4. Write the multiplication sentence that is represented by the diagram at right. 6. Use the distributive property to determine each product.

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1 Polynomials Practice Questions Complete the following on a separate piece of paper.. Write the prime factorization of 0.. Given the numbers, 5, and 7, determine the: GCF LCM. Use algebra tiles or a diagram to model each of the following binomial multiplication statements, then epress the product of the multiplication as an epanded polynomial in simplest form. + + ( )( + ) ( )( ). Write the multiplication sentence that is represented by the diagram at right. 5. Epand and collect like terms. ( a+ )( a+ ) ( n )( n ). Use the distributive property to determine each product. n(5n n+ ) kk ( 5k+ ) ( a )( a + a+ ) ( + )( ) 7. Multiply and then collect like terms. ( a ) ( )( ) ( )( + ) + ( 5) ( a b)( a+ b) ( a b) 8. A side of a cube is ( ) + cm long. Write a polynomial epression for the volume of the cube and then epand and collect like terms. 9. Write a simplified epression for the area of the shaded region: 0. Use algebra tiles to factor +. Monday, January, 0 ::09 PM MT

2 . Use algebra tiles or a diagram to factor the trinomial Factor the following. a a ab b Factor the following polynomials. 5y y+ y y Factor, if possible y y+ (g) m 8m (f) y y 0 + 7y+ y 5. Factor the following, if possible. 8 5y (f) What is the factored form of the trinomial 0 5y 0y? 7. The CN Tower in Toronto has an area that can be epressed as 5 + square units. Factor 5 + to find binomials that could represent the length and the width of the tower. 8. The area of a children s playground measures a + 8a 0 square units. Factor the polynomial to find the binomials that could represent the length and the width of the playground. If a represents m, what are the length and the width of the playground, in metres. 9. The area of a square can be given by the epression 9 +, where represents a positive integer. Write a possible epression for the perimeter of the square. Eponents and Radicals Practice Monday, January, 0 ::09 PM MT

3 . What is the value of each epression?. Evaluate each of the following State whether each number is a perfect square or a perfect cube. Show your work Simplify each epression. ( )( )( ) (7 y)( y) 7 5 ( 7 ab)( ab) y y 7 8 ( )( ) abc 8 5 abc (f) 5ab 9ab 5. Simplify the following, leave all of your answers as powers using positive eponents, then evaluate. 9 ( ) ( ) ( ) ( ) ( ). Simplify each of the following as far as possible. Leave your answer with positive eponents. 5 y ( ab)( ab ) ( y )( y ) y 7. Use the laws of eponents to simplify. Leave your answers with positive eponents, if applicable a 5 a 7 mn 8. Epress each power as an equivalent radical and vice versa. 5 ( ) 7 ( ) y (9 ) (f) (g) 0 y 9. Epress each mied radical as an equivalent entire radical. Monday, January, 0 ::09 PM MT

4 5 7 8 (f) 9 0. Epress each entire radical as an equivalent mied radical Arrange the following from least to greatest:, 5, 5,. Use estimation to order the following numbers from greatest to least.,,,. The stopping distance of a vehicle on an icy road depends on its speed and its mass. A typical formula for estimating the stopping distance, d, in metres is: d = 0.75sm, where s is its speed in kilometers per hour and m is its mass in tonnes. Estimate the stopping distance for a 000 kg car travelling at 00 km/h. Note: tonne = 000 kg.. The pressure, P, in kilopascals, eerted on the floor by the heel of a shoe is given by the 00m formula: P =, where m is the wearer s mass, in kilograms, and is the width of the heel, in centimetres. Find the pressure eerted by a 0 kg woman wearing shoes with heels cm wide. 5. The astronomer Johann Kepler found a formula which can be used to determine the number of Earth-days it takes each planet to travel once around the sun. The formula is: N B 0.R, where R is the mean distance from the planet to the sun in millions of kilometers and N is the number of Earth-days. Determine the number of Earth-days in the year of Saturn if Saturn is 00 million kilometers away from the sun.. The Japanese board game of Tai Shogi is an epanded version of chess. Like chess, it is played on a square board covered with small squares. If each small square has a side length of cm, the diagonal of the whole board measures 5000 cm. How many squares are on the board? Polynomials Practice Answer Key Monday, January, 0 ::09 PM MT

5 . 0 = g g ( + )( ) = a + a+ n 5n+ a a+. 5n n + n k + 5k k a a + 5ab 0b n 0. + ( ). ( )( ). ( a+ )( a+ b) ( )( + ). 5( y ) y(7 + y ) (5 + + ). ( + )( + 0) ( + 5)( ) ( y )( y ) mm ( + )( m ) (+ )( + ) (f) ( + y)( + y) (g) (y+ )(y 5) 5. ( + 9)( 9) (+ 5 y)( 5 y) not possible ( 9) ( + 7) (f) 5( ). 5( y)(+ y) 7. 5 and + 8. a+ 0 and a OR a+ 5 and a or Eponents & Radicals Practice Answer Key Monday, January, 0 ::09 PM MT

6 .. 0. Perfect Square Perfect Cube 0. y 7 a b 5. =. 7. a b y y = = ( ) 9 5 y 8. ( ) 5 or 5 ( ) y ( ) a 7 m n abc 8 - or ( ) (f) ( ) (g) ( ) y (f) a b or ( ) (f) ,5,, 5.,, 0, m. 500 kpa days. 5 squares Monday, January, 0 ::09 PM MT