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1 Pm 9 Final Exam Review Simplify the following +. ( + 7 ) ( ) + ( ). 9 + ( ) 8 ( ). 0 ( ) Order the following from least to greatest. Show on a number line.,,0.9,, 0.8. Determine the volume of a cube with side length of 8 cm.. Simplify ( ) 6. Simplify 7. Evaluate Calculate the side length of a square with an area of. cm 9. Express 9 to decimal places :

2 0. Complete the table. Power Base Exponent Repeated Multiplication Value 7. Evaluate the following. Answer in fraction form if necessary. (No decimals) a) e) 6 b) ( ) c) ( ) 0 f) ( 0.) g) d) 0 h) ( ) 98. Evaluate: a) c) 8 ( ) + b) ( ) 0 ( ) + d). Express as a power with a base of. 0 ( ) Express the following as a single power with the lowest base. Show all steps answers produced by calculator only will not receive full marks. a) 9 b) c) A cube has a volume of cm. Determine the length of one side and express your answer as a power with the lowest possible base. 6.. Express as a single power, where possible. 6 a) ( ) ( ) ( 7 ) b) ( 7 ) d) c) ( 0 )( 0 ) 0 e) ( ) f) ( 7 ) 8

3 7.. Determine the value of the missing number. 6 a) 6 ( ) = b) 6 = 6 c) 6 = 8.. A cube has a side length of cm. a) Show the volume of the cube as a power, with the lowest base. b) Show the surface area as a power, lowest base. c) Another cube has a volume of cm. How many times greater is the volume of the larger cube? 9. Simplify into expressions containing positive exponents a) b) ( ) c) 6 d) 0. The area of a square is.9 cm. Find the side length of the square.. Determine the length of the missing side of the right triangle 9... Ryan drew a scale drawing of a rectangular field that is 80m by 0m. He used a scale in which cm represents. m. Determine the dimensions of the scale drawing.. Show that CAT is similar to ODG

4 . Measure the dimensions of the rectangles and determine if they are similar. Show work and explain your answer.. ABC ~ DEF. Determine the lengths of EF and DF. F 7 8 D 6 E 6. A person.8 m tall has a shadow. m long. At the same time, a lamppost has a.m shadow. Calculate the height of the lamppost. 7. Draw a similar shape using the following scale factors. Show your work, the measures of the angles, and the lengths of each side. a) A reduction by a scale factor of 80%. b) An enlargement by a scale factor of.

5 8. Find the surface area of the following composite shapes a) cm b) cm 0 cm 0 cm 6 cm cm cm cm 0 cm 0 cm c) 6 cm cm 6 cm 0 cm 9. Find the area of the composite shape 8 cm 6 cm 0 cm

6 0. Find the diameter of the circle below Find the values of the missing angles, below y x z w 0. Find the values of the missing angles, below 7 x y. Find the value of x for the diagram below 0 x. Find the unknown angles for the diagram below 0 x y

7 . Find the measures of the missing angles in the diagram below x y 0 z 6. Find the measures of the angles in the diagram below z 0 y 0 x 7. Find the perimeter of ABC B A C 8. Dave mows the grass at a golf course. He charges $6/h plus a flat fee of $0. If h represents the number of hours he works, and C represents his total fee, determine the equation that represents what he charges. 9. Determine the relation that matches the table of values. x y Determine the relation that matches the table of values. x y 7

8 . Determine the rate of change for the relation y = x.. Ben has $0 in his account. Each month he deposits $. Let t represent the time in months and A represent the account balance. Create a table from t = 0 to 6 then graph. What is the rate of change?. Graph and label x y = using a table of values. Graph and label x =. Determine which situation matches the graph. 0 Earnings Hours A. David earns $/h tutoring. C. Sandra earns $/h babysitting. B. Eric earns $6.0/h painting. D. Henry earns $.0/h mowing lawns. 6. Solve the following equations x x a) =. b) ( x + ) = x c) x + = d) x + x = x x The perimeter of a rectangle is 8 cm. The length is cm less than the twice the width. Determine the dimensions of the rectangle.

9 8. Determine the inequality that matches the number line Determine which inequality matches the number line For the linear relation y = x +, create a table of values then graph on the grid provided. x - y 0 6. A linear relation passes through (-, ) and (, 9). What is the rate of change? 6. Graph the following inequalities. a. x, where x is an Integer b. < x, where x is a Real Number 6. Solve and graph the following inequalities. a. 6x, where x is an Integerb. a > a, where x is a Real Number

10 6. Jesse is three times Ryan s age. In five years, the sum of their ages will be. Write and solve an equation to determine Ryan s current age. 6. Determine the degree of the polynomial xy x y + x. 66. Determine the coefficient of x in the polynomial x. 67. Determine the constant term in the polynomial x + x. 68. Evaluate the polynomial x + x if x = Determine the sum( x x 7) ( x x ) Subtract ( x x 6) ( x 7x ) Determine the product of -x and ( 7x ). 7. Determine the product of ( a )( a + ) 7. Determine the quotient of x y x y + xy xy. (6 ) ( ) 7. Determine the missing factor in (? )( x + ) = 0x.

11 a) b) c) 7. Complete the table for each polynomial. # of Degree terms x y 7xy a b ab + b 6 x yz + yz 8z Coefficients Variables 76. Express the perimeter of this rectangle as a polynomial and simplify. x + x A rectangle has a perimeter of (6x + ) cm. If the width is (x + ) cm. find the length. 78. The perimeter of the triangle below is x 6y. Show an expression that determines the length of the missing side and then simplify completely.? 9x 7y x+y 79. The diameter of a large circular pipe is m. There is water running through the pipe; the water covers only the bottom part of the pipe. The width of the water s surface across the pipe is 6 m. How deep is the water?

12 Math 9 Final Exam Review ---Key ) -9 ) -7 ) 8 ) ) 6) 7) 8) - 9) ) 0 ) - ) 0 7 ) -.,,, -0.8, 0.9 ) cm ) 6) 8 7) 9 7 8).8 cm. 9).0 0) ; 7; x x x x x x ; 8 ) a) 6 b) 8 c) d) e) f) g) - h) 6 ) a) 6 b) - c) - d) 0 ) ) a) b) c) ) 6) a) 8 b) 7 8 c) 0 d) 6 e) 0 f) 6 7) a) b) c) 8) a) 6 b) 6 c) 9) a) b) ( ) c) 6 d) 0) 6.8 ) 8.8 ) cm by 8 cm ) 9 6. = = 6.8. =. =. ) 6: =. :.8 =. Not similar ) EF = 9., DF = 0.8 6). m high 7) 8) a) 68 cm b) 8800 cm c) 0. cm 9) 608 cm 0) 7.09 ) x = 70, y = 6, z = 0, w = 6

13 ) x = 0, y = 0 ) x = 6 ) x = 60, y = 0 ) x = 6, y = 0, z = 6) x = 90, y = 0, z = 60 7) P = 8) C = 6h + 0 9) y = x + 0) y = -x + 0 ) r/c = ) A = t + 0; r/c = ) ) (,0) (0,-) ) Choice A 6) a) x = b) x = - c) x = 8 d) x = 7) by 8) x, x Rationals 9) x, x Integers 60) 6) r/c = (0,) 6) a) b) -

14 6) a) x 0 b) a < 0 6) Ryan is 8 years old 6) degree is 66) co-efficient is 67) constant is 68) 77 69) 8x x + 70) 6x 8x 7) x + 6x 7) a + a 7) x + xy 6 7) (-) 7) a) 6; ; and 7; x and y; b) 7; ; - and and ; a and b c) ; ; and and 8; x and y and z 76) P = x ) x ) x y 79) The water is.06 m in depth