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1 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) 4(3-1) 3-2(4-2) 3 11) ) ) A hill is at 502 feet above sea level, and a crater next to it is at 259 feet below sea level. What is the difference in height between the hill and the crater? Reduce the rational number to its lowest terms. 4) ) ) Rationalize the denominator. 8 14) 5 Perform the indicated operation. Simplify the answer when possible. 15) Perform the indicated operation(s). Where possible, reduce the answer to lowest terms. 1 5) Perform the indicated operations. If possible, reduce the answer to its lowest terms. 6) ) Of the 807 people polled about gardening, 269 replied that they plant a garden. What fractional part of those polled, expressed in lowest terms, plant a garden? Use a calculator with a square root key to find a decimal approximation for the square root. Round the number displayed as indicated. 8) 567 to the nearest thousandth Simplify the square root. 9) Perform the indicated operation. Simplify the answer when possible. 10) 3 4 Use properties of exponents to simplify the expression. Express answer in exponential form. 16) ) 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. 18) 48x4 y -4 8x 8 y -7 Perform the indicated operation and express the answer in decimal notation. 19) ( )( ) 20) Perform the indicated operation by first expressing each number in scientific notation. Write answer in scientific notation. 21) (280,000,000)(2,000,000,000) 1
2 Evaluate the algebraic expression for the given value(s) of the variable(s). 22) x 3-5x ; x = -4 Plot the point in the rectangular coordinate system. 33) (-6, 5) Simplify the algebraic expression. 23) 3(5x - 4) - 4(x - 2) Solve and check the equation. 24) -4y - 6 = 7 + 4y 25) 5(2y - 4) = 9(y + 4) Solve and check the equation. Begin your work by rewriting the equation without fractions. 26) 7x 3 - x = x Graph the equation. Select integers for x, -3 x 3. 34) y = -6x - 2 Solve the proportion. 27) 2 7 = 7 x 28) x = 1 5 Use a proportion to solve the problem. 29) The ratio of a basketball player's completed free throws to attempted free throws is 3 to 4. If she completed 12 free throws, find how many free throws she attempted. Round to the nearest whole number if necessary. 35) y = x 2-5 Indicate whether the equation has no solution or is true for all real numbers. If neither is the case, solve for the variable. 30) 8x - 2(6 + 4x) = -12 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 -10, the result is equal to 13 times the number. Find the number. Solve the formula for the specified variable. 32) d = rt for r 2
3 Use the x- and y-intercepts to graph the linear equation. 36) x - 2y = -4 43) A dress regularly sells for $77. The sale price is $57. Find the percent decrease of the sale price from the regular price. The graph shows the level of subsidized daycare spending in a foreign country for the period Use the graph to answer the question. 44) Find the percent increase in daycare spending from 1997to Round to the nearest percent. 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) (10, -19), (4, -8) Graph the linear function using the slope and y-intercept. 38) y = 1 2 x + 2 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 = $170 r = 3% t = 4 years Express the percent as a decimal. 39) 5 7 % 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. 40) 25% of 24 is what number? 41) 16 is what percent of 50? 42) 10% of what number is 84? A = P 1 + r n nt P = A 1 + r n 46) Principal: $8500 Rate: 5.5% Compounded: monthly Time: 3 years nt A = Pe rt 3
4 47) A mother invests $10,000 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? 48) How much money should be deposited today in an account that earns 11% compounded quarterly so that it will accumulate to $3900 in 10 years? Use dimensional analysis to convert the quantity to the indicated units. If necessary, round the answer to two decimal places. 49) 16 yd to ft Convert the given measurement to the unit indicated. 50) 9.59 m to cm Use dimensional analysis to convert the unit indicated. 51) 3 m to yd Selecting from milligram, gram, kilogram, and tonne, determine the best unit of measure to express the given weight. 56) a pad of paper Convert the given unit of weight to the unit indicated. 57) 163 mg to g Use dimensional analysis to convert the given quantity to the units indicated. When necessary, round answers to two decimal places. 58) 520 lb to kg Convert the given Celsius temperature to its equivalent temperature on the Fahrenheit scale. Where appropriate, round to the nearest tenth of a degree. 59) 99 C Find the measure of the complement of the angle. 60) Find the complement of 26. Find the measures of angles 1, 2, and 3. 61) Select the best estimate for the measure of the given quantity. 52) the length of a bedroom wall A) 5.6 m B) 5.6 mm C) 5.6 km D) 5.6 cm 103 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) ml to cm 3 Use dimensional analysis to convert the given square unit to the square unit indicated. Where necessary, round the answer to two decimal places. 54) 22.3 ha to acres 62) 58 55) The population of a certain county is 771,313 and its area is 295,165 square miles. Find the population density of the county to the nearest tenth. 4
5 The figure shows two parallel lines intersected by a transversal. One of the angle measures is given. Find the measure of the indicated angle. 63) 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. 66) 12 km 20 km 28 Find the measure of 6. Find the measure of angle A for the triangle shown. 64) b Find the perimeter of the figure shown. Express the perimeter in the same unit of measure that appears on the given side or sides. 67) 24 in. 5 in. 8 in. 5 in. 3 in. 19 in. 26 Use similar triangles and the fact that corresponding sides are proportional to find the length of the side marked with an x. 65) 14 m 21 m Use the Pythagorean Theorem to solve the problem. Use your calculator to find square roots, rounding, if necessary, to the nearest tenth. 68) 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? Use formulas to find the area of the figure. 69) 0.36 in in in in. 10 m 15 m 20 m 70) 10 yd 0.36 in yd 19 yd 5
6 71) What will it cost to tile a rectangular floor measuring 222 feet by by 73 feet if the tile costs $19 per square foot? 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. 76) Find the circumference and area of the circle. Round the answer to the nearest whole number. 72) 25 ft Find the volume of the figure. If necessary, round the answer to the nearest whole number. 73) 37 b = 130 cm 77) At a certain time of day, the angle of elevation of the sun is 63. To the nearest foot, find the height of a pole whose shadow at that time is 14 feet long. a 6 ft 16 ft ft 74) 16 m 78) A kite flies to a height of 33 feet when 76 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. 79) Which one of the following is true according to the graph? 18 m 6 m Use the given right triangle to find the trigonometric function. 75) sin A A) More people had 4 years of education beyond high school than 3 years. 6
7 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. Find the standard deviation for the group of data items (to the nearest hundredth). 86) 13, 13, 13, 16, 19, 19, 19 80) The stem-and-leaf plot below displays the ages of 30 attorneys at a small law firm. Stems Attorneys What is the age of the oldest attorney? What is the age of the youngest attorney? Find the mean for the group of data items. Round to the nearest hundredth, if necessary. 81) 9, 5, 1, 4, 10, 12, 3, 1 Find the median for the group of data items. 82) 10, 6, 4, 0, 1, 1, 1, 0, 0 Find the mode for the group of data items.if there is no mode, so state. 83) 95, 95, 90, 31, 79, 95 Find the midrange for the group of data items. 84) 12, 7, 5, 7, 1, 5, 1 Find the range for the group of data items. 85) 15, 19, 15, 19, 15, 19, 15, 19 7
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