SOME OF EVERYTHING FINAL REVIEW

Transcription

1 SOME OF EVERYTHING FINAL REVIEW

2 Hilltop High School Math 9 Review Complete this review package to help ensure you are ready for Math 10C! Operations with positive and negative numbers Multiplying and Dividing positive and negative numbers: If the signs are the same (both positive or both negative) the answer will be positive. If the signs are different (one positive and one negative), the answer will be negative Adding and Subtracting positive and negative numbers: Adding a positive number Subtracting a negative number Subtracting a positive number Adding a negative number Addition (move to the right on a number line) Subtraction (move to the left on a number line)

3 More Practice the more you practice mental math, the better you will get and the faster you will get without having to resort to using your calculator. Roll several dice and add, subtract, or multiply the values without using a calculator. Using a deck of cards, flip up two or more cards and add or multiply the values together. For an etra challenge, let the black cards be positive numbers and the red cards be negative. You can also flip them into fractions to add, subtract, multiply or divide.

4 Pythagorean Theorem Helpful Reference: Tips: Identify and label each side Fill in the blanks in your formula Solve for the unknown Remember to take the square root to find the final answer! Solve for the unknown side in each of these triangles. Round to the nearest tenth if necessary

5 What is the length of bd? 11. a = 1 ; b = ; c = 1. a = 1 ; b = ; c = a = ; b = ; c = Are these right triangles? How do you know? a) b) 1. To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must walk 4 meters south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond?

6 Fraction Operations Simplify the following fractions: Multiplying and dividing fractions. Your final answer should always be in simplest form: Adding and Subtracting fractions. Your final answer should always be in simplest form:

7 Eponent laws Eponent Law Product Law Quotient Law Power of a Power Power of a Product Power of a Quotient Zero Power 1 Eample Simplify each of the following into a single power. Do not evaluate:

8 Simplify each epression using the eponent laws:

9 Order of operations - BEDMAS What is the first step for each of the following? Evaluate using the order of operations

10 Equation solving

11 Polynomials Adding and Subtracting Polynomials

12 Multiplying Polynomials Dividing Polynomials

13 PM 9 Final Eam Review 1 Name: Ch 1 Simplify the following. +. ( + 1 ) ( ) + 16 ( 4). 8+ ( 4) 6 10 ( ) 1. 1 ( ) Order the following from least to greatest. Show on a number line: 4 1.4,,0.9,, 0.4 Ch 1. Determine the volume of a cube with side length of 1 cm.. Simplify ( 4 ). Simplify 4. Evaluate 49. Calculate the side length of a square with an area of 8.1cm. 6. Epress 4 61 to decimal places. 7. Complete the table. Power Base Eponent Repeated Multiplication Value

14 8. Evaluate the following. Answer in fraction form if necessary. (No decimals) a) e) 4 9. Evaluate: a) 4 10 c) 10. Epress b) ( 4) c) ( 4) 0 1 f) 4 g) d) + b) ( ) d) 16 as a power with a base of h) ( 1) Epress the following as a single power with the lowest base. Show all steps answers produced by calculator only will not receive full marks a) 7 b) 8 c) 9 1. A cube has a volume of 79 cm. Determine the length of one side and epress your answer as a power with the lowest possible base. 1. Epress as a single power, where possible. 4 a) ( ) ( ) ( ) 4 b) 7 d) 4 ( ) 14. Determine the value of the missing number. c) ( 10 4 )( 10 ) 10 e) ( 6 ) 4 f) ( 9 4 ) 11 6 a) 8 ( ) = b) 49 = 7 c) 6 = 4 1. A cube has a side length of 8 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. 16. Simplify into epressions containing positive eponents a) 4 b) ( ) c) d) 17. The area of a square is 1.84 cm. Find the side length of the square. 1 4

15 18. Determine the length of the missing side of the right triangle Ch 1. Shane drew a scale drawing of a rectangular field that is 80m by 110m. He used a scale in which 1 cm represents. m. Determine the dimensions of the scale drawing.. Show that ΔCAT is similar to ΔODG. D 4. A.6.4 T C. O 4.8 G. Measure the dimensions of the rectangles and determine if they are similar. Show work and eplain your answer. 4. Δ ABC ~ ΔDEF. Determine the lengths of EF and DF. F D. A person 1.8 m tall has a shadow. m long. At the same time, a lamppost has a.m shadow. Calculate the height of the lamppost. 6. 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 1. 1 E

16 Ch 4 1. Find the surface area of the following composite shapes 1 cm a) b) 1 cm 0 cm 0 cm 6 cm 4 cm 1 cm 0 cm 40 cm cm 8 cm c) 8 cm cm 6 cm 1 cm. Find the area of the composite shape to the right. 1 cm 4 cm Ch cm 1. Dan mows the grass at a golf course. He charges $8 per hour plus a flat fee of $1. If h represents the number of hours he works, and C represents his total fee, determine the equation that represents what he charges.. Determine the relation that matches the table of values:. Determine the relation that matches the table of values: 4. Determine the rate of change for the relation y =. 1 y y Graph and label the following using a table of values: a) y = + 4 b) y = c) = 4

17 6. Determine which situation matches the graph. 0 Earnings Hours A. David earns $/h tutoring. C. Sandra earns $4/h babysitting. B. Eric earns $6.0/h painting. D. Henry earns $4.0/h mowing lawns. 7. Solve the following equations a) + = 1 b) 4( 1) = + c) 4 = 6 d) + = The perimeter of a rectangle is 8 cm. The length is cm more than the twice the width. Determine the dimensions of the rectangle. 9. Determine which inequality matches the statement: A number is greater than or equal to. 10. Determine the inequality that matches the number line Determine which inequality matches the number line Solve and graph the solution to the following inequalities a) > b) c) For the linear relation y = 1, create a table of values then graph on the grid provided y

18 14. A linear relation passes through (, 4) and (7, 6). What is the rate of change? 1. Solve the following equations. a. 4 7= b. 10 4= Graph the following inequalities. a. 4, where is an Integer b. 1<, where is a Real Number 17. Solve and graph the following inequalities. a , where is an Integer b. a > 4a 1, where is a Real Number 18. Bill is twice Andrea s age. Seven years ago, the sum of their ages was 1. Write and solve an equation to determine Andrea s current age. 19. A rectangle has a perimeter of cm. It is 8 cm longer than it is wide. Write and solve an equation to determine the dimensions of the rectangle. Ch 6 1. Determine the degree of the polynomial Determine the coefficient of in the polynomial.. Determine the constant term in the polynomial Evaluate the polynomial if =.. Determine the sum ( 7 1) ( 4 6) Subtract ( 1 ) ( 9 4) Determine the product of and ( 4 ). 8. Determine the product of ( 4+ )( ) 9. Determine the quotient of (10 1 ) ( ) Determine the missing factor in (? )( ) =

19 11. Complete the table for each polynomial. Degree # of terms Coefficients Variables a) y 7 y b) c) ab ab + b yz + 4yz 8z 1. Simplify the polynomial Determine the sum ( 4 ) ( 6 ) Determine the difference of ( 4 1) ( 7 ) Determine the product of ( )( 6 ) Determine the product of ( )( 4) Determine the quotient of ( 4 y 8 y 1) ( 4) Epress the perimeter of this rectangle as a polynomial and simplify Epress the area of this rectangle as a polynomial and simplify A rectangle has a perimeter of (16 + 4) cm. If the width is ( + 4) cm. find the length. 1. The perimeter of the triangle below is 1 8y. Show an epression that determines the length of the missing side and then simplify completely.? - y y

20 Ch 8 1. A rectangular playground has dimensions 4 m by 16 m. What are the dimensions of a 1 playground drawing that has a scale factor of. 00. A reduction of each object is to be drawn with the given scale factor. Determine the corresponding length in centimetres on the scale diagram. 1 a) Fishing rod length 80 cm, scale factor 0 b) Boogie board length 1. m, scale factor 0.0 c) Jogging route 10 km, scale factor A surveyor wants to determine the width of a river. She measures distances and angles on land, and sketches this diagram. What is the width of the river, PQ? 4. Draw the image of ΔPAM after each reflection below. Write the coordinates of the larger shape formed by ΔPAM and its reflection images. Draw the lines of symmetry of the larger shape. a) Reflect ΔPAM in the y-ais. b) Reflect ΔPAM in the -ais. c) Reflect ΔPAM in the line y =.. Which polygons have rotational symmetry? State the order of rotation and the angle of rotation symmetry for each. a) b) 6. Draw the rotation image for each transformation of quadrilateral ABCD. a) 180 about verte B b) 90 clockwise about verte A c) 90 counterclockwise about point E d) 180 about the origin

21 7. For each pair of shapes, determine whether they are related by line symmetry, by rotational symmetry, by both line and rotational symmetry, or by neither. Describe the symmetry, if any. a) b) Ch 9 1. What is the value of and y in the diagram to the right? z 10 y 1. In the diagram to the right, what is the value of angle a?. If two angles of a triangle are and 9, what is the third angle? 4. Determine the measure of the central angle subtended by arc AB. The radii divide the circle into equal parts a. Determine the measure of E in the circle: 6. Determine the measure of C : 7. In the circle to the right, PR = 0, OQ = 1. What is the length of diameter? P Q O Find the values of each of the angles. State a geometric reason for your answer = R y y =

22 9. = 140 y = y 10. O 116 z = y = y z = Find the values of each of the indicated angles. y = = y = y z y = y = z = = y = 1. y y = y = = y =

23 Find the length of the indicated side P 8 y C 1cm S = = y = 19. Given: CQ =6 cm, PR = 16 cm 0. Given :AC = 1 m, AD = 7m R P Q C A y D B C R = = y = 1. In the circle shown, XZ = 18 cm and CY = cm. What is the length of YW? X Y Z C W. The diameter of a large circular pipe is 0 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 1 m. How deep is the water?. Solve for. 6

24 PM 9 ANSWER KEY Ch ,,, -0.4, 0.9 Ch cm cm ,, -()()()()(), -4 8a. 1 1 b. 64 c. 1 d. 7 8 e. 16 f g. -1 h. 1 9a. -1 b. 6 c. 09 d a. 1 b. 9 6 c , 1a. 11 b. ( )( ) c d. 8 e. (6 8 )( 8 ) f. 0 14a. 9 b. 4 c. 6 1a. 9 b. (6)( 6 ) a. b. c. 4 ( ) d cm Ch 1. cm 44cm..6 = 4. = 4.8 = 1.. See Key 4. EF=1., DF= m 6. See Key Ch 4 1a. 68 cm b cm c cm. 09 cm Ch 1. C = 1 + 8h. y = 4. y = See Key 6. A 7a. 0 b. 9 c. 1 d cm 1 cm , R 11., I 1a. 1 < b. 4 c See Key a.. b See Key 17a. b. a years 19. 9cm 17cm Ch a. 4,,,-7,,y b.,,-,-1,1,a,b c. 4,,,4,-8,,y,z

25 y y y + Ch cm 8cm a..6 cm b cm c. 0.0 m. 16m 4. See Key a. 1, 60 b., See Key 7. See Key Ch , Inscribed angles ½ of central angles, Inscribed angles ½ of central angles 9. 0 Circle around a point = 60, 110 Inscribed angles ½ of central angles Tangent to a radii is 90, 64 Quadrilateral=60, 8 Inscribed angles ½ of central angs , ,, , , , cm, 1cm cm 0. cm, 10.9cm 1. 1.cm..4m. 8.

26 Types of questions I need to work on

27 Pm 9 Final Eam Review Simplify the following +. ( ) ( ) + 1 ( ). 9 + ( ) ( ) ( ) Order the following from least to greatest. Show on a number line 1.,,0.9, 1, Determine the volume of a cube with side length of 8 cm. 1. Simplify ( 4 ) 16. Simplify Evaluate Calculate the side length of a square with an area of. cm 19. Epress 19 to decimal places :

28 0. Complete the table. Power Base Eponent Repeated Multiplication Value 7 1. Evaluate the following. Answer in fraction form if necessary. (No decimals) a) e) b) ( ) 4 c) ( ) 0 f) ( 0.) g) d) 0 h) ( 1) 98. Evaluate: a) c) 8 ( 1) + b) ( ) 0 ( ) + d). Epress as a power with a base of ( ) Epress 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 1 cm. Determine the length of one side and epress your answer as a power with the lowest possible base. 6.. Epress as a single power, where possible. 6 4 a) ( ) ( ) ( 7 ) b) 4 ( 7 ) d) 4 4 c) ( 10 )( 10 )4 10 e) ( ) 4 f) ( 7 ) 8

29 7.. Determine the value of the missing number. 6 a) 16 ( ) = b) 6 = 6 c) 16 = 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. 4 c) Another cube has a volume of cm. How many times greater is the volume of the larger cube? 9. Simplify into epressions containing positive eponents a) b) ( 4) c) 6 d) 0. The area of a square is cm. Find the side length of the square. 1. Determine the length of the missing side of the right triangle Ryan drew a scale drawing of a rectangular field that is 80m by 10m. He used a scale in which 1 cm represents. m. Determine the dimensions of the scale drawing.. Show that CAT is similar to ODG

30 4. Measure the dimensions of the rectangles and determine if they are similar. Show work and eplain your answer.. ABC ~ DEF. Determine the lengths of EF and DF. F D 6 E 6. A person 1.8 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 1.

31 8. Find the surface area of the following composite shapes a) 1 cm b) 1 cm 0 cm 0 cm 6 cm cm 4 cm 1 cm 0 cm 40 cm c) 6 cm 4 cm 6 cm 10 cm 9. Find the area of the composite shape 8 cm 16 cm 0 cm

32 40. Find the diameter of the circle below Find the values of the missing angles, below y z w Find the values of the missing angles, below 7 y 4. Find the value of for the diagram below Find the unknown angles for the diagram below 0 y

33 4. Find the measures of the missing angles in the diagram below y 10 z 46. Find the measures of the angles in the diagram below z 10 y Find the perimeter of ABC B A C 48. Dave mows the grass at a golf course. He charges $6/h plus a flat fee of $10. If h represents the number of hours he works, and C represents his total fee, determine the equation that represents what he charges. 49. Determine the relation that matches the table of values. 1 y Determine the relation that matches the table of values. 1 y 7 4 1

34 1. Determine the rate of change for the relation y = 4.. Ben has $10 in his account. Each month he deposits $1. 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 y = 4 using a table of values 4. Graph and label =. Determine which situation matches the graph. 0 Earnings Hours A. David earns $/h tutoring. C. Sandra earns $4/h babysitting. B. Eric earns $6.0/h painting. D. Henry earns $4.0/h mowing lawns. 6. Solve the following equations a) =. b) ( + ) = 4 c) + 1 = d) 4 + = The perimeter of a rectangle is 48 cm. The length is 1 cm less than the twice the width. Determine the dimensions of the rectangle.

35 8. Determine the inequality that matches the number line Determine which inequality matches the number line For the linear relation y = +, create a table of values then graph on the grid provided. -1 y A linear relation passes through (-1, ) and (, 9). What is the rate of change? 6. Graph the following inequalities. a. 4, where is an Integer b. 1<, where is a Real Number 6. Solve and graph the following inequalities. a , where is an Integerb. a > 4a 1, where is a Real Number

36 64. Jesse is three times Ryan s age. In five years, the sum of their ages will be 4. Write and solve an equation to determine Ryan s current age Determine the degree of the polynomial y y Determine the coefficient of in the polynomial Determine the constant term in the polynomial Evaluate the polynomial + if = Determine the sum( 7) ( ) Subtract ( 11 6) ( 7 ) Determine the product of - and ( 7 ). 7. Determine the product of ( a 1)( a + 4) 7. Determine the quotient of y y + y y. ( ) ( 4 ) 74. Determine the missing factor in (? )( + ) = 10.

37 a) b) c) 7. Complete the table for each polynomial. # of Degree terms y 7y 4 a b ab + 4b 6 yz + 4yz 8z Coefficients Variables 76. Epress the perimeter of this rectangle as a polynomial and simplify A rectangle has a perimeter of (16 + 4) cm. If the width is ( + 4) cm. find the length. 78. The perimeter of the triangle below is 1 6y. Show an epression that determines the length of the missing side and then simplify completely.? 9 7y +y 79. The diameter of a large circular pipe is 4 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 16 m. How deep is the water?

38 Math 9 Final Eam Review ---Key 1) -9 ) -7 ) 8 4) ) ) 1 7) 1 8) -1 9) ) ) - 1) ) -.,, 1 1, -0.8, ) 1 cm 1) 16) 8 17) ).8 cm. 19) 1.0 0) ; 7; ; 18 1) a) 11 6 b) 8 c) 1 d) 4 e) 1 f) g) -1 h) 1 64 ) a) 16 b) - c) -14 d) 10 ) 1 4) a) 1 b) 1 c) 1 ) 6) a) 18 b) 7 18 c) 10 d) 1 6 e) 1 0 f) 16 7) a) b) 4 c) 4 8) a) 6 b) 4 6 c) 1 9) a) 1 b) ( 4 ) 1 c) 6 d) 0) ) 8.84 ) cm by 48 cm ) = = = 1. = 1. 4) 6:4 = 1. 4:.8 = 1.4 Not similar ) EF = 19., DF = ). m high 7) 8) a) 68 cm b) 8800 cm c) 0.44 cm 9) 608 cm 40) ) = 70, y = 46, z = 0, w = 6

39 4) = 10, y = 0 4) = 6 44) = 60, y = 0 4) = 6, y = 0, z = 11 46) = 90, y = 0, z = 60 47) P = 4 48) C = 6h ) y = + 0) y = ) r/c = ) A = 1t + 10; r/c = 1 ) 4) (4,0) (0,-) ) Choice A 6) a) = 1 b) = - c) = 8 d) = 7) 1 by 11 8) 1, Rationals 9), Integers 60) 61) r/c = (0,) 6) a) b) -1

40 6) a) 0 4 b) a < 0 64) Ryan is 8 years old 6) degree is 66) co-efficient is 1 67) constant is 68) 77 69) ) ) ) a + 11a 4 7) 4 + y 6 74) (-) 7) a) 6; ; and 7; and y; b) 7; ; - and 1 and 4; a and b c) 4; ; and 4 and 8; and y and z 76) P = ) ) 4 y 79) The water is.06 m in depth