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Name _____________ Place the following numbers in the correct category. {1/3, 0, Π , 2/9, -4, 7, -30, 16, 2, 20/4 } Whole Natural 0,7,sq.rt.16,20/4 7,sq.rt16,20/4 Integers 0, -4, 7, -30, 16,20/4 Rational Irrational Everything but pi and sq rt 2 Pi and sq rt 2 Place the following numbers in order from least to greatest: {4, -8, 0, 16, -14, -21, 2, 7} ( -21, -14, -8, 0, 2, 4, 7, 16) Place the following numbers in order from greatest to least {19, -12, -45, -3, -4, 17, -22, 22} ( 22, 19, 17, -3, -4, -12, -22, -45) Round - to the nearest tenth. 6.435 6.4 - to the nearest hundredth. 23.8613 23.86 - to the nearest thousandth. 17.42667 17.427 Absolute Value | 19 – 25 | 6 Exponents Simplify 28 256 |-3| + |2| 5 45 1024 |-5 – 10 | 15 62 36 Scientific Notation Express in scientific notation 0.00074 643,000 0.00354 7,000,000 7.4 x 10 ^-4 6.43 x 10 ^5 3.54 x 10 ^-3 7 x 10 ^6 Express in standard form 4 x 107 4.32 x 10-4 40,000,000 .000432 8.9 x 10 5 890,000 6 x 10-2 .006 Scientific Notation Add, Subtract, Multiply and Divide **Express your final answer in scientific notation!! (6.3 x 104 ) • (4.6 x 10 -2 ) 63000 x .046 = 2.898 x 10 ^3 (5x 105 ) ÷ (2 x 102 ) (4.2 x 105 ) + (3.41 x 10 500000 / 200 = 2.5 x 10 ^3 2 ) (4.58 x 10-3 ) - (4 x 10 -2) Substitution a=3 b = -9 420000 + 341 = 4.20341 x 10 ^5 .00458 - .004 = 5.8 x 10 ^-4 c=5 a+b+c 3 + -9 + 5 = -6 + 5 = -1 b2 + c2 81 + 25 = 106 (c – a) 2 5 – 3) ^2 = 2 ^2 = 4 Square Roots 324 =18 144 256 = 12 16 25 =5 81 9 Is the sq. root of 66 closer to 8 or 9? _____8______ If the area of a square is 225 square feet, what is the side length of the square? Sq. root 225 = 15 feet What is the perimeter? 4 x 15 = 60 feet Written Expressions Write the following expressions. Five less than a number n - 5 Twice as many pencils 2p The quotient of a number and 4 n 4 A number increased by 7 n + 7 Order of Operations (42 + 4) ÷ 4 20 ÷ (-2 – 2) + 22 ( 16 + 4) / 4 = 5 20 / -4 + 4 = -5 + 4 = -1 Combine Like Terms -3n + 12 – 4n -7n + 12 23x – 7x + 4x 16x + 4x = 20x Distributive property (multiply everything inside parenthesis) 8(y - -2x) = 8y + 16x 5(n + 13y) = 5n + 65y 3(w – 4) = 3w - 12 Distributive Property and Combine Like Terms 4(2r + 6y) – 3r – 2y = -8r + 24y -3r – 2y = -11r +22y -9(2x + 8) + 21 = -18x – 72 + 21 = -18x - 51 2(3p – 5p) = 6p – 10p = -4p Equations ½ x = 20 a = -28 13 42 = -14p -33 = x + 16 X = 40 a = -364 p = -3 -49 = x 22 = 2y + 8 6x – 4 = -10 7 = y x = -1 Distribute, Combine Like Terms AND Solve 5(x +7) – 2x = 44 -4(2y + 7) - 10 = 2 x = 3 y = -5 Solving Equations with variables on both sides 41 – 2n = 2 + n n = 13 6x – 9x – 4 = -2x – 2 x = -2 Express each percent as a fraction 73% 73 100 18% 9 50 4% 1 25 Express each decimal as a percent .7 70 % .324 32.4 % .65 65 % Express each fraction as a percent 14/15 93.3 % 2/5 40 % 18/93 19.4 % Find the values of a when the perimeter is 279 17 - a 7a 32a + 13 = 279 (solve) a = 8.3125 5a - 2 9a 12a-2 Find the value of y 15y – 10 + 14y – 7 + 3y + 3 = 180 5(3y-2) 22y -14 = 180 (solve) Y = 8.82 7(2y – 1) 3(y + 1) Rates $330 for 3 days Cost per day 432 beats per minute number of beats per second Divide = $110 per day Divide by 60 = 7.2 Ratio Write in simplest form 2 cups to 18 cups 1/9 12 boys : 18 girls 2/3 Proportions Solve 4 = 12 5 n n = 15 Is Of = 8 = n 3 27 n = 72 8 = 5 n 2.45 n = 3.92 % 100 19% of 400 73 is what percent of 400 96 is 30% of what number 19 = x 100 400 x = 73 100 400 30 = 96 100 x x = 76 x = 18.25 x = 320 Discounts and Sales Tax A $159.99 TV is on sale for 20% off. Find the sale price of the TV. Show your work! 160 x .20 = 32 , 160 – 32 = $128 Michelle bought a new car for $10, 599. A sales tax of 6% is applied to the price. Find the price of the car after the sales tax. Show your work! 10,600 x .06 = 636, 10600 + 636 = $11,236 Best Buy is advertising a CD player for $79.99 at 30% off. Find the total cost after the discount and 5% sales tax is applied. 80 x .30 = 24, 80 – 24 = $56 56 x .05 = 2.80, 56 + 2.80 = $58.80 final price. Graphing Name the quadrant or the axis the point lies on. U ____(-6, 8)______________ K _____(-4, -8)_____________ L ____(2, 0)______________ Q ___(0, 0)_______________ J _____(0, -1)______________ Complete the (x,y) tables and graph the coordinates. Be sure you connect your points to make a straight line!! y = 2x - 8 x y 0 -8 2 -4 5 2 8 8 y = -3x + 7 x -2 -1 0 1 2 y 13 10 7 4 1 *can you use slope-intercept ?? Slope Determine the slope of the following points. (9, 1) and (6, 3) 1 – 3 9 – 6 -2 = 3 (3, 2) and (-7, -8)) 2 - -8 3 - -7 10 10 = 1 What is the slope and y – intercept of the following equations? y = -3x + 5 m = -3 y-intercept = 5 -5 + ½ x = y m = 1/2 y-intercept = -5