College Readiness Math Final Eam Review Sheet Solve the equation. 1) r + 6 = r + 8 3 6 Solve the equation for the specified variable. Use the distributive propert to factor as necessar. 2) -9s + 8p = tp - 8 for p Solve the formula for the specified variable. 3) S = 2πrh + 2πr 2 for h Find the equation in slope-intercept form of the line satisfing the conditions. 4) m = 2, passes through (, -4) Find an equation of the line satisfing the conditions. Write the equation in slope-intercept form. ) Through (-6, ); parallel to -7 + = 7 Solve the sstem b elimination. If the sstem is inconsistent or has dependent equations, sa so. 6) - + 6 = 3-3 - 6 = -7 Identif the polnomial as a monomial, binomial, trinomial, or none of these. Also give the degree. 7) 18c6-4c + 3c4 Write the polnomial in descending powers of the variable. Give the coefficient of the highest degree. 8) -2 - - 184 + 48 Identif the polnomial as a monomial, binomial, trinomial, or none of these. Also give the degree. 9) 142 Appl the product rule for eponents, if possible. ) (8)(-7-2-4) Appl the quotient rule for eponents, if applicable, and write the result using onl positive eponents. Assume all variables represent nonzero numbers. 11) 7 13 Add or subtract as indicated. 12) ( + 7 + 87 + 96) + (96 - + + 77) 13) (83 + 2 + 3) - (-33 + - 8) Find the product. 14) (9-7)(812 + 63 + 49) 1
1) (4 + 12)( + 2) 16) (r - 3)(r + 3) Add or subtract as indicated. Write the answer in lowest terms. 17) 3 r + 9 r - 2 18) 3 14 + 9 2 19) 2-16 - 2 + + 4 Solve the problem. 20) The weight of a liquid varies directl as its volume V. If the weight of the liquid in a cubical container 4 cm on a side is 192 g, find the weight of the liquid in a cubical container cm on a side. 21) If varies inversel as 2, and = when = 6, find when = 2. 22) The distance it takes to stop a car varies directl as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 62 miles per hour? 23) The intensit of a radio signal from the radio station varies inversel as the square of the distance from the station. Suppose the the intensit is 8000 units at a distance of 2 miles. What will the intensit be at a distance of 11 miles? Round our answer to the nearest unit. 24) If m varies directl as p, and m = 6 when p = 7, find m when p is 9. Perform the indicated operation and epress in lowest terms. 2) z 2 + 9z + 20 z2 + 11z + 28 z2 + z z2 + 4z - 21 26) 4p - 4 p 8p2 p - Solve the equation. 27) 1 + 1 = 42 2 28) 6-6 = 1 + 8 + 6 29) 4-6 2 + 1 = 2-1 + 3 2
Use the discriminant to determine how man solutions the quadratic equation has. Do not actuall solve. 30) v2 - v + 3 = 0 31) 82 = -3-2 Use the quadratic formula to solve the equation. (All solutions are real numbers.) 32) (2-1)( + 1) = 6 33) 2n2 = -12n - 1 Use the square root propert to solve the equation. 34) 2-22 = 0 Solve the equation. 3) = 2-36) - 6 = 7 37) 22 + 11 = + 6 38) - 2 = 1 + 12 + 2 Solve the problem. 39) A lot is in the shape of a right triangle. The shorter leg measures 90 m. The hpotenuse is 30 m longer than the length of the longer leg. How long is the longer leg? Determine the intervals over which the function is decreasing and increasing. 40) - (-1, 0) - 3
41) - (0, -2) - Graph the function. 42) f() = -3, if 1-4 -, if < 1 6 4 2-6 -4-2 2 4 6-2 -4-6 43) f() = + 4, if < 0 22-1, if 0 - - - - 4
44) f() = -, if < 0 -, if 0 - - - - Find the verte of the parabola. 4) f() = 22-12 + 13 46) f() = 22-12 + 17 47) f() = 32-18 + 22 Without graphing, decide whether the graph is smmetric to the -ais, -ais, or origin. 48) = 2-3 49) = - 0) 3 = 32 + 3 Evaluate the determinant b epansion b minors about an row or column. 1) 7 2 8 6 2) 3-1 1 3 Solve the sstem b using the inverse of the coefficient matri. 3) + 4 = 8 4-2 = 22 4) + 3 = -8 21 + 6 = 3
Find the measure of each angle in the problem. ) 6) Perform the calculation. 7) 340 42 + 32 44 8) 78 26-16 Convert the angle to decimal degrees and round to the nearest hundredth of a degree. 9) 20 28 Convert the angle to degrees, minutes, and seconds. 60) 1.38 Use the properties of angle measures to find the measure of each marked angle. 61) Find the measure of the marked angles. a = (4 + 7) b = (2 + 39) Classif the triangle as acute, right, or obtuse and classif it as equilateral, isosceles, or scalene. 62) 6
63) The triangles are similar. Find the missing side, angle or value of the variable. 64) a = 41 b = 40 c = 9 d = 82 e = 80 6) a = 12 b = 18 c = 8 d = 12 e = 16 Solve the problem. Round answers to the nearest tenth if necessar. 66) A tree casts a shadow 31 m long. At the same time, the shadow cast b a 41-centimeter-tall statue is 79 cm long. Find the height of the tree. 67) A triangle drawn on a map has sides of lengths 7 cm, 12 cm, and 1 cm. The shortest of the corresponding real-life distances is 96 km. Find the longest of the real-life distances. 7
Evaluate for all si trigonometric functions from Angle B. Write our answer as a fraction in lowest terms. 68) 123 27 120 Write the function in terms of its cofunction. Assume that an angle in which an unknown appears is an acute angle 69) csc 6 70) sin 30 Find a solution for the equation. Assume that all angles are acute angles. 71) sin(2β + ) = cos(3β - 1 ) 72) tan(3θ + 29 ) = cot(θ + 1 ) Find the reference angle for the given angle. 73) 8 74) 204.7 7) -29.2 Use a calculator to find the function value. Give our answer rounded to two decimal places, if necessar. 76) sec 66 3 77) cos 261 17 Solve the problem. 78) The grade resistance F of a car traveling up or down a hill is modeled b the equation F = W sin θ, where W is the weight of the car and θ is the angle of the hill's grade (θ > 0 for uphill travel, θ < 0 for downhill travel). What is the grade resistance (to the nearest pound) of a 3000-lb car traveling uphill on a 3 grade (θ = 3 )? 79) The grade resistance F of a car traveling up or down a hill is modeled b the equation F = W sin θ, where W is the weight of the car and θ is the angle of the hill's grade (θ > 0 for uphill travel, θ < 0 for downhill travel). What is the grade resistance (to the nearest pound) of a 200-lb car traveling downhill on a 6 grade (θ = -6 )? Solve the right triangle. 80) a = 3.7 cm, b = 3.6 cm, C = 90 8
Solve the problem. 81) When sitting atop a tree and looking down at his pal Joe, the angle of depression of Mack's line of sight is 40 28'. If Joe is known to be standing 27 feet from the base of the tree, how tall is the tree (to the nearest foot)? 82) From a boat on the lake, the angle of elevation to the top of a cliff is 12 49'. If the base of the cliff is 1647 feet from the boat, how high is the cliff (to the nearest foot)? Graph the function. State the amplitude and period of the function. 83) = sin 3 4 84) = 2 cos 9
Answer Ke Testname: FINAL EXAM REVIEW SHEET 1) {-4} 2) p = 9s - 8 8 - t 3) h = S - 2πr 2 2πr 4) = 2-14 ) = 7 + 67 6) {(1, 9)} 7) Trinomial; 6 or p = -9s + 8 t - 8 8) - - 184 + 48-2 9) Monomial; 2 ) 12143 11) 1 6 12) 17 + 186 + 2 + 13) -3 + 92-2 + 9 14) 7293-343 1) 42 + 20 + 24 16) 0r2-9 17) 12r - 6 r(r - 2) 18) 19) 3( + 21) 702 2-4 + 20 ( - 4)( + 4)( + 1) 20) 37 g 21) 4 22) 269.08 ft 23) 264 units 24) 72 2) z - 3 z 26) 32p 27) {-7, 6} 28) {,-12} 17 29) 6 30) Two irrational solutions 31) Two nonreal comple solutions 32) 33) -1 + 7-1 - 7, 4 4-6 + 34-6 - 34, 2 2
Answer Ke Testname: FINAL EXAM REVIEW SHEET 34) {1, -1} 3) {1} 36) {-1, 7} 37) {} 38) {6, -8} 39) 120 m 40) Increasing [-1, ); Decreasing (-, -1] 41) Increasing (-, 0]; Decreasing [0, ) 42) 6 4 2-6 -4-2 2 4 6-2 43) -4-6 - - - - 44) - - - - 4) (3, -) 46) (3, -1) 47) (3, -) 11
Answer Ke Testname: FINAL EXAM REVIEW SHEET 48) -ais 49) Origin 0) -ais 1) 26 2) 3) {(4, -3)} 4) {(1, -3)} ) 0 and 80 6) 70 and 20 7) 373 26 8) 61 31 9) 20.09 60) 1 22 48 61) 71, 71 62) Right, scalene 63) Obtuse, scalene 64) = 18 6) = 24 66) 16.1 m 67) 20.7 km 68) cos B = 40 41 69) sec 34 70) cos 60 71) 20 72) 11. 73) 72 74) 24.7 7) 29.2 76) 2.47091 77) -0.11484 78) 17 lb 79) -261 lb 80) A = 4.8, B = 44.2, c =.2 cm 81) 23 ft 82) 37 ft 12
Answer Ke Testname: FINAL EXAM REVIEW SHEET 83) 2 1-4π 3 4π 3-1 -2 84) 4 2-2π -π π 2π -2-4 13