2. How many cans of paint does Mary need? How much will the paint cost her?

9 Unit #2: Exponents and Power Laws 18. Complete the following table: Power Base Exponent Repeated Multiplication Standard Form (Answer) 3 3 (-2) (-1)(-1)(-1)(-1)(-1) (-7) 5 (-3) 3 -(3) Write the following using base 10: a. 62= b. 24.2= c = 20. Compare and contrast -6 3, (-6) 3, and (6) 3 : 21. Can you use the exponent laws to simplify ? Explain

10 22. Evaluate the following, being careful to following exponent laws. a) 5 4 x 5 2 b) 3 3 x 3 4 x 3 0 c) d) e) (2 4 ) 2 f) (8 3 ) g) 5 9 h) i) x j) k) ((2 3 ) 1 ) 2 l) (3 2 ) 5 (3 3 )(3 4 ) 23. Write the following as a product of a power or a quotient of a power and then evaluate: a) (6x4) 4 b) ( 8 3 )3

11 c) ( 4 5 )2 d) (5x2) Use the product of a power or quotient of a power laws in reverse to write each of the following as a single power, and then evaluate. a) b) (9 4 )(2 4 ) 25. Samantha completed the following math problems. Determine her error and complete a correct solution. Samantha s solution ( ) =( )3 =(3 2 ) 3 =3 6 = Apply all exponent laws possible, and then evaluate: a. 3 2 x2 2 x x2 b. 4 3 x c. (((-2) 3 ) 2 ) 2 x ((-2) 2 ) 1 d. 2 4 x x3 2

12 Unit #3: Rational Numbers 27. Identify each of the following as a rational number, or an irrational number. For each, give an explanation for your answer. Possible explanations include but are not limited to: whole number, non-terminating decimal, terminating decimal, repeating decimal, fraction. Number Rational or Irrational? Explanation π Order the following rational numbers from least to greatest. You may use a number line to help you, but it is not necessary , 1, 10, 2 1 7, 2.14, 0.25, 0, 0.21, 7 8, Simplify each of the following expressions b. c a. 5 2 d e f. -8 (-15)

13 g / h. -9 (-27) i j k l m. ( 2 14 ) ( ) ( 3 1 ) (5 5 ) n o p q r. ( 2 3 ) ( 5 3 ) ( 9 10 ) 30. Jimmy has a busy day ahead of him. First he has to go to the mall, which will take him 1 5 hours to drive to, and where he will spend 2 hours. He then needs to go to the bank, which will take 3 him an additional 1 hours to drive to, and where he will spend 1 hours of his time. Finally, 15 3 Jimmy plans on going grocery shopping, which will take him 2 hours to drive to. Jimmy thinks 15 he will spend 1 1 hours shopping here (He needs A LOT of food..). 15 How long will Jimmy spend running errands. Express your answer as an improper fraction.

14 31. Ensure that you are following the order of operations, and simplify each of the following expressions: 12 a. (3 6) b c d e. 12 / f g. ( )2 h. ( (42 )(4 3 ) 3 ) 0 i. ( x 0.25)-1.46 j ( ) k l. ( ) 3 3 5

15 32. Yuvon has $ in her bank account. She goes to the grocery store and buys a turkey for $21.32, a bag of potatoes for $3.77, a loaf of bread for $3.29, a box of butter for $3.43, and a bunch of carrots for $0.97. Yuvon then makes a cash donation equivalent to 1 of 5 what she spent. How much money does Yuvon have in her bank account when she leaves the store? Unit #4: Linear Relations 33. What are the properties of a linear relationship? What will the graph look like? 34. Determine the slope of a line with the following sets of points: a) (2,-2) and (-4,2) b) (3,1) and (10, 1) c) (-4, -10) and (-7, 4) d) (-3, -1) and (6, 3) e) (1, 3) and (1, -2) f) (6, 3) and (2, 9)

16 35. Determine the equation (y=mx+b) described by the following, and graph the line. a) A line with a slope of 3 and a y-intercept of 4 b) A line with a slope of 4 and a y-intercept of 5-3 c) A line which goes through (0, 5) and (-2, -1) d) A line which goes through (7, -1) and (-7, -4) e) A line which goes through (1, 4) and has a y-intercept of 6 f) A line which goes through (2, 5) and has a y-intercept of -3

17 36. Create a table of values for each of the equations, and then graph the function: a. y=3x-2 x y b. y = 3 5 x + 3 x y 37. Determine the equation of the following graphs: a. b. c. d.

18 38. John is taping a commercial for toothpaste. He is getting paid $ to tape the commercial and then a royalty (money each time the commercial aired) of $1.50. a. What are the variables in this situation? b. Create an equation to model this situation. i. What is your slope? ii. What is your y-intercept? c. If John s commercial airs 20 times a day, for a year (52 weeks) on television station, how much money will he earn? d. If John earns $12000 total, how many times did he commercial air? e. Create a graph to model this situation. 39. Billy Jean and Bobby Sue are heading out on a road trip! Starting 10 km from home, they drive 100 km/hour. a. Identify your variables: b. Create an equation to model this situation: c. Is this data continuous or discrete? Explain. d. If they drive for 4 hours, how many km from home are they? e. Create a graph to model this situation.

19 Unit #5: Polynomials: 40. Complete the following table: Polynomial Degree Type of function Coefficient(s) Variable(s) Constant Term 4x 2-5x+2 2 Trinomial 4, -5 X 2-2x 2 +x-5 8g 2 h+g-4 2 Binomial -3 3 Monomial 3 Trinomial 10 1 Monomial h, g Draw the algetiles to represent the following polynomials: a. 2x 2-3x+y-1 b. -3xy+2y Simplify the following: a) (2x 2 +3x-2)+(3x 2-5x+3) b) (3xy 2 +2xy -6) + (2xy 2-3xy +x 2 +2) (4x 2 +10) c) (2x 2-3y 2 +10z+3) (4x -3y 2-5z 2 ) + (2x 2 +3y 2 ) d) (15x 2 y 3-5x 2 y-3y 2-2) (-4x 2 y 3-5xy 2 +15y 2 +10)

20 42. Expand and simplify the following: a) 3(2x 2 +5) b) 2x 2 (3x ) c) (-x+2)(2x-15) d) (2x +7)(3x-4) e) (x+14)(-3x-3) f) (4x-3)(2x 2-3x+5) g) 4xy(2x 2-3y) h) (2x-y)(4x+3y) 43. Find the quotient of the following: a) 12x 3 b) 15x3 +25x 2 15x c) 2x2 14x 2x d) 16x2 +24x 4x

21 44. Use the area model to solve each of the following: a) (3x+2)(2x-1) b) (2x+6)(-x+4) 45. Factor the following using the GCF: a) 5x 2-10 b) 14x 3 y + 18x 2 y 2 28x 2 y c) -17x 2 y + 25xz 2 d) 3x 2 y 3 z -15x 3 yz + 21yz e) 18xyz xz 33xyz 4 f) -8w 2 y 2 z -24w 5 y 3 z 2

22 46. Simplify the polynomials below, and then evaluate when x=4 a. 3x 2 6x 3x 2 9x b. 4x 2 4x 4x 47. Jimmy has two decks in his backyard. The larger deck has an area of 6x 2 + 3x, while the smaller deck has an area of 4x 2 +4x+2 a) Using what we know about simplifying polynomials, how much bigger is the larger deck then the smaller deck? b) If x= 2 meters, determine the size of both of Jimmy s decks Lager deck: Smaller deck: 48. A rectangle has an area of 25x 3 y 2, and a width of 5x 2 a. Draw this rectangle below: b. What is the length of the rectangle? c. Determine a simplified expression for the perimeter of the rectangle.

23 Unit #6: Solving Linear Equations and Inequalities 49. In each of the following problems, solve for x. a) 3x =6 b) -4=8x c) 2x+7=3 d) 5x-3=-13 e) -6x+11=-3x+17 f) -2x+4=6x-16 g) 5x+9=7x-3 h) 2.5m+3=5m-6.25 i) -5(2y-4)=6(-2y-2) j) 8 2x 6 3 2x 9

24 50. Solve the following equations and check your solution: a. 2g-17=-8g+13 Check b. 3(h+1)=-2(h-9) Check c. 4x 3 2 = x 12 4 Check d. 3(2m+4)=-8(-m-3) Check e. 2y 8 = 6 3y 2 3 Check

25 51. Solve the following linear inequalities and graph your solution on the number line provided. a. 8x 6 10x 18 b. 4(2y 5) 6(2x 6) c. x 6 3x 9 4 6

26 52. Solve the following linear inequality, and provide 3 possible values for x. Show that each of the possible values works in the original inequality. 7(-2x+3) > 5(-3x+1) 53. Shyanne is organizing a neighbourhood dance. It will cost her $500 to hire the DJ, and $140 to book the community center for the evening. Shyanne doesn t want to make any money on the dance, but she will charge each guest $4.00 to help cover the cost. a. Identify your variable(s). b. Create an inequality to represent this situation. c. How many people would Shyanne need, minimally, to attend the dance for her to break even?

27 54. Toby has a new job for the summer; he will be a strawberry picker! He has two options to get paid. Option A: Earn $30 per day, and $0.50 per container of strawberries picked. Option B: Earn $20 per day, and $0.75 per container of strawberries picked. a. Define the variables in this situation: b. Create an equation to model each option: Option A: Option B: c. How many containers of strawberries would Toby need to pick before both options would give him the same amount of money? d. What is the advantage to each plan? 55. Provide a situation that could be modeled by the following equation: a. y=25x+5 b. y=-5x+3

28 Unit #7: Probability and Statistics 56. Explain, in your own words, how a survey can be biased. 57. Identify the problem with each of the following situations, and provide a possible solution. a. Jinyung surveyed her classmates on the day before their Math exam to ask them what they think of their Math teacher. Problem: Solution: b. Toliver asked people at Prince Andrew High School if they think their hockey team is better than Dartmouth High s hockey team. Problem: Solution: c. Larissa asked people Do you think that its rude to be on your cell phone when somebody is talking to you as she took a SnapChatted a selfie of herself. Problem: Solution: d. Victoria asked other parent s at her son s swimming lessons if they think it is important for children to learn to swim. Problem: Solution: 58. Identify the sample and the population in the following situations: a. Bell Aliant sent out a survey to everybody who spoke to a customer service rep asking them if they were satisfied with their service people responded. Sample: Population: b. Francois asked the people in the front row of the new Avengers movie who their favorite character is. Sample: Population: c. Jennifer asked everybody sitting by the aisle in the bus if they like country music. Sample: Population: d. Donald Trump asked all of the people working in Trump Tower if they think he would make a good president. Sample: Population: Additional Questions: Textbook: Page , #1-12, Unit reviews and Cumulative Test #1 review (available on my website)

29 Unit 1: Square Roots and Surface Area: Math 9 Final Exam Formula Sheet

Linear Relations: b m Unit 5: Polynomials: Materials permitted during the exam: Pencil Eraser Scrap Paper Calculator

30 Unit 2: Exponents and Power Laws: Product Law: a m x a n = a (m+n) Quotient Law: am an= am-n Power of a Power Law: (a m ) n = a (mxn) Power of a Product Law: (a x b) m = a m x b m Power of a Quotient Law: ( a b )m = am Unit 4: Linear Relations: b m Unit 5: Polynomials: Materials permitted during the exam: Pencil Eraser Scrap Paper Calculator A book to read if you finish the exam early Materials not permitted during the exam: Cell Phones Earbuds Notes and Textbooks

Number Line: Comparing and Ordering Integers (page 6)

LESSON Name 1 Number Line: Comparing and Ordering Integers (page 6) A number line shows numbers in order from least to greatest. The number line has zero at the center. Numbers to the right of zero are