MTH 095 Final Exam Rev

MTH 095 Final Exam Rev - MTH095 Beginning Algebra Final...

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Unformatted text preview: MTH095 Beginning Algebra Final Exam Review Fall 2009 . Name The ﬁnal exam will be 50 multiple choice questions. Each question will have 4 answer choices. Write the sentence as a mathematicalstatement. 1) Twelve is less than or equal to thirteen Tell which set or sets the number belongs to: natural, whole, integer, rational, irrational, real. 2)0 Find the absolute value. 3) | —6.9 I Evaluate the expression. 4) —62 Evaluate. 5)x-(y+z) forx=20,y=10,andz=4 Decide whether the given number is a solution of the equation. 6)8p+3p-8=14; 2 Add. 7&4"; Evaluate the expression when a = 5, b = —2, and c = 8. 8) 2a — 5c + |b| Evaluate the expression for the given values. 9) —4x +5y+8a forx=1,y:—4,a=—2 Find the reciprocal. 8 10 —— ) 9 Divide. 5 9 11 ——+ -— ) 11 ( 11 Name the property illustrated by the statement. 12) (8+7)+3=(7+8)+3 13) (2-8)-6:2-(8-6) Indicate whether the terms in the list are like or unlike. 14) ab, 21ba Simplify the expression by combining like terms. 15) 0.8x8 - 1.5x8 - 1.5x8 Remove parentheses and simplify the expression. 16) (82 + 12) _ (22 _ 1) Write the phrase as an algebraic expression and simplify if possible. Let x represent the unknown number. 17) The product of --21 and the sum of a number and 32. Solve the equation. 18) 4(22 - 3) : 7(z + 5) n 19)—5—_11 20)%f—4=1 21) —0.01y + 0.14(200 - y) = 0.10y 22) 9x+3—4x-9=2x+3x—9 23) 2(x+3)—(2x+6)=0 Write an equation that may be used to solve the problem. Do not solve the problem. 24) A promotional deal for long distance phone service charges a \$15 basic fee plus \$0.05 per minute for all calls. If Joe's phone bill was \$46 under this promotional deal, how many minutes of phone calls did he make? Substitute the given values into the formula and solve for the unknown variable. 25) V=%Bh; V:40,h=5 Solve the formula for the specified variable. 9 26) F=gC+32 forC Write an inequality statement that may be used to sovle the problem. “Solve. 27) A student scored 72, 82, and 94 on three algebra tests. What must he score on the fourth test in order to have an average grade of at least 85? Solve the inequality. Graph the solution set and write it in interval notation. 28) 15x — 35 > 5(2x - 11) (—+——|—+—-l—-—l—t—l 29) 2x+10—4x<6-4x+4 (—F—I—‘—i—+——I—+—-—l Complete the ordered pair or pairs so that each is a solution to the given linear equation. 30) 9x + y = —22 (—3, ), (0, ), (1, ) Graph the linear equation. 31) —3y = x — 2 32)8x+y=0 Graph the linear equation by finding and plotting its intercepts. 35) 4y — 2x = —10 37) Find the slope of the line. 38) y : —3 39) 6x + 11y = —5 40)x=6 Determine whether the lines are parallel, perpendicular, or neither. 41) 9x+ 3y: 12 24x+ By: 34 42) 3x— 2y: 3 2x+ 3y: 2 43) 3x— 4y: 6 16x+ 8y: —2 Find the slope of the line and write the slope as a rate of change. Don't forget to attach the proper units. 44) The graph shows the total cost y (in dollars) of owning and operating a mini—van where x is the number of miles driven. 10000 8000 6000 (10,000, 5454.5) 4000 3272.7) 2000 i 5000 10000 15000 20000 25000 Write the equation of the line with the given slope, m, and y—intercept, b. 45) m : —9; b = 4 Use the slope—intercept form to graph the equation. 46) y = —2x + 1 Find an equation of the line with the given slope that passes through the given point. Write the equation in the form y = mx + b. 47) m = — g; (4, 2) Find an equation of the line passing through each pair of points. Write the equation in the form y = mx + b. 48) (—4, 1) and (0, —8) Solve. Assume the exercise describes a linear relationship. 49) The average value of a certain type of automobile was \$15,060 in 1994 and depreciated to \$7860 in 1997. Let y be the average value of the automobile in the year x, where x = 0 represents 1994. Write a linear equation that models the value of the automobile in terms of the year x. Find the domain and the range of the relation. 50) {(8, 1), (—10, 0), (-2, —2), (12, —10)} Determine whether the relation is also a function. 51) {(-4, 43) (-2, -2), (-1r ~6), (7, —8)} Determine Whether the graph is the graph of a function. 52) 53) Given the following function, find the indicated values. Then write the corresponding ordered pairs. 54) Find h(—1), h(O), and h(—9) when h(x) = —4 Determine whether the ordered pair is a solution of the system of linear equations. 2 = -5 — 55) (-2. -1), {3:2 _8 _ Zyy Solve the system by graphing. 2x+ y:-1 56) 3x+3y=3 Does the system have one solution, no solution, or an infinite number of solutions? x+y=2 57) x + y = 3 x+2y=0 1 58) yz—Ex 3x— y=16 59) x+3y=12 Solve the system of equations by the substitution method. 60) —6y=x+21 3x+5y=—11 61) 3x+y=11 9x+3y=33 Solve the system of equations by the addition method. 62) {x + 5y = —26 —6x+5y=16 63) {x+y=9 x+y=—7 Solve. 64) Devon purchased tickets to an air show for 9 adults and 2 children. The total cost was \$252. The cost of a child's ticket was \$6 less than the cost of an adult's ticket. Find the price of an adult's ticket and a child's ticket. 65) Jamil always throws loose change into a pencil holder on his desk and takes it out every two weeks. This time it is all nickels and dimes. There are 7 times as many dimes as nickels, and the value of the dimes is \$7.80 more than the value of the nickels. How many nickels and dimes does Jamil have? Given the cost function, C(x), and the revenue function, R(x), find the number of units x that must be sold to break even. 66) C(x) : 81x + 1750 R(x) = 106x Evaluate the expression with the given values. 67) y2; y= —3 Simplify. Write the result using only positive exponents. 68) (4X)(9X4)(X2) 69) (y2>8 223 70) [3—3 2"] 5 151403)?) 75 ) 11(r5)-2 Write the number in scientiﬁc notation. 76) 68.3575 77) 0.0000069615 Write in standard notation. 78) 1.494 x 106 79) 6.92 x 10—4 Complete the table for the polynomial. 80) —1x4 — 7x3 + 6x + 10 Term Coefﬁcient Identify the polynomial as a monomial, binomial, trinomial, or none of these. Give its degree. 81)6y5—9y4+2 Evaluate the polynomial at the given replacement values. 82) —2x2 — 8x + x4 when x = —3 Simplify the polynomial by combining like terms. 83) —4r — 514 + 1014 — 9r 84) 16ab + 4 + 19ab2 + 7 + 2ab2 + 15ab + 9a2b2 100) x2 + 3x — 28 Perform the indicated operations. 101) )(2 + 9xy + 14y2 85) (7x2 — xy- y2) + (x2 + 9xy + 8y2) 102) x2 — x — 40 86) Subtract (3x — 30) from the sum of (—2x + 2) and (9x — 8). 103) 3x7 + 36x6 + 1055 Add or subtract as indicated. 87) (12x2y2 + 9y4) — (—15x4 — 6x2y2 + 9y4) 104) 6x2 + 13x + 6 Simplify. 105) 50x3 + 50x2 + 12x 88) (§x8)(§x6) 106) x2 — 4xy + 4y2 89) -5x4(—5x — 4) 107) 16x2 - 25 90) (x + 3y)3 108) x2 + 9 91) (x — 12)(x2 + 9x — 6) 109) 256 - x4 92) (5p + 3)(5p — 3) 110) t3 + 64 93) (4x — ll)(5x — 1) 111) x3 - 343 20x4 + 28x3 + 16x2 4X3 Solve the equation. 112) (x—7)(x+6)=0 94) Find the quotient using long division. 113 5 247 12 :0 3t3—15r2—14r—24 )(y+ X“ ) 9 5) r — 6 114) x2 — x = 20 96) 4x3 + 12x2 + 3x + 7 2x + 3 115) 9x2 = 36 Factor completely. If the polynomial cannot be factored, 116) 11d2 _ 4d = 0 state that it is prime. 9 7_ 3 97)36m +28m 8m 117)XZ_49:48X 98) 14a(a-b)+(a-b) 118) 49t3—9t20 99) 12x2 — 8x — 15x + 10 119) (x — 1)(x2 — 8x + 7) z 0 Represent each given condition using a single variable, x. 120) The length and width of a rectangle whose width is three times its length. 121) The base and height of a triangle whose height is ﬁve less than six times its base. Solve the problem 122) The sum of a number and its square is 56. Find the number. 123) One leg of a right triangle is 21 inches longer than the smaller leg, and the hypotenuse is 24 inches longer than the smaller leg. Find the lengths of the sides of the triangle. ...
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