2. Write each number as a power of 10 using negative exponents.

Transcription

1 Q Review 1. Simplify each expression. a. 1 0 b c. d. e. (7) 2 f. 6 1 g. 6 0 h. (12x) 2 i. 1 j. 6bc k. (11x) 0 l m. m 8 p 0 n. 5a 2c k ( mn) o. p. 8 p 2m n q. 8 2 q r 5 r. (10a) b xy z v s. t. 1 5m 7 9( ab) c 2. Write each number as a power of 10 using negative exponents. 1 1 a b. 10

2 . Write each expression as a decimal. a. 10 b Write each number in scientific notation. a.,200,000,000,000 b Write each number in standard notation. a b Simplify. Write each answer using scientific notation. a. 5(.2 10 ) b. 0.0( ) 7. Rewrite each expression using each base only once. a b Simplify each expression. a. (2h 5 )(h ) b. mn 2 m 2 n mn 1 c. (12mn)( m n 2 p 5 )(2m) d. (6a b 2 )( ab 8 ) e. (z 5 ) f. (g 5 ) 5 (g 6 ) 2 g. (b c 2 ) 6 c h. 5x 5 y 2 (2x 1 ) i. j. k. 2 21m 2 m 2 5 m n l. m. 2m mn 8 x 2y 6 9 xy 2 5 xy 5

3 9. Simplify each expression. Write each answer in scientific notation. a. (7 10 )( ) b. ( 10 6 )( ) c. ( ) 2 d. ( ) e Complete each equation. a. (p ) = p 8 b. ( x y ) 1 x 8 y Error Analysis A student simplifies the expression as follows: [(6 ) ] (2 ) 6. What mistake did the student make in simplifying the expression? What is the correct simplification? 12. The area of a triangle is 80x 5 y. The height of the triangle is x y. What is the length of the base of the triangle? 1. The radius of a cylinder is cm. The height of the cylinder is cm. What is the volume of the cylinder? (Hint: V = πr 2 h) 1. The side length of a cube is ft. What is the volume of the cube? 15. Find the balance in each account after the given period. a) $8000 principal earning 5% compounded annually, after 6 yr b) $500 principal earning % compounded quarterly, after 10 yr 16. A business purchases a computer system for $000. If the value of the system decreases at a rate of 15% per year, how much is the computer worth after years?

4 17. Find the degree of each monomial. a) 2b 2 c 2 b) d e c) 12 d) 7y Write each polynomial in standard form. Then name each polynomial based on its degree and number of terms. a) 5x + 2x 2 x + x b) 12t x + 8 2x 19. A local deli kept track of the sandwiches it sold for three months. The polynomials below model the number of sandwiches sold, where s represents days. Ham and Cheese: s 28s 2 + s Pastrami: 7.s 2 + 2s Write a polynomial that models the total number of these sandwiches that were sold. 20. Simplify. a) (g g ) + ( g + 8g) b) 6j 2 2j j 2 + j 6 c) ( 12h + h) ( 6h + h 2 h) d) d 2 + 8d 2 (2d 2 7d + 6) 21. The fence around a quadrilateral-shaped pasture is a a + 9 long. Three sides of the fence have the following lengths: 5a, 10a 2, a 2 7. What is the length of the fourth side of the fence? 22. Simplify each product. a) v (2v 2 v + 5) b) (n + 7)5n c) m(m 8m 2 + m)

5 2. Find the GCF of the terms of each polynomial. a) 8a + 2a 0a 2 b) 12x + 2x 2 16x c) 9m + 0m 2 2. A circular hedge surrounds a sculpture on a square base. The radius of the hedge is 6x. The side length of the square sculpture base is x. What is the area of the hedge? Write your answer in factored form. 25. Simplify each product. a) (2x 6)(x + ) b) (p 2 + 2)(p 1) c) (a 2 + a + )(2a 6) d) (2c + 8)(2c 2 c 1) 26. Simplify each expression. a) (5s + 2) 2 b) (m + n) 2 c) (m ) 2 d) (6s t) The figures below are squares. Find an expression for the area of each shaded region. Write your answers in standard form.

6 12. Simplify each product. a) (x + 12)(x 12) b) (r 2 + 5s)(r 2 5s) 28. Factor each expression. Check your answer. a) n 2 12n + 5 b) x x + 6 c) z 2 + z 0 d) a 2 7a 18 e) 6r 2 10r 2 f) 2c 2 2c + 11 g) 25k 2 20 h) 25x 2 1 i) 8b b The area of a rectangular computer screen is x x The width of the screen is 2x + 8. What is the length of the screen? 0. Find two different values that complete each expression so that the trinomial can be factored into the product of two binomials. Factor your trinomials. a) x 2 + x + 12 b) 9m 2 m Find the GCF of the first two terms and the GCF of the last two terms for each polynomial. a) 12x + x x + 5 b) 10s + 5s 2 + 6s Factor each expression. a) 18r 12r r 1 b) 5w 6w + 15w 2 12w. A shipping box in the shape of a rectangular prism has a volume of 12x + 2x x. What linear expressions can represent possible dimensions of the box?

7 . Identify the vertex of each graph. Tell whether it is a minimum or a maximum Order each group of quadratic functions from widest to narrowest graph. a) b) y = x 2, y = 2x 2, y = 6x 2 6. For a physics experiment, the class drops a golf ball of a bridge toward the pavement below. The bridge is 75 feet high. The function h = 16t gives the golf ball s height h above the pavement (in feet) after t seconds. Graph the function. How many seconds does it take for the golf ball to hit the pavement? 22. Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of each function. a) y = x 2 + x 6 b) y = x Graph each function. Label the axis of symmetry and the vertex. Find the Domain and Range, Y-Intercept. Maximum / Minimum Value a) f (x) = 2x 2 + 8x 10 b) f (x) = 2x 2 12x A punter kicked the football into the air with an upward velocity of 62 ft/s. Its height h in feet after t seconds is given by the function h = 16t t + 2. What is the maximum height the ball reaches? How long will it take the football to reach the maximum height? How long does it take for the ball to hit the ground? 9. Solve each equation by finding square roots. If the equation has no realnumber solution, write no solution. a) z = 0 b) d 2 1 = 50 c) 16x 2 9 = 0

8 0. Find the value of x for the square. If necessary, round to the nearest tenth. 1. Use the Zero-Product Property to solve each equation. a) (f + 2)(f 5) = 0 b) d(d 8) = 0 c) (2x 7)(x + 10) = 0 2. Solve by factoring. a) a 2 15a + 56 = 0 b) s s = 2 c) 8x x + = 0. Ling is cutting carpet for a rectangular room. The area of the room is 2 ft 2.The length of the room is feet longer than twice the width. What should the dimensions of the carpet be?. Reasoning for the equation, find k and the value of any missing solutions. x 2 kx 16 = 0 where 2 is one solution of the equation. 5. Find the value of c such that each expression is a perfect-square trinomial. a) b b + c b) g 2 20g + c 6. Solve each equation by completing the square. If necessary, round to the nearest hundredth. a) r 2 + 8r + 1 = 0 b) y y = 17 c) 2k 2 + k = 5

9 7. The height of a triangle is x inches and the base is (5x + 1) inches. The area of the triangle is 500 square inches. What are the dimensions of the base and height of the triangle? 8. Use the quadratic formula to solve each equation. a) 2x 2 6x + = 0 b) 7d 2 + 2d + 9 = 0 c) 2j 2 j = 1 9. Find the number of real-number solutions of each equation. a) x 2 x 8 = 0 b) 2x 2 + x + 2 = 0 c) x 2 8x + 7 = 0 6. A basketball is passed through the air. The height h of the ball in feet after the distance d in feet the ball travels horizontally is given by h = d d + 5. How far horizontally from the player passing the ball will the ball land on the ground? 50. Which type of function best models the data in each table? Use differences or ratios. a) b) c)