Directions: Solve each problem. Write your answer as a simplified radical!

Transcription

1 Directions: Simplify completely! 1) 7 ) 7 10 ) ) ) ( ) 6) (6w 8 w ) 7) ) 7 ( ) 9) ) 90m n 11) 1) 5m 8 m r r r 1) 5 18k m 14) 7 km 7km Directions: Solve each problem. Write your answer as a simplified radical! 15) In a rectangle, the length is 68 meters and the width is meters. What is the area? 16) An 18 foot ladder leans against a tree, reaching a point that is 14 feet above the ground. How far is the foot of the ladder from the bottom of the house? 17) What is the side length of the large square in the picture? Directions: Label the following algebraic expressions as Rational or Irrational. 18) 47 19) 1 5 0) 0. 1) Directions: Simplify. Determine if your solution is Rational or Irrational. ) 18 1 ) (6 )(6 ) 4) )

2 Directions: Determine if the following statement is ALWAYS true, SOMETIMES true, or NEVER true. 6) The product of two rational numbers is irrational. 7) The sum of two irrational numbers is rational. 8) The product of two irrational numbers is rational. 9) The sum of a rational and an irrational number is rational. 0) The product of a non-zero rational and an irrational number is irrational. Directions: Simplify completely. 1) (x 6x + ) (4x x + 9) ) ( 10x 4y + ) + (4x + 4y 1) ) (5x 4 + x) (x 5 + x 4 8x + 5x) 4) 5(x y) + (5x 17y) 5) (4 + x)( x) 6) x (4x 5x + ) 7) (5x + 8)(x + 7) 8) 7(m ) 9) (x 4)(x x + ) 40) (x + 1)(x + x + 1) Directions: Solve. 41) What is the area of the right triangle 4) Lucy is building a rectangular garden that is (x 8) below? units long and (x + ) units wide. What algebraic expression would represent the area of this garden? 4) What is the expression that would represent the perimeter of the rectangular garden in question #4? 44) The amount of money a company makes per month can be modeled by the expression 5x - 7x The amount of money it must spend each month can be modeled by the expression 4x + x 1. The net profit is the difference between how much it makes and how much it spends. What is the net profit for this company? 45) If the sum of (x 4) + (x + 5x 7) = ax + bx + c, find the value of b. 46) Simplify: (1x + 7x 11x + 4) (5x + 8x 1) (x x - 7x + 6) 47) x 5 4 x 48) The dimensions of a sandbox were 8ft by 9ft. Each dimension was increased by the same amount. What algebraic expression could be used to represent the area of this sandbox?

3 Algebra I 1) Rewrite: 7 5 ) Is the sum of and 1 rational or irrational? ) Is the sum of and 8 rational or irrational? 4) A rectangle has a length of meters and a width of 40 centimeters. What is the perimeter of the rectangle? 5) Consider the expression n + n +. a. What is the coefficient of n? b. What terms are being added in the expression? 6) Look at one of the formulas for the perimeter of a rectangle where l represents the length and w represents the width: (l + w). What does the represent in this formula? 7) The dimensions of a rectangle are shown. What is the perimeter, in units, of the rectangle? 8) Rewrite the expression (x + x x) ( x + x + 6). 9) The dimensions of a patio, in feet, are shown. What is the area of the patio, in square feet?

4 Directions: Complete each statement with <, >, or =. 1) 1.5 hg 1. kg ),400 lb 1. T ) 6cm x 0cm 5000cm 4) 1 c 14 fl oz Directions: Convert to the specified unit! 5) 50 c to quarts 6) 190 mm to meters 7) 0 feet per second to inches per minutes 8) 1 gallons per 5 pounds to pints per ounces 9) 4000 ounces per 80 meters to pounds per cm 10) 7 yards per 700 seconds to feet per hours Directions: Solve each problem using dimensional analysis! 11) How many hours are in a year? 1) If 0.61 mi = 1.00 km, how many miles will a person run during a 10 kilometer race? 1) The average American student is in class 0 minutes/day. How many hours/day is this? 14) Sixty miles/hour is how many yd/sec? 15) To travel 100 miles, it will cost $0 in gas. What is this rate in yards per Euros? One dollar is equivalent to Euros. 16) Carrie drinks 5 cups of coffee each day. Luke drinks 14 pints of coffee each day. Sami drinks quarts of coffee each day. Who drinks the most coffee in 1 month? 17) If a person weighs 15 lbs, 8 oz., how many ounces does he or she weigh? 18) A city has an elevation of 6.0 x 10 5 mm. How many km is this elevation?

5 Directions: Determine whether the situation requires an exact answer, an approximation, or an estimate. 1) A recipe that calls for cups of flour is being doubled. ) A party planner needs to determine how many entrees to order. The client suggests there will be between 100 to 150 guests in attendance. ) A square with a diagonal of 15 has a side length of 10.6 units. 4) The temperature on a thermometer reads ) An elevator can hold up to 1T. The average weight of the passengers is 00 lb. Based on this average and the fact that there are 8 people on the elevator, there is a total of 1600 lb. Directions: Choose the best answer. 6) Which of the following represents an estimated quantity? a. A square with a diagonal of 1 has a side length of 6 units. b. A female dog had 10 pups. c. Weather.com predicts a low temperature of 0 F today. d. The maximum capacity of an elevator is 1,500 pounds. 7) For which of the following situations would you need an approximate answer? a. The number of bananas on a peanut butter banana sandwich. b. The number of people in a city. c. The number of passengers on a school bus. d. The length of a hypotenuse on a right triangle with legs of and 5. Directions: Answer each question using the function f(x) = x + 4x 1. 8) Identify each term. 9) Identify each coefficient. 10) Identify each constant. 11) Identify each factor. 1) Identify each exponent. Directions: Answer each question. 1) Write an expression with 4 terms, containing the coefficients, 4, and 6. 14) Translate x 1 into a verbal expression. 15) Translate the phrase five less than one sixth of a number into an equation. 16) Ruler A can measure in inches. Ruler B can measure in centimeters. Is Ruler A or Ruler B more precise in measurement? 17) Which unit of measurement would be the most precise in measuring the weight of a diamond chip: gram, kilogram, or milligram? 18) Lucy uses a ruler to measure a card and finds the card to be about.1875 inches in width. She writes 1 inch down 5 on her paper. Is this answer an estimate or an approximate answer? 19) Two times a number is equivalent to 15 more than ½ of this number. What equation represents this situation? 0) What are the coefficients of the previous equation?