# Basic Fraction and Integer Operations (No calculators please!)

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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: y-intercept: 8. Graph the line y = - 6 Slope = 9. Graph the line x = 3 Slope = Graph the line for y x 5 7 Slope: y-intercept: 31. Graph the line 5xy 1 x-intercept: y-intercept:

5 P5 3. Write the equation of the line that passes through the points (15, -5) and (-4, 1). Write the equation in point-slope 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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