Olympic College Math 94 – Test on Topics 9 to 11 1. Simplify the following expressions (The answers are to have only positive exponents.): 3 4 (a) (4x )(5x ) 12a 9 = (b) (c) (d) = 3a 3 3 2 6 x 2 y 2 y 3 (– 4x ) =  5x   2 x  2  2  (e) = (f) (2x 3 y 2 ) 2 (3x 3 y) = Page | 1

Olympic College Math 94 – Test on Topics 9 to 11 2. Simplify the following expressions (The answers are to have only positive exponents.): z 6 (a) (b) (c) z  4 2 3 –3 5 4x y =  x  10 x 3 y 2 (d) 2 x 0 y 3 = 3 Express each number in scientific notation: (a) (b) 87,000 0.0023 = 4. Express each number without exponents: 5 – 3 (a) 5.2 X 10 (b) 4.6 X 10 = 12 5. There are approximately 5.9 X 10 miles in one light year. How many miles are there in 3,500 light years? Write your answer in scientific notation. Page | 2

Olympic College Math 94 – Test on Topics 9 to 11 6. Express each polynomial in descending order. Give the degree of each polynomial: 2 3 (b) t – 3t2 – 4 = 3 3 2 2 2 9. Multiply each of the following (a) 5(4x – 2) = 2 (c) 2x (4x – x + 3) = 3 2 Page | 3

(3x + 1)(2x – 3) 10x 4  15x 3  20x 2 5x 2 11. Simplify the following Olympic College Math 94 – Test on Topics 9 to 11 10. Multiply each of the following (a) (b) (3x + 1)(2x – 3) (4x – 5y)(2x + 3y) = = 11. Simplify the following 18x  9 3 (a) = 10x 4  15x 3  20x 2 (b) = 5x 2 Page | 4

Olympic College Math 94 – Test on Topics 9 to 11 Solutions 1. Simplify the following expressions (The answers are to have only positive exponents.): (a) (4x3)(5x4) = 20 x3 + 4 = 20 x7 12a 9 3a 3 4a 9 a 3 (b) = = 4a6 (c) (– 4x3)2 = (– 4)2 (x3)2 = 16 x6 6 x 2 y 3x 2 y 3x 2 (d) 2 y 3 = y 3 = y 2  5x   2 x  2  5  2 52 (2 x) 2 25 4 x 2 (e)  2    =  2 x  = = (f) (2x 3 y 2 ) 2 (3x 3 y) = (4 x6 y4 )(3x3 y ) = 12 x6 + 3 y4 + 1 = 12 x9 y5 2. Simplify the following expressions (The answers are to have only positive exponents.): z 6 z  4 2 3 –3 5 z6 – (– 4) = x2(–3) = 4 y 5 x 3 (a) (b) (c) = z10 x – 6 =  x  1 x 6 4x y 10 x 3 y 2 0 3 30 y 2( 3) = = 5 x 5 x3 y1 = 5 x 3 y (d) 2 x y 3 Express each number in scientific notation: (a) 87,000 = 8.7 x 104 (b) 0.0023 = 2.3 x 10 - 3 4. Express each number without exponents: (a) 5.2 X 105 (b) 4.6 X 10 – 3 = 520,000 = 0.0046 Page | 5

Olympic College Math 94 – Test on Topics 9 to 11 5. There are approximately 5.9 X 1012 miles in one light year. How many miles are there in 3,500 light years? Write your answer in scientific notation. (5.9 x 1012) x 3500 = 2.065 x 1016 6. Express each polynomial in descending order. Give the degree of each polynomial: (a) 2x2 – x3 + 7x = – x3 + 2x2 + 7x degree = highest power = 3 (b) t – 3t2 – 4 = – 3t2 + t – 4 degree = highest power = 2 7. Add: (3x3 – 5x) + (7x3 + 9x2) = = 3x3 – 5x + 7x3 + 9x2 3x3 + 7x3 + 9x2 – 5x 10x3 + 9x2 – 5x 8. Subtract: (5x2 – 3x + 1) – (x2 + 3x – 1) = = 5x2 – 3x + 1 – x2 – 3x + 1 5x2 – x2 – 3x – 3x + 1+ 1 4x2 – 6x + 2 9. Multiply each of the following (a) 5(4x – 2) = 20x - 10 (b) 3x2(2x – 6) = 6x2 + 1 – 18x2 = 6x3 – 18x2 (c) 2x3(4x2 – x + 3) = 8x3+2 – 2x3 +1 + 6x3 = 8x5 – 2x4 + 6x3 10. Multiply each of the following (a) (3x + 1)(2x – 3) = 6x2 – 9x + 2x – 3 = 6x2 – 7x – 3 (b) (4x – 5y)(2x + 3y) = 8x2 + 12xy – 10xy – 15y2 = 8x2 + 2xy – 15y2 11. Simplify the following 18x  9 3 18x 3 9 3 (a) =  = 6x – 3 10x 4  15x 3  20x 2 5x 2 10x 4 5x 2 15x 3 5x 2 20x 2 5x 2   (b) = = 2x2 – 3x + 4 Page | 6