Name___________________________________ MAT1100 - Practice Final MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Simplify the expression. |10(-2)| - |1 - 6| 1) -12 A) 2) 5 4 1) B) - 5 4 C) 25 12 D) - 25 12 6(2 + 1) - 6(1 + 1) 6(4 - 2) - 2 3 A) 3 2) B) 3 5 C) 3 4 D) 3 2 Find the value of the algebraic expression at the given replacement value. y 3x when x = -3, y = 5 3) 7x + xy A) - 7 18 B) 2 3 C) 1 9 3) D) - 5 18 List all the elements of B that belong to the given set. 5 6 4) B = 6, 7, -2, 0, , - , 4.3, 4 6 5 Whole numbers A) 6, -2, 0, 4 B) 6, 0, 4 4) C) 6, 0 D) 6, -2, 0 Solve the problem. 5) Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 300 miles in the same time that Dana travels 264 miles. If Chuck's rate of travel is 6 mph more than Dana's, and they travel the same length of time, at what speed does Chuck travel? A) 58 mph Solve. B) 44 mph C) 50 mph D) 42 mph 6) A recent advertisement claimed that 2 out of every 3 doctors recommend a certain herbal supplement to increase energy levels. If a local hospital employs 130 doctors, how many doctors would you expect to recommend the supplement? (Round to the nearest whole number, if necessary.) A) 780 doctors B) 195 doctors C) 43 doctors 7) Enrollment in a business seminar increased from 66 people to 87 people. By what percentage did A) 24.1% B) 75.9% C) 31.8% 6) D) 87 doctors Solve the problem. enrollment increase? 5) D) 68.2% 7) 8) By switching service providers, a family's telephone bill decreased from about $50 a month to about $46. By what percent did the monthly bill decrease? A) 4% B) 8.7% C) 8% 9) If m varies directly as p, and m = 27 when p = 9, find m when p is 8. A) m = 81 B) m = 9 C) m = 64 D) 9% D) m = 24 10) The force required to compress a spring varies directly as the change in the length of the spring. If a force of 18 pounds is required to compress a certain spring 4 inches, how much force is required to compress the spring 7 inches? A) 31.5 pounds B) 21 pounds C) 10.3 pounds B) (6 + s)(5 + r) Factor completely. 12) 729c3 + 8 A) (9c - 2)(81c2 + 18c + 4) C) (729c + 2)(c2 - 18c + 4) C) (6 + s)(5 - r) 9) 10) D) 35 pounds Factor by grouping. 11) 30 - 5s - 6r + sr A) (6 - s)(5 + r) 8) D) (6 - s)(5 - r) 11) 12) B) (9c + 2)(81c2 - 18c + 4) D) (9c + 2)(81c2 + 4) Use a combination of rules for exponents to simplify. Write answers with only positive exponents. Assume that all variables represent nonzero real numbers. 28x-2 13) 13) (4x)2 A) 7 64x 4 14) (-2x5 y2 )3 A) -8x8 y5 B) 7 x4 B) -8x15y6 Solve the equation by using the square root property 15) (p - 1)2 = 5 A) {± 5 - 1} B) { 5 - -1} Solve the equation by factoring, then using zero-factor rule 16) 2k2 = -30k - 100 A) {-10, -20} 17) x2 + 6x - 16 = 0 A) {-2, 8} B) - 5, -10 B) {2, 8} C) C) 7 4x4 -2x8 y5 C) { 5 + 1} C) 10, - 5 C) {-8, 2} D) 7x4 4 D) -2x15y6 D) {± 5 + 1} D) 10, 5 D) {-8, -2} Solve the equation by using the quadratic formula. Simplify any radicals to simpliest form. 18) x2 + 8x = 7 A) -4 ± 23 B) -4 ± 2 23 C) -1 ± 23 D) 4 + 23 14) 15) 16) 17) 18) Restate the equation in slope-intercept form. 19) 9x - 5y = 7 A) y = 9x - 7 B) 9 7 y= x5 5 C) 5 7 y= x+ 9 9 D) 9 7 y= x+ 5 5 Write the slope-intercept form of the equation of the line satisfying the given conditions. 20) Through (8, -3); slope = -9; A) y = -9x + 69 B) y = -9x + 67 C) y = 9x + 68 D) y = -9x + 70 Write the slope-intercept form of the equation for the line passing through the given pair of points. 21) (3, -5) and (8, -7) A) 2 19 y=- x5 5 C) y = B) 8 169 x15 15 8 169 y=x15 15 5 22) 4x + 7y = 26 21) 5 3 7 A) Slope ; y-intercept 0, 4 26 B) Slope - ; y-intercept 0, 4 26 C) Slope ; y-intercept 0, 3 7 D) Slope - ; y-intercept 0, 7 20) 2 19 D) y = x - Find the slope and the y-intercept of the line. 4 19) 26 7 7 4 7 26 Find an equation of the line. Write the equation in standard form. 23) Through (3, 5); perpendicular to 3x - 4y = 3 A) 4x + 3y = 27 B) 3x - 4y = 27 C) 3x + 4y = 27 22) D) 4x - 3y = 27 23) Find the simple interest. The rate is an annual rate unless otherwise noted. Assume 365 days in a year and 30 days per month. Use the formula i = prt 1 24) $8000 at 6% for 2 years 24) 2 A) $1200.00 B) $192.00 C) $3333.33 D) $120.00 Find the compound interest earned by the deposit. Round to the nearest cent. 25) $3000 at 2% compounded annually for 10 years A) $540.00 B) $656.98 C) $600.00 D) $585.28 Solve the problem. 26) A lot is in the shape of a right triangle. The shorter leg measures 180 m. The hypotenuse is 60 m longer than the length of the longer leg. How long is the longer leg? A) 360 m B) 180 m C) 300 m D) 240 m 25) 26) Solve and graph. 27) 21n - 9 3(6n - 2) 27) A) (- , 1] B) (- , 1) C) [1, ) D) [- , -5) Solve the system of equations. 28) x - 2y = 4 2x - 3y = 3 A) (-7, -4) 28) B) C) (-6, -5) D) (6, -4) Solve the problem. 29) Carole's car averages 12.1 miles per gallon in city driving and 25.8 miles per gallon in highway driving. If she drove a total of 565.3 miles on 32 gallons of gas, how many of the gallons were used for city driving? A) 21 gallons B) 18 gallons C) 19 gallons D) 13 gallons Find the midpoint of the line segment joining the two points. 30) (4, -4) and (-2, 8) A) (2, 4) B) 1, 2 C) (6, -12) 29) D) 3, - 6 30) Find the y- and x-intercepts for the equation. Then graph the equation. 31) 25y - 5x = -10 31) A) 0, - 2 , (-2, 0) B) (0, 2), - 2 , 0 C) 0, - 2 , (2, 0) D) 0, 2 , (-2, 0) 5 5 5 5 Find the median. 32) 17, 22, 35, 47, 63, 72, 90 A) 49 B) 35 C) 63 D) 47 Find the indicated decile or percentile. 33) The weekly salaries (in dollars) of sixteen government workers are listed below. Find the eighty-first percentile P81. 787 628 820 673 475 621 533 645 570 698 875 520 599 460 562 490 A) 720 B) 787 C) 698 32) 33) D) 673 Evaluate the permutation. 34) 6 P2 A) 120 B) 6 C) 1 D) 30 34) 35) How many ways can a president, vice-president, secretary, and treasurer be chosen from a club with 9 members? Assume that no member can hold more than one office. A) 126 B) 36 C) 3024 D) 24 36) A student is told to work any 6 out of 10 questions on an exam. In how many different ways can he complete the exam? (The correctness of his answers has no bearing.) A) 5040 B) 1,000,000 C) 24 37) Three fair coins are tossed. Find the probability of getting exactly two tails. A) B) 1 4 C) 5 8 D) 1 2 38) A card is drawn at random from a standard 52-card deck. Find the probability that the card is not a queen. 1 A) 4 B) 1 13 C) 12 13 36) D) 210 Find the probability. 3 8 35) D) 3 4 37) 38) Answer Key Testname: MAT1100PRACTICEFINALBF 1) B 2) D 3) A 4) B 5) C 6) D 7) C 8) C 9) D 10) A 11) D 12) B 13) C 14) B 15) D 16) B 17) C 18) A 19) B 20) A 21) A 22) B 23) A 24) A 25) B 26) D 27) A 28) C 29) C 30) B 31) C 32) D 33) C 34) D 35) C 36) D 37) A 38) C