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GEOMETRY HONORS SUMMER REVIEW Name ________________________ Evaluate each expression. 1.) 382 5 1 2.) 25 (18 9) 3 2 82 2 2 8 3.) 28 4.) 4(1 5)2 8 Name the reciprocal of each number. 7.) 1 15 8.) 2 11.) 3x 9 3 12.) 13.) 3x 8 22 14.) x 2 21 3 15.) 4(2 y 1) 10( y 5) 16.) 2 1 x5 x4 3 2 5.) 2 3 6.) 0 3 7 Simplify. 9.) 7 8 10 10.) 7 2 5 Solve. 70 x 30 y 5 Solve for x. 17.) x y d c 18.) 5(2a x) 3b Determine the slope of the line passing through each pair of points. 19.) (-3, 6), (-5, 9) 20.) (2, -5), (-7, -5) 21.) (7, -4), (9, -1) State the slope and y-intercept of the graph of each equation. 23.) y 5 x 3 24.) 3 y 8 x 2 Graph each equation using x and y intercepts. 25.) 4 x 5 y 20 26.) x 1 y4 2 22.) (6, -1), (6, 10) Graph each equation using the slope and y-intercept. 27.) y 2 x 1 3 28.) 3 1 x y 4 4 2 Write an equation in slope-intercept form of the line having the given slope that passes through the given point. 29.) 3; (5, -2) 5 30.) ; (3, 5) 3 Use the values from #29-30 to write the point-slope form of an equation of the line having the given slope that passes through the given point. 31.) 32.) Write an equation in slope-intercept form of the line that passes through each pair of points. 33.) (-1, 7), (8, -2) 34.) (-6, 2), (3, -5) Use the values from #33-34 to write an equation in point slope form of the line that passes through each pair of points. 35.) 36.) 37.) Write an equation of the line that is parallel to 2 x 3 y 1 and passes through (4, 2). Use slope intercept form. 38.) Write the equation of the line that is perpendicular to 5 x 3 y 7 and passes through (8, -2). Use slope intercept form. Solve the systems of equations using elimination or substitution. 39.) 2x y 1 x y 8 40.) 6x 7 y 5 2x 3y 7 41.) 9x 2 3y y 3x 8 Simplify each radical. 42.) 75 43.) 5 40 44.) 3 5 2 45.) 7 3 48.) 7 30 46.) 2 6 5 10 47.) 5 60 49.) 4 3 5 5 10 3 50.) 2 20 3 24 180 52.) 24a 2b 2 18ab 53.) x 2 7 x 12 55.) x 2 9 x 36 56.) 2 x 2 3x 20 1 2 9 2 x y 4 16 59.) 9 x 2 12 x 4 Factor each polynomial. 51.) 13 x 26 y 54.) x2 5x 6 57.) 28 x 2 13 x 6 58.) Solve each equation by factoring. 60.) 2 x 2 98 0 61.) 2 x 2 13x 24 62.) 6 x3 29 x 2 28 x 0 Solve each equation by using the quadratic formula. 63.) 24 x 2 2 x 15 0 64.) x 2 6 x 3 0 65.) 4 x 2 13 16 x SOLUTIONS 1.) 2 2.) 16 11.) x + 3 3 19.) 2 3.) 6 4.) 18 12.) -14x + 6y 3 20.) 0 21.) 2 25.) 3 5.) 2 13.) x = 10 14.) x = 69 22.) undefined 15.) y = 3 23.) m = 5, b = -3 26.) 7 8 34.) y 9 x 3 44.) 45 45.) 51.) 13(x – 2y) 21 3 3 14 38.) y 5 x 5 46.) 2 2 47.) 10 3 52.) 6ab(4ab – 3) 39.) (3, -5) 48.) 84 5 53.) (x + 3)(x + 4) 35 10.) 2 7 9.) 80 17.) x = cd – y 16.) x = -6 8 18.) x 3b 10a 5 2 24.) m 3 , b 3 28.) 5 32.) y + 5 = 3 (x + 3) 31.) y + 2 = 3(x – 5) 35.) y – 7 = -1(x + 1) OR y + 2 = -1(x – 8) 2 14 37.) y 3 x 3 7 8.) 17 27.) 5 30.) y 3 x 10 29.) y 3 x 17 15 7.) 1 6.) undefined 33.) y = -x + 6 7 7 36.) y – 2 = 9 x 6 OR y + 5 = 9 x 3 40.) (2, -1) 41.) no solution 49.) 14 3 5 5 42.) 5 3 43.) 10 10 50.) 2 5 6 6 54.) (x – 1)(x + 6) 55.) (x – 12)(x + 3) 3 1 3 1 56.) (2x + 5)(x – 4) 57.) (7x + 2)(4x – 3) 58.) 2 x 4 y 2 x 4 y 5 3 3 4 7 61.) , 8 62.) 0, , 63.) 6 , 4 64.) 3 2 3 3 2 2 59.) (3x – 2)2 65.) 4 29 2 60.) {-7, 7}