INTERMEDIATE ALGEBRA REVIEW FOR TEST 1 Write the set using the roster method. 1) a) { is a counting number less than 7} b) { is a whole number between 4 and 8} Let A = {0, 2, 4, 6, 8, }, B = {0,, 6, 9}, C = {0, 1, 2,, 4,, 6, 7, 8, 9, }, and D = {0, 4, 8}. Answer True or False to the statement. 2) a) A C b) A c) C B d) D D Evaluate the epression for the given value of the variable. 11) 4 + 2 for = - 12) ( + 6) + 6 for = - 1) z2 - z + for z = 4 14) -22 + + 7 for = - Fill in the blank with the appropriate smbol, or. ) a) -9 { is an integer} b) 0 {2, 4, 6,...} 1) 2 - + 2 + 2-1 for = - List all the elements of B that belong to the given set. 4) B = {17, 8, -, 0, 2, 4, 0.62, -8π, 0.444...} a) Whole numbers b) Integers c) Rational numbers d) Irrational numbers e) Real numbers 16) 7 + 9 for = - 8 17) If a rock falls from a height of 0 meters above the ground, the height H (in meters) after seconds is approimatel H = 0-4.92. Evaluate the epression for = 2 seconds. (Round our answer to the nearest tenth.) Perform the indicated operation. ) a) - 8-7 Evaluate the epression. (-4) - 1-11 6) -96 b) - 6 (- ) Simplif the algebraic epression b combining like terms. 18) a) 9 + - 4 + b) 2-1 4 + 1 12 c) ( + 8) - d) -7(r + ) + 6(2r + 7) 7) 24 - [7 - (4 - )] + (4-6) 8) 6 + (-) 2 + 7 4 7 ( - ) Determine which of the given numbers are in the domain of the variable. 1 19) ; = -, = 0, =, = 1-9) 2-4 - 1 + 2 20) ; = -6, = 0, = 1, = 6 2-6 Epress the English phrase using an algebraic epression. ) a) The sum of a number and 97 b) The product of 8 and a number c) 4 less than 7 times a number z d) The product of -6 and the sum of a number and 11 e) The quotient of 21 times a number and -8 + 21) ; = -9, = -, = 0, = 9 2 + 14 + 4 Determine if the number is a solution to the equation. 22) 4m - 2 = -m - 9, m = -
Solve the equation. 2) - 6 = 12 24) - 9.9 = -.4 2) 8 + 12 = 2 + 48 26) ( - 6) = 7-0 27) -2(k - 4) - (-k + 7) = 2 Page 2 ) A canoe and a motorboat travel toward each other from a distance of 70 miles. The motorboat travels 12 miles per hour faster than the canoe. The two boats pass each other after 2. hours. How fast does each boat move? Solve for. 6) 2 - = 7 7) A = 1 bh for b 2 28) 6-8 = 9 8) A = P + Prt for P 29) + 4 4 - - 12 = 1 Identif each equation as being an identit, contradiction, or conditional equation. 0) a) -( + ) - 8 = 2-7( + ) b) - + 7( - ) = -1-4 c) 24 + 1( + 1) = 7( + 1) - 24 Solve the problem. 1) Inclusive of a 6.9% sales ta, a diamond ring sold for $248.70. Find the price of the ring before the ta was added. (Round to the nearest cent, if necessar.) 2) After a 17% price reduction, a boat sold for $ 2,240. What was the boat's price before the reduction? (Round to the nearest cent, if necessar.) ) Nanc invested $600 at a simple interest rate of 9% for 4 ears. How much interest did she earn? Write an algebraic equation and use it to solve the problem. 4) A freight train leaves a station traveling at 2 km/h. Two hours later, a passenger train leaves the same station traveling in the same direction at 2 km/h. How long does it takes the passenger train to catch up to the freight train? 9) aw = b2w - c for w Solve. 40) The formula for the perimeter of a rectangle is P = 2L + 2W. Solve the formula for L. Use this formula to find the length of the rectangle if the perimeter, P, is 4 feet and the width, W, is 9 feet. 41) The surface area S of a right circular clinder is given b the formula S = 2πrh + 2πr2, where r is the radius and h is the height. a) Solve the formula for h. b) Determine the height of a clinder whose surface are is 72π square centimeters and whose radius is 4 centimeters. Write the interval as an inequalit involving. Graph the inequalit. 42) a) > -2 b) 4 c) -4 0 d) < 7 Solve the linear inequalit. Epress the solution using interval notation. Graph the solution set. 4) a) + < 4 b) - 2 > 4 + 4 c) 6 + 6 < -27 2 d) 4 > 1 (2 - )
Write the interval as an inequalit involving. Graph the inequalit. 44) a) (1, ) b) [-, -1] c) (-, -7] d) (-, 1) Graph the equation. 4) + = -1 Graph the equation. 4) a) = -4 b) = Find the slope of the line, or state that the slope is undefined if appropriate. ) a) Page 46) = 2-4 47) = 1-48) = 4 - - 49) 2 - = 6 Graph the line. 0) + = 2( + 4) b) 1) - = - 1 ( - 2) - Find the coordinates of the -intercept and the coordinates of all -intercepts. 2) - - - - - Find the slope of the line containing the given pair of points. If the slope is undefined, state so. 6) a) (1, 2) and (9, 12) b) (-4, -8) and (-2, 1) Graph the specified line. 7) The line with slope 1 that passes through the 4 point (0, 2) Find the following for the given equation. ) -2 + = a) the -intercept b) the -intercept c) the slope d) Graph the equation. Find an equation of the line containing the given pair of points. Write our final answer in slope-intercept form. 8) (-, -1) and (-1, -9) 9) (, -4) and (, -7)
Answer Ke Testname: IAREVIEW1SU 1) a) {1, 2,, 4,, 6} b) {, 6, 7} 2) a) True b) True c) False d) False ) a) b) 4) a) 17, 0, 4 b) 17, -, 0, 4 c) 17, -, 0, 2, 4, 0.62, 0.444... d) -8π e) {17, 8, -, 0, 2, 4, 0.62, -8π, 0.444...} ) a) 1 6 6) - 48 7) 8) 4 14 b) - 1 6 9) 19 ) a) 97 + or + 97 b) 8 c) 7z - 4 d) -6( + 11) e) 21-8 11) -18 12) -14 1) 7 14) -20 1) 40 7 16) 17 17).4 meters 18) a) + 8 b) 1 2 29) 24 0) a) Contradiction b) Conditional equation c) Identit 1) $200 2) $28,000 ) $216 4).2 hours ) canoe: 8 mph motorboat: 20 mph 6) = 2-7 7) b = 2A h 8) P = 9) w = A 1 + rt -c a - b2 40) L = 8 feet 41) a) h = S - 2πr 2 2πr b) centimeters 42) a) (-2, ) -7-6 - -4 - -2-1 0 1 2 4 6 7 b) (-, 4] -7-6 - -4 - -2-1 0 1 2 4 6 7 c) [-4, 0] -7-6 - -4 - -2-1 0 1 2 4 6 7 d) [, 7) -7-6 - -4 - -2-1 0 1 2 4 6 7 c) + 77 d) -8r - 28 19) = -, = 0, = 1 20) = -6, = 1 21) = 0, = 9 22) No 2) 6 24) -0. 2) 6 26) 0 27) 1 28) 216
Answer Ke Testname: IAREVIEW1SU 4) a) (-, -1) 46) -8-7 -6 - -4 - -2-1 0 1 2 4 6 b) (6, ) -1 0 1 2 4 6 7 8 9 11 12 1 c) (-, -) -14-1 -12-11 - -9-8 -7-6 d) - 12 7, - - - - 44) a) > 1-6 - -4 - -2-1 0 1 2 47) -7-6 - -4 - -2-1 0 1 2 4 6 7 b) - -1-7 -6 - -4 - -2-1 0 1 2 4 6 7 c) -7 - - - -12-11 - -9-8 -7-6 - -4 - -2-1 0 1 2 d) - < < 1 48) - -7-6 - -4 - -2-1 0 1 2 4 6 7 4) - - - - - - - -
Answer Ke Testname: IAREVIEW1SU 49) ) a) -intercept: (-, 0) b) -intercept: (0, 2) c) slope: 2 - - - - - - 0) - d) 4) a) - - - - - - - 1) - - b) - - - 2) (0, -), (-4, 0) - - - - - ) a) - 2 b) 0 6) a) 4 b) 9 2
Answer Ke Testname: IAREVIEW1SU 7) - - - - 8) = -4-1 9) = - - 1