MATH 9 YEAR END REVIEW

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1 Name: Block: MATH 9 YEAR END REVIEW Complete the following reviews in pencil. Use a separate piece of paper if you need more space. Please pay attention to whether you can use a calculator or not for each question. This is to help build your basic calculation skills. There is an answer key at the end of the booklet. Please check your answers and do your corrections. Make sure you understand each question! Ask for help if needed Chapter I get all of it I get it, but made some errors I get only some of it I don t get it at all 0 Integers and Fractions Review Powers and Exponent Laws 3 Rational Numbers Polynomials 6 Linear Equations 4 Linear Relations 7 Similarity

2 Chapter 0 Integers and Fractions Evaluate without a calculator: ( 1) 3. ( 4) ( ) 4. ( 6) 3. ( ) 4 6. ( 9 ) + ( 3) ( 6) ( 3) ( 7) 9. ( 7) + ( 3) ( ) 8 Evaluate without a calculator: 11. (7)( 9) 1. ( )(4) 13. ( )( 9) 14. (3)( 10) 1. ( 1)(10)( 7) 16. ( 7)(0) 17. ( 11)( 6) 18. (0)( 0)( 1)( ) 19. ( 8)(46)(0)( 1) 0. ( )( 4)(3)( 1)( ) Evaluate without a calculator: 1. 1 ( ) ( ) ( 80) ( 16) 9. ( 1) Follow the order of operations to evaluate without a calculator: 31. ( 3) 3. [ 3( + ( 4)) ] Evaluate without a calculator: ( 3)(4) 6( 3) (3 ) ( 3) (4 4) [ 6 ( 4) ] ( 1) (3 )

3 Chapter Powers and Exponent Laws * DO ALL WITHOUT USING A CALCULATOR 1. What is the difference between 3 and 3?. Which of the following are equal? 3, ( 3 ), (3), ( 3) 3. Evaluate: (a) ( 3) 4 (b) ( ) (c) 4 (d) ( 4) (e) 7 0 (f) ( 7) 0 4. Evaluate: [3 ( ) 3 + 4]. Evaluate: 1 ( 4) Why do ( 4) and 4 give different answers? 7. When powers with the same base are multiplied, you can the exponents. When powers with the same base are divided, you can the exponents. When a power is raised to another power, you can the exponents. 10. Simplify: (a) Express as a single power, then evaluate: (a) ( ) 4 ( ) (b) (c) [( 1) ] Simplify, then evaluate: (a) ( 3) 6 ( 3) 4 ( 3) 9. Simplify: (a) (b) (c) 1. A student answered the following skill testing question to try to win a prize: ( 4) 3 ( ) (b) (b) ( ) 10 The student s answer was. Did they win the prize?

4 Chapter 3 Rational Numbers 1. Which of the following are NOT rational numbers? Why? 3.1, 1., 3., π,, 3 0.3, 9,. (T / F) Converting rational numbers to the same form is a good idea when you are trying to compare them. 3. Order the following from least to greatest without a calculator: 7 4 4, 3.6,, 1, 7 4. (a) (T / F) A common denominator is required to add or subtract fractions. (b) (T / F) You add or subtract the denominators when adding or subtracting fractions. (c) (T / F) A common denominator is required to multiply or divide fractions. (d) (T / F) It is a good idea to convert mixed numbers to improper fractions first before doing any operations.. Evaluate without a calculator (a) ( 1.9) (b) 4. ( 13.7) (c) (d) Evaluate without a calculator: (a) (b) (a) (T / F) Following BEDMAS is only needed some of the time. (b) Evaluate: (.1)(18.) Evaluate without a calculator: (a) (b) (c) Evaluate: [ 7. ( 9.1)] 0. + ( 0.8) 9. During the month of July, Bruce earned $ cutting lawns and $89. weeding flower beds. He spent $3.94 on an MP3 player and purchased 3 Blu rays at $.39 each. (a) Write an addition statement for Bruce s balance at the end of July. (b) What is Bruce s balance? 3

5 Chapter Polynomials 1. Match each letter to the appropriate description: (i) What is the 3 called in 3x 4 +? (ii) What is the x called in 3x 4 +? (iii) What is the called in 3x 4 +? (iv) What is 3x 4 called in 3x 4 +? (v) y is an example of what type of polynomial? (vi) 3x 4 + is an example of what type of polynomial? (vii) x + y + z is an example of what type of polynomial? (viii) 3x 4 6x + 4x is an example of what? A. Variable B. Term C. Binomial D. Monomial E. Constant F. Trinomial G. Polynomial H. Coefficient. (a) Find the sum of the following algebra tiles. Recall that white tiles are positive and shaded tiles are negative. (b) Which of the following can be represented by the same set of algebra tiles and are therefore equivalent? 7x 4 + 3x 7x x 3x + 4 7x 3x 7x (a) (T / F) 3x + 4x = 7x 3 (b) (T / F) 3x 8x x + 4x = x + x (c) (T / F) Like terms have the same variable and the same exponents. 4. Simplify each polynomial: (a) a 4 9a + (b) 4m 3n + m 3n + m + n. Add or subtract: (a) (3s s + 6) + (7s 4s 3) 6. Determine each product or quotient: (a) 9(3s 7s + 4) (b) ( x + 8x ) (x + 3x 4) (c) ( 8x + 7x + 9) (6x x + ) (b) 7m(3m 9) 3 49w 6w (c) 7 (d) ( 1d + 18d) ( 6d) 4

6 1. Solve each equation: (a) 9x = 7. (b) a.7 4 Chapter 6 Linear Equations. Solve each equation: c (a) 6.s.7 = 30 (b) Solve without a calculator: (a) 4x + 1 = 3x (b) x + 3 = x 3 4. Solve each equation: (a) 7d = 8 d (b) 3.8v = 4.v. Solve: (a) 6(n 8.) = 18.6 (b) (t 8) = 4(t 19) 6. (a) (T / F) To eliminate fractions, multiply both sides by the lowest common denominator. (b) Solve: 7 8 c 7. Solve: m 1 m 3 8. Solve: Two taxi companies charge different amounts. Company A charges $4 plus $1. per km travelled, while Company B charges $6 plus $1 per km travelled. Write and solve an equation to determine at what distance the companies charge the same amount.

. Use your answer from question 1: (a) Determine the value of the 4 th term. (b) Which term number has a value of 33

(a) x = (b) y = 1 (c) x + y = 3 4. Graph each equation by making a table of values: (a) y = 3x. Carl is cycling across Canada.

7 Chapter 4 Linear Relations 1. The pattern in this table continues: Term #, n Term value, v Write an equation that relates v to n.. Use your answer from question 1: (a) Determine the value of the 4 th term. (b) Which term number has a value of 33? 3. Does each equation describe a vertical line, horizontal line, or oblique (slanted) line? How do you know? (a) x = (b) y = 1 (c) x + y = 3 4. Graph each equation by making a table of values: (a) y = 3x. Carl is cycling across Canada. This graph shows the distance he covers in 10 days. 6. Match each equation with a graph below. (a) x + y = (b) x + y = (c) x y = (a) Estimate how many days it will take him to cycle 700 km. (b) x + 3y = 9 (b) Predict how far Carl will cycle in 13 days. (c) In answering (b), did you use interpolation or extrapolation? Explain. 6

Chapter 7 Similarity 1. Determine the scale factor. The original image is on the left.. A drawing of a bedbug is. cm long. The actual size is 0.9 cm. Determine the scale factor. 3.

8 Chapter 7 Similarity 1. Determine the scale factor. The original image is on the left.. A drawing of a bedbug is. cm long. The actual size is 0.9 cm. Determine the scale factor. 3. A hockey rink measures 60 m by 6 m. A model of a hockey rink measures 1. m by 0.6 m. (a) What is the scale factor? 4. Bobbi wants to determine the height of a building. When Bobbi s shadow is. m long, the shadow of the building is 1 m long. Bobbi is 1.7 m tall. What is the height of the building to the nearest tenth of a metre? (b) A hockey goal is 1.8 m by 1. m. What are the dimensions of a goal on the model hockey rink? 7

ANSWER KEY 1.. 3. 4. 9. 9 6. 14 7. 10 8. 4 9. 13 10. 3 11. 63 1. 8 13. 4 14. 30 1. 70 16. 0 17. 66 18. 000 19. 0 0. 48 Chapter 0 Integers and Fractions 1. 3 31. 13. 3. 6 3. 1 33. 1 4. 0 34.. 40 3.

9 ANSWER KEY Chapter 0 Integers and Fractions or or or Chapter Powers and Exponent Laws 1. 3 = = 8 but 3 = 3 3 = 9. 3, (3), and ( 3 ) all equal 9. ( 3) equals 9 (positive). 3. (a) 81 (b) (c) 16 (d) 16 (e) 1 (f) ( 4) = ( 4)( 4) = 16 but 4 = (4)(4) = add; subtract; multiply 8. (a) ( ) 6 = 64 (b) 6 = 36 (c) ( 1) 8 = 1 9. (a) (b) (c) (a) 1 (b) 11. (a) ( 3) 4 = 81 (b) 8 = No, the answer is 43. Chapter Polynomials 1. (i) H (ii) A (iii) E (iv) B (v) D (vi) C (vii) F (viii) G. (a) 3x 4x + 9 (b) nd, 3rd, and 4 th expressions are the same 3. (a) F (b) T (c) T 4. (a) 7a + 1 (b) 6m + m 3n n. (a) 10s 6s + 3 (b) 3x 8x + 6 (c) 14x + 1x (a) 7s 63s + 36 (b) 1m 63m (c) + 7w + 8w or 7w + 8w (d) d 3 Chapter 4 Linear Relations 1. v = n + 3. (a) 1 (b) (a) vertical line (b) horizontal line (c) oblique line 4. (a) (b) Chapter 3 Rational Numbers π and. T 3. 4, 3.6,,, (a) T (b) F (c) F (d) T (a) 10.3 (b) 9. (c) (d) 1 or (a) or 18 (b) 3 3 or 1 7. (a) F (b) 40. (c) (a) (b) or (a) ( 3.94) + 3(.39) (b) $3.14 Chapter 6 Linear Equations 1. (a) x = 0.8 (b) a = (a) s = 4. (b) c = 4 3. (a) x = 3 (b) x = 4. (a) d = 6 (b) v = (a) n =.1 (b) t = (a) T (b) c = m = or 3 8. r = km Chapter 7 Similarity 1. SF = 3. SF =.3 3. (a) SF = 0.0 (b) 0.04 m by 0.03 m (or 4. cm by 3 cm) m. (a) approx.. days (b) approx km (c) extrapolation 6. (a) Graph B (b) Graph C (c) Graph A 8

Example #3: 14 (5 + 2) 6 = = then add = 1 x (-3) then. = 1.5 = add

Example #3: 14 (5 + 2) 6 = = then add = 1 x (-3) then. = 1.5 = add Grade 9 Curricular content Operations with rational numbers (addition, subtraction, multiplication, division and order of operations) -incudes brackets and exponents (exponent laws) -exponents includes