Basic Fraction and Integer Operations (No calculators please!)


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1 P1 Summer Math Review Packet For Students entering Geometry The problems in this packet are designed to help you review topics from previous mathematics courses that are important to your success in Geometry. Please do each problem and show the work that supports that answer. This packet will be collected and graded the first week of school. There will also be a test over this material the first week of school. It will be your first test grade. There are no retakes on this test. Enjoy your summer! We look forward to seeing you in August! Basic Fraction and Integer Operations (No calculators please!) Simplify. Leave each answer as reduced fractions (no decimals). Show all work ¾ ½ ( 18) ( 14) 11. (5) ( ) ( 3) 16. Match the correct property with the statement given: = (1) = (34) = 9( ) = (9 6) 10 = 9 (6 10) = 13 A. Commutative Property B. Associative Property C. Distributive Property D. Identity Property of Addition E. Identity Property of Multiplication
2 P 17. Write each phrase as an algebraic expression or equation. a) Let x be an integer, write an expression for b) Let y be an integer, write an expression for the next consecutive integer the next consecutive odd integer c) If the length of a rectangle is three more d) Let n be a number, write an expression for than twice the width (w), write an expression the 8 less than the square of the number to represent the length 18. Evaluate the expressions for the given value(s) of the variable(s) a) s 3 t for s =  and t = 4 b) r 0 s s 3 for r = 8 and s = Name the first fifteen perfect square numbers, beginning with 1. _1_,,,,,,,,,,,,,, 0. Simplify the following. a) 4m + 9 7m + m 17 b) 7(4x + x) 3(6x 7x) 1. Solve each equation. Simplify solutions. Leave each answer in reduced form (no decimals). Show all work. a) 3(x 4) = 9 b) 3x 9 4x 9 c) (6x 8) (5x 9) = 3 d) 3 9 x 3 1 e) x 4x3 f) n 8 ( n1) 3
3 P3. Solve the following literal equations for the variable identified. 3V a) Solve r h for V Inequalities 3. Solve and graph the following inequalities, write interval notation on all solutions. a) d b) 4x 6 > 3x + Inequality Statement: Interval Notation: Inequality Statement: Interval Notation: Linear Equations 4. Identify the correct form of the equation: Point Slope form a) Ax By C Slope Intercept form b) y y1 m( x x1) Standard form c) y = n Direct Variation form d) y mx b Horizontal line form e) x = n Vertical line form f) y kx 5. What is the slope of the line for each of the following: a) a line that runs through the points (4, ) and (7, 9). b) a horizontal line that runs through the point (4, 8) c) a line parallel to the line with equation 5y 7x = 10. d) a line that is perpendicular to the line with equation y = ¾x + 1
4 P4 6. Graph the line for y x 1 5 Point: Slope: 7. Graph the line y 6 x 1 Slope: yintercept: 8. Graph the line y =  6 Slope = 9. Graph the line x = 3 Slope = Graph the line for y x 5 7 Slope: yintercept: 31. Graph the line 5xy 1 xintercept: yintercept:
5 P5 3. Write the equation of the line that passes through the points (15, 5) and (4, 1). Write the equation in pointslope form, slope intercept form and standard form. Graph the line. Slope = Point Slope Form: Slope Intercept Form: Standard Form: 33. Solve the system of equations by using the Substitution Method. Write your solution as an ordered pair. Check your answer. xy 3 11x y 37 Solution: 34. Solve the system of equations by using the Elimination Method. Write your solution as an ordered pair. Check your answer. x 3y 3 5x7 y 15 Solution: 35. Solve the system of equations using any method. Write your solution as an ordered pair. 1 y 7 x x y 15 a) b) 3x y 50 x y4
6 P6 EXPONENTS 36. Simplify No Negative Exponents! Polynomial Answers should be in standard form. a) 5x 3 b) 0 5 c) 0 ( 5) d) 5 9 e) 3 3 x x f) x Quadratic Equations & Functions 37. Multiply. a) (x5)(3x 7) b) ( x5)( x 5) c) (x 3) d) (x 3)( x 5x 7) 38. Factor the following if possible or write Not Factorable : a) x 6x 7 b) x 11x 4 c) x 5x 7 d) x y x y x y e) x y f) 10x 6x 8 g) 3 x 4x 3x 6 h) 5x 9y
7 P7 39. Solve by factoring. (Leave answers in exact form do not convert to decimals.) a) x x b) x c) 1x 4x 3x 1 0 d) 6 4 x x e) 9 14 x x f) 4x 0x Solve each quadratic equation by using of the quadratic formula. (Leave answers in exact form AND give answers rounded to the nearest hundredth.) a). x + 10x = 5 b) 8x 5x = 0 RADICALS 41. Simplify the radicals. a) 15 b) 9 11 c) 8 d) e) 6 1 f) 5 7 g) 1 75 h) 5 7 i) 45 0 j) k) 15 5 l) 1 0
8 8 in P8 4. Find the area and perimeter of each figure 1 in a) b) c) d) 19 yd 9 mm 15 mm 9 yd 3 3 yd 3 3 yd 7 yd 1 mm 43. Find the area and circumference of the circle.
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