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Math 95 Online Final Review - Final Exam Review This is not...

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Unformatted text preview: Final Exam Review This is not an exhaustive list of all possible problems you may see on the final. Be sure to review all homework problems assigned from the book and online. This review is just meant to get you started in the studying process to find out what types of problems you understand and those you do not understand and need to review further. This review only includes problems from sections covered after the midterm through the end of the semester, so be sure to take a look at the Midterm Review for problems from the first half of the semester. The final includes all sections covered in the course. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Identify the intercepts. A) (7,0), (-7, 0), (0,6), (0, —6) B) (6,0), (—6, 0), (0, 7), (o, —7) C) (6, 0), (-6, 0) D) (0, 7), (0, —7) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Graph the linear equation by finding x— and y— intercepts. 2) —6x — 24y : 24 2) Graph the linear equation. 3) y=—3 3) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the slope of the line that goes through the given points. 4) (—8,—9) and (41,46) 4) 3 25 7 7 _ B __ _. _ _ A) 7 ) 19 C) 3 D) 3 Find the slope of the line. 5) y= —5 5) A) In : 0 B) In : 1 C) m : -—1 D) undefined slope Determine whether the lines through the pairs of points are parallel, perpendicular, or neither. 6) (1,6) and (—1,8); (0,5) and (1, 6) 6) A) parallel B) perpendicular C) neither Determine the slope and the y—intercept of the graph of the equation. 7) —x+ 11y:44 7) A)m=T11-; (0,4) B)m:11;(0,—44) C)m=—T11-; (0, 4) D)m:—1;(0,44) Determine whether the lines through the pairs of points are parallel, perpendicular, or neither. 8) 12X+ 4y: 16 8) 27x + 9y 2 40 A) parallel B) neither C) perpendicular Use the slope—intercept form of the linear equation to write an equation of the line with given slope and y-intercept. 9) Slope %; y—intercept (0, 2) 9) A)y:-%x—2 B)y:%x—2 C)y:——%x+2 D)y=%x+2 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use the slope—intercept form to graph the equation. 10) 5x + 4y : 20 10) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Evaluate the expression. 11) -53 11) A) 125 B) -15 C) —125 D) 15 12) (—5)3 12) A) 125 B) -125 C) —15 D) 15 Evaluate the expression with the given replacement values. 13) —2x3y; x : 2 and y = —3 13) A) 36 B) —48 C) 48 D) 24 Use the product rule to simplify. Write the results using exponents. 14) (5x)(8x3)(x4) 14) A) 14x8 B) 40x7 C) 40x8 D) 13x7 Use the power rule and the power of a product or quotient rule to simplify the expression. 2 3 3 15) .P_V4_ 15) s3 9 12 6 7 9 12 9 12 A) 3PV_ ,3) Eu C) ELL D) £11; 56 s6 s9 59 Use the quotient rule to simplify the expression. 16 8 16) 221.1; 16) 7m15n4 A) 5m31n12 B) 5mn4 C) 35mn4 D) 5:14 Simplify the following. 17) —5y0 17) A) 0 B) —4 C) —5 D) 1 Simplify. 18) If P(x) = —-2x + 7, find P(-5). A) —17 B) —3 C) 3 D) 17 Solve. 19) A projectile is fired upward from the ground with an initial velocity of 300 feet per second. Neglecting air resistance, the height of the projectile at any time t can be described by the polynomial function P(t) : -l6t2 + 300t. Find the height of the projectile at t = 4 seconds. A) 1136 ft B) 1200 ft C) 944 ft D) 1044 ft Perform the indicated operations. 20) (6x2 + 7x — 8) — (—9x2 + 10) A) 38 + 7x + 2 B) 15x2 + 7x — 18 C) -3x2 — 3x — 8 D) 15x2 — 3x — 8 Simplify. 21) If P(x) : 4x - 9 and Q(X) = —4x2 + 3x + 6, find P(x) + Q(x). A)4x2+7x—3 B)—4x2+7x+3 C)-—4x2-7x-3 D)—4x2+7x—3 Find the following product. 22) (92 + 5)2 A) 8122 + 25 B) 922 + 902 + 25 C) 8122 + 902 + 25 D) 922 + 25 23) 12x(—12X — 9) A) —12x2 — 108x B) —144x2 — 108x C) —252x2 D) —144x2 — 9x Find the product using the FOIL method. 24) (5x — 3)(6x — 1) A) 30x2 + 13x + 3 B) 11x2 — 4 C) 30x2 + 3 D) 30x2 — 23x + 3 Find the product. 25) (12 + m)(12 — m) A) 144 + 24111 — m2 B) 24 - m2 C) 144 — 24m — m2 D) 144 — m2 Simplify the expression. Write the result using positive exponents only. 26) —3-4 A) — —1— B) —81 C) i D) 81 81 12 —3 2 3 27) 20r (r ) 7(I3)—3 2 12 A) g B) 20r C) 20r D) 20 712 7 7 7r12 Write the number in scientific notation. 28) 0.000946 A) 9.46 x 10-3 B) 9.46 x 10-4 C) 9.46 x 10-5 D) 9.46 x 104 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) Write in standard notation. 29) 6.26 x 104 A) 626,000 Perform the division. —10x10 + 45x6 —5x2 A) 2x8 — 9x4 30) x2+5x+6 1 3) x+2 A)x-4 Find the GCF for the list. 32) 60, 70 A) 5 33) 14m5, 56m8 A) 141115 B) 62,600 B) —10x10 — 9x4 B)x2+3 B)1 B) 784m3 Factor out the GCF from the polynomial. 34) 21x3 - 6x2 + 15x A) 3(7x3 - 2x2 + 5x) C) 3.x(7x3 — 2x2 + 5x) Factor by grouping. 35) 2x — 20 + xy — 10y A) (y - 10)(2x + y) Factor the polynomial completely. If the polynomial cannot be factored, write prime. 36) x2 — 8x- 33 A) (X — 33)(x + l) 37) x2 — 12x + 35 A) (x + 5)(x + l) 38) 3x2 — 21x + 36 A) 3(x — 3)(x — 4) 39) 3x2— x-24 A) (3x — 3)(x + 8) 40) 22 — 6.2 + 9 A) (z — 3)(z + 3) B) (y - 10)(x + 2) B) (x + ll)(x — 3) B) (x + 5)(X — 7) B) (x - 3)(3x — 12) B) (3x + 8)(x — 3) B) (z + 3)2 C) 6260 C) —7x14 C)x3—4 C)2 C) 56m5 B) 3x(7x2 - 2x + 5) D) x(21x2 - 6x + 15) C) (X — 10)(2 + y) C) (x — ll)(x + 3) C) (X - 5)(>< _ 7) C) 3(x _ l,2)(x + 1) C) (3x - 8)(x + 3) C) <2 — 3)2 U“! D) 250.4 D) 2x8 + 45x6 D)x+3 D) 10 D) 14m3 D) (X - 10Y)(2 + Y) D) prime D) prime D) prime D) (3x + 3)(x — 8) D) (2 ~ 6)(z + 6) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39) 40) 41) 8x2 + x — 124 A) (8x — 4)(x + 31) B) (8x + 4)(x — 31) C) (8x — 31)(x + 4) D) (8x + 31)(x — 4) 42) 25 — 49x2 A) (5 + 7x)2 B) (5 + 7x)(5 — 7x) C) (5 — 7x)2 D) prime 43) x3 - 125 A) (x + 5)(x2 — 5x + 25) B) (x — 5)(x2 + 25) C) (X — 5)(X2 + 5X + 25) D) (x +125)(x + 1)(x - 1) Solve the equation. 44)x2+7x— 18:0 A)X=—9,x=1 B)x=9,x=-2 C)x=9,x=2 D)x=-9,x=2 45)16x2—1=0 1 1 1 1 1 : _ — B : _/ : - — : _ —/ A)x 4 )x 4x 4 C)x 4 D)x 4x 46) y3 + 14y2 + 49y = 0 A)y=0,y=7 B)y=7,y:—7 C)y=0,y:—7,y=7 D)y=0,y=—7 Represent each given condition using a single variable, x. 47) The length and width of a rectangle whose width is two times its length. A) length = x; width 2 2x B) width : x; length = x + 2 C) length = x; width = x + 2 D) width : x; length = 2x Solve the problem. 48) The perimeter of the quadrilateral is 88 inches. Find the lengths of the sides. x + 2 ,//\‘x 214 + 1 x - 5 Z..— 2 q x - a}: A) 12 in, 21 in., 70 in., 5 in. B) 3 in, 3 in, —2 in, -4 in. C) 11 in., 19 in., 54 in., 4 in. D) 10 in, 20 in, 54 in, 4 in. 49) The sum of a number and its square is 72. Find the number. A)80r9 B) —80r—9 C) —80r9 D)80r—9 50) The width of a rectangle is 6 kilometers less than twice its length. If its area is 80 square kilometers, find the dimensions of the rectangle. A) width 2 8 km, length = 10 km C) length = 3 km, width : % km B) length : 5 km, width 2 4 km D) length = 8 km, width : 10 km 41) 42) 43) 44) 45) 46) 47) 48) 49) 50) Decide whether or not the ordered pair satisfies the system of linear equations. 51) (3,1); 51) 4x : -ll — y {2X 2 —2 - 4y A) Yes B) No Determine whether the system is consistent or inconsistent and whether the equations are dependent or independent. 52) Y‘5X=2 52) 4y=20x+8 A) system is consistent; equations are independent B) system is consistent; equations are dependent C) system is inconsistent; equations are independent D) system is inconsistent; equations are dependent Without graphing, determine whether the system has one solution, no solution, or an infinite number of solutions. 53) 53) x:—y y+x=5 A) no solution B) infinite number of solutions C) one solution Without graphing, determine whether the graphs of the equations are identical lines, parallel lines, or lines intersecting at a single point. 54) 54) x + 2y : 12 y:—%X+6 A) lines intersecting at a single point B) identical lines C) parallel lines Solve the system of equations by the substitution method. 55) 55) y : 2x — 4 {4y + 20x 2 —72 A) (—2, —8) B) (-8, —2) C) infinite number of solutions D) no solution 5Q SQ 1 5X — 2y 2 1 x — 10y = 5 AHLfi) mfinh C) infinite number of solutions D) no solution Solve the system of equations by the addition method. 5% 5% —2x + 7y 2 6 5x + 3y : 26 An4pm BH4D CH42) DM4Q) %) fl) 1 l: 2+2 1 l_l= 4 4 2 1A)(5/_3) B)(-3,5) C) infinite number of solutions D) no solution Solve. 59) A chemist needs 150 milliliters of a 56% solution but has only 48% and 63% solutions available. 59) Find how many milliliters of each that should be mixed to get the desired solution. A) 75 ml of 48%; 75 ml of 63% B) 70 ml of 48%; 80 ml of 63% C) 75 ml of 48%; 80 ml of 63% D) 80 ml of 48%; 70 ml of 63% 60) A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 2 bags of potato 60) chips for $7.00. Another customer buys 4 hot dogs and 5 bags of potato chips for $15.00. Find the cost of each item. A) $2.50 for a hot dog; $1.00 for a bag of potato chips B) $2.50 for a hot dog; $1.25 for a bag of potato chips C) $1.00 for a hot dog; $2.50 for a bag of potato chips D) $2.75 for a hot dog; $1.25 for a bag of potato chips 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. 61) C(x) : 84x + 1620 61) R(x) = 102x A) 90 units B) 14 units C) 92 units D) 91 units Solve. 62) A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 2 hot dogs, 4 bags 62) of potato chips, and 3 soft drinks for $10.00. The price of a hot dog is $0.50 more than the price of a bag of potato chips. The cost of a soft drink is $100 less than the price of two hot dogs. Find the cost of each item. A) $1.25 for a hot dog; $1.50 for a bag of potato chips; $0.75 for a soft drink B) $1.25 for a hot dog; $0.75 for a bag of potato chips; $1.50 for a soft drink C) $0.75 for a hot dog; $1.25 for a bag of potato chips; $1.50 for a soft drink D) $1.50 for a hot dog; $1.00 for a bag of potato chips; $1.50 for a soft drink Answer Key Testname: MATH 95 ONLINE FINAL REVIEW 4) D 5) A 6) B 7) A 8) A 9) D 10) Answer Key Testname: MATH 95 ONLIN E FINAL REVIEW 14) 15) 16) 17) 18) 19) [\J o >UUWOUWOUOWUO 10 ...
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