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Math 155 Course Review Questions 1 - 38 can be used as a study plan for the midterm. All questions should be studied for the final exam. Use the order of operations to find the value of the expression. 1) 7(4 - 2)3 - 2(5 - 3)3 Use a calculator with a square root key to find a decimal approximation for the square root. Round the number displayed as indicated. 8) 423 to the nearest thousandth Objective: (5.2) Use the Order of Operations Agreement Objective: (5.4) Simplify Square Roots 2) 52 - 25 ÷ 5 · 2 + 9 Simplify the square root. 9) 2 300 Objective: (5.2) Use the Order of Operations Agreement Objective: (5.4) Simplify Square Roots Solve the problem. 3) A hill is at 500 feet above sea level, and a crater next to it is at 254 feet below sea level. What is the difference in height between the hill and the crater? Perform the indicated operation. Simplify the answer when possible. 10) 5 · 25 Objective: (5.4) Perform Operations with Square Roots Objective: (5.2) Use the Order of Operations Agreement 11) Reduce the rational number to its lowest terms. 21 4) 35 45 5 Objective: (5.4) Perform Operations with Square Roots Objective: (5.3) Reduce Rational Numbers 12) Perform the indicated operation(s). Where possible, reduce the answer to lowest terms. 1 1 7 ÷ 5) 5 6 9 13) Objective: (5.3) Use the Order of Operations Agreement with Rational Numbers Solve the problem. 7) Of the 648 people polled about gardening, 216 replied that they plant a garden. What fractional part of those polled, expressed in lowest terms, plant a garden? Objective: (5.3) Solve Problems Involving Rational Numbers 24 18 - 8 Objective: (5.4) Perform Operations with Square Roots Objective: (5.3) Add and Subtract Rational Numbers Perform the indicated operations. If possible, reduce the answer to its lowest terms. 2 1 4 1 6) - ÷ 3 6 5 2 6+ Objective: (5.4) Perform Operations with Square Roots Rationalize the denominator. 7 14) 5 Objective: (5.4) Rationalize Denominators Perform the indicated operation. Simplify the answer when possible. 15) 2 - 5 128 - 2 72 Objective: (5.4) Perform Operations with Square Roots Use properties of exponents to simplify the expression. Express answer in exponential form. 16) 33 · 3 -5 Objective: (5.6) Use Properties of Exponents Last Revised 201130 17) Solve and check the equation. Begin your work by rewriting the equation without fractions. 8x x 9 -x= 26) 7 28 4 55 53 Objective: (5.6) Use Properties of Exponents Objective: (6.2) Solve Linear Equations Containing Fractions Use properties of exponents to simplify the expression. Express answers in exponential form with positive exponents only. Assume that any variables in denominators are not equal to zero. 10x3y-5 18) 2x7y-11 Solve the proportion. 2 9 27) = 3 x Objective: (6.2) Solve Proportions Objective: (5.6) Use Properties of Exponents 28) Perform the indicated operation and express the answer in decimal notation. 19) (8 × 108 )(9 × 10 -6 ) Objective: (6.2) Solve Proportions Objective: (5.6) Perform Computations Using Scientific Notation 20) x-6 3 = 5 10 Use a proportion to solve the problem. 29) The ratio of a basketball player's completed free throws to attempted free throws is 4 to 5. If she completed 8 free throws, find how many free throws she attempted. Round to the nearest whole number if necessary. 3 × 104 15 × 10- 2 Objective: (5.6) Perform Computations Using Scientific Notation Objective: (6.2) Solve Problems Using Proportions Indicate whether the equation has no solution or is true for all real numbers. If neither is the case, solve for the variable. 30) 4x - 2(4 + 2x) = -8 Perform the indicated operation by first expressing each number in scientific notation. Write answer in scientific notation. 21) (220,000,000)(2,000,000,000) Objective: (6.2) Identity Equations with No Solution or Infinitely Many Solutions Objective: (5.6) Perform Computations Using Scientific Notation Let x represent the number. Use the given conditions to write an equation. Solve the equation and find the number. 31) If 3 times a number is added to -8, the result is equal to 11 times the number. Find the number. Evaluate the algebraic expression for the given value(s) of the variable(s). 22) x3 - 3x 2 + 1 ; x = -2 Objective: (6.1) Evaluate Algebraic Expressions Simplify the algebraic expression. 23) 6(2x - 1) - 8(x - 3) Objective: (6.3) Use Linear Equations to Solve Problems Objective: (6.1) Simplify Algebraic Expressions Solve the formula for the specified variable. 32) d = rt for t Solve and check the equation. 24) -3y - 3 = -1 + 10y Objective: (6.3) Solve a Formula for a Variable Objective: (6.2) Solve Linear Equations 25) 4(2y - 2) = 7(y + 2) Objective: (6.2) Solve Linear Equations 2 Plot the point in the rectangular coordinate system. 33) (-5, 4) Use the x- and y-intercepts to graph the linear equation. 36) x - 2y = -10 Objective: (7.1) Plot Points in the Rectangular Coordinate System Graph the equation. Select integers for x, -3 34) y = -2x + 5 x Objective: (7.2) Use Intercepts to Graph a Linear Equation 3. Calculate the slope of the line passing through the given points. If the slope is undefined, so state. Then indicate whether the line rises, falls, is horizontal, or is vertical. 37) (-19, -1), (-3, -13) Objective: (7.2) Calculate Slope Graph the linear function using the slope and y-intercept. 1 38) y = x + 2 3 Objective: (7.1) Graph Equations in the Rectangular Coordinate System 35) y = x2 + 3 Objective: (7.2) Use the Slope and y-Intercept to Graph a Line Express the percent as a decimal. 3 % 39) 10 Objective: (8.1) Express a Percent as a Decimal Objective: (7.1) Graph Equations in the Rectangular Coordinate System Solve the problem. 40) 75% of 24 is what number? Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts 3 The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. Find how much money will be in the account after the given number of years (Assume 360 days in a year.), and how much interest was earned. 41) 19 is what percent of 50? Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts 42) 40% of what number is 98? Objective: (8.1) Solve Applied Problems Involving Sales Tax and Discounts A=P 1+ 43) A dress regularly sells for $117. The sale price is $89. Find the percent decrease of the sale price from the regular price. r nt n P= A r nt 1+ n A = Pert 46) Principal: $9500 Rate: 7.5% Compounded: monthly Time: 4 years Objective: (8.1) Determine Percent Increase or Decrease Objective: (8.3) Use Compound Interest Formulas The graph shows the level of subsidized daycare spending in a foreign country for the period 1995-1999. Use the graph to answer the question. 44) Find the percent increase in daycare spending from 1997to 1998. Round to the nearest percent. Solve the problem. 47) A mother invests $9000 in a bank account at the time of her daughter's birth. The interest is compounded quarterly at a rate of 8%. What will be the value of the daughter's account on her twentieth birthday, assuming no other deposits or withdrawals are made during this period? Objective: (8.3) Use Compound Interest Formulas Solve the problem. 48) How much money should be deposited today in an account that earns 5% compounded quarterly so that it will accumulate to $6900 in 2 years? Objective: (8.3) Calculate Present Value Use dimensional analysis to convert the quantity to the indicated units. If necessary, round the answer to two decimal places. 49) 13 yd to ft Objective: (8.1) Determine Percent Increase or Decrease Objective: (9.1) Use Dimensional Analysis to Change Units of Measurement The principal P is borrowed at simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume 360 days in a year and round answer to the nearest cent. 45) P = $160 r = 8% t = 2 years Convert the given measurement to the unit indicated. 50) 5.49 m to cm Objective: (9.1) Convert Units Within the Metric System Objective: (8.2) Calculate Simple Interest Use dimensional analysis to convert the unit indicated. 51) 7 m to yd Objective: (9.1) Use Dimensional Analysis to Change to and from the Metric System 4 Select the best estimate for the measure of the given quantity. 52) the length of a bedroom wall A) 4.2 m B) 4.2 mm C) 4.2 km D) 4.2 cm Find the measure of the complement of the angle. 59) Find the complement of 33°. Objective: (10.1) Solve Problems Involving Angle Measures Find the measures of angles 1, 2, and 3. 60) Objective: (9.1) Understand and Use Metric Prefixes Use the fact that a solid with a volume of 1000 cubic centimeters has a capacity of 1 liter, along with dimensional analysis, to convert the given unit to the unit indicated. 53) 510.6 mL to cm3 148° Objective: (9.2) Use English and Metric Units to Measure Capacity Use dimensional analysis to convert the given square unit to the square unit indicated. Where necessary, round the answer to two decimal places. 54) 13.1 ha to acres Objective: (10.1) Solve Problems Involving Angle Measures 61) Objective: (9.2) Use Dimensional Analysis to Change Units for Area Selecting from milligram, gram, kilogram, and tonne, determine the best unit of measure to express the given weight. 55) a pocket calculator 56° Objective: (9.3) Apply Metric Prefixes to Units of Weight Objective: (10.1) Solve Problems Involving Angle Measures Convert the given unit of weight to the unit indicated. 56) 165 mg to g Objective: (9.3) Convert Units of Weight Within the Metric System The figure shows two parallel lines intersected by a transversal. One of the angle measures is given. Find the measure of the indicated angle. 62) Use dimensional analysis to convert the given quantity to the units indicated. When necessary, round answers to two decimal places. 57) 860 lb to kg Objective: (9.3) Use Dimensional Analysis to Change Units of Weight to and from the Metric System 40° Convert the given Celsius temperature to its equivalent temperature on the Fahrenheit scale. Where appropriate, round to the nearest tenth of a degree. 58) 62°C Objective: (9.3) Understand Temperature Scales Find the measure of 1. Objective: (10.1) Solve Problems Involving Angles Formed by Parallel Lines and Transversals 5 Find the perimeter of the figure shown. Express the perimeter in the same unit of measure that appears on the given side or sides. 66) 15 yd Find the measure of angle A for the triangle shown. 63) 12° 3.5 yd 5 yd Objective: (10.2) Solve Problems Involving Angle Relationships in Triangles 7 yd Use similar triangles and the fact that corresponding sides are proportional to find the length of the side marked with an x. Objective: (10.3) Solve Problems Involving a Polygon's Perimeter 64) 18 m 8 yd 1.5 yd Use the Pythagorean Theorem to solve the problem. Use your calculator to find square roots, rounding, if necessary, to the nearest tenth. 67) If you drive 9 miles south, then make a left turn and drive 12 miles east, how far are you, in a straight line, from your starting point? 27 m Objective: (10.2) Solve Problems Using the Pythagorean Theorem 14 m 21 m Use formulas to find the area of the figure. 68) 0.13 cm 28 m Objective: (10.2) Solve Problems Involving Similar Triangles 0.07 cm Use the Pythagorean Theorem to find the missing length in the right triangle. Use a calculator to find square roots, rounding, if necessary, to the nearest tenth. 65) 12 m 0.02 cm 0.07 cm 0.13 cm Objective: (10.4) Use Area Formulas to Compute the Areas of Plane Regions and Solve Applied Problems 20 m b 69) Objective: (10.2) Solve Problems Using the Pythagorean Theorem 10 in. 10.5 in. 15 in. Objective: (10.4) Use Area Formulas to Compute the Areas of Plane Regions and Solve Applied Problems 6 Use the given right triangle to find the trigonometric function. 74) sin B Solve the problem. 70) What will it cost to tile a rectangular floor measuring 229 feet by by 27 feet if the tile costs $10 per square foot? Objective: (10.4) Use Area Formulas to Compute the Areas of Plane Regions and Solve Applied Problems Find the circumference and area of the circle. Round the answer to the nearest whole number. 71) Objective: (10.6) Use the Lengths of the Sides of a Right Triangle to Find Trigonometric Ratios 19 ft Find the measure of the side of the right triangle whose length is designated by the lowercase letter. Round your answer to the nearest whole number. 75) Objective: (10.4) Use Formulas for a Circle's Circumference and Area Find the volume of the figure. If necessary, round the answer to the nearest whole number. 72) a 30° b = 130 cm 10 cm Objective: (10.6) Use Trigonometric Ratios to Find Missing Parts of Right Triangles 20 cm Solve the problem. 76) At a certain time of day, the angle of elevation of the sun is 64°. To the nearest foot, find the height of a pole whose shadow at that time is 13 feet long. Objective: (10.5) Use Volume Formulas to Compute the Volumes of Three-Dimensional Figures and Solve Applied Problems 73) 3m 64° 13 ft Objective: (10.6) Use Trigonometric Ratios to Solve Applied Problems 13 m 77) A kite flies to a height of 35 feet when 74 feet of string is out. If the string is in a straight line, find the angle that it makes with the ground. Round to the nearest tenth of a degree. 7m Objective: (10.5) Use Volume Formulas to Compute the Volumes of Three-Dimensional Figures and Solve Applied Problems Objective: (10.6) Use Trigonometric Ratios to Solve Applied Problems 7 79) The stem-and-leaf plot below displays the ages of 30 attorneys at a small law firm. 78) Which one of the following is true according to the graph? Stems 4 5 6 7 8 9 Attorneys 99 00112589 1234458 1233458 0137 12 What is the age of the oldest attorney? What is the age of the youngest attorney? Objective: (12.1) Organize and Present Data Find the mean for the group of data items. Round to the nearest hundredth, if necessary. 80) 10, 5, 7, 6, 11, 3, 1, 7 Objective: (12.2) Determine the Mean for a Data Set Find the median for the group of data items. 81) 10, 8, 4, 0, 2, 1, 2, 0, 0 A) More people had 4 years of education beyond high school than 3 years. B) If the sample is truly representative, then for a group of 50 people, we can expect about 32 of them to have one year of education beyond high school. C) The graph is based on a sample of approximately 62 thousand people. D) The percent of people with years of higher education greater than those shown by any rectangular bar is equal to the percent of people with years of education less than those shown by that bar. Objective: (12.2) Determine the Median for a Data Set Find the mode for the group of data items.If there is no mode, so state. 82) 99, 99, 92, 39, 70, 99 Objective: (12.2) Determine the Mode for a Data Set Find the midrange for the group of data items. 83) 10, 7, 4, 7, 2, 4, 2 Objective: (12.2) Determine the Midrange for a Data Set Objective: (12.1) Organize and Present Data Find the range for the group of data items. 84) 15, 18, 15, 18, 15, 18, 15, 18 Objective: (12.3) Determine the Range for a Data Set Find the standard deviation for the group of data items (to the nearest hundredth). 85) 9, 9, 9, 12, 15, 15, 15 Objective: (12.3) Determine the Standard Deviation for a Data Set 8