MATH 110 Chapter 1 Review 05-11 - The Learning Lab at HFCC
MATH 110 Chapter 1 Review 05-11 - The Learning Lab at HFCC
MATH 110 Chapter 1 Review 05-11 - The Learning Lab at HFCC
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<strong>MATH</strong> <strong><strong>11</strong>0</strong>: CHAPTER 1 REVIEWCan you solve linear equ<strong>at</strong>ions in one variable algebraically and check your answers by hand? (1.5)(1) (a) ( ) ( )10 a + 8 − 8 = 2 36 + 4a + 2a(b) 3 t + 2 8 − 2 t= − 43 4(c)m − 2 1−4m− = 23 53 4 ⎛ 3 ⎞+ ⎜ − 6 ⎟ = 2 + 1 + 62 3 ⎝ 8 ⎠(d) x x ( x )Can you solve linear equ<strong>at</strong>ions in one variable by using a graphing calcul<strong>at</strong>or? (1.5)(2) (a) ( x ) x ( x )2 − 8 + = 3 − 6 + 2(b) 3 x − 2 5 − 2 x= − − 43 4(c)x − 3 4 − x− = 22 53 4 ⎛ 3 ⎞+ ⎜ + 6 ⎟ = 2 −1 − 62 3 ⎝ 8 ⎠(d) x x ( x )Revised <strong>05</strong>/<strong>11</strong> 1
Can you set up and solve word problems involving linear equ<strong>at</strong>ions? (1.6)(3) (a) Twice the difference of a number and 3 is the same as 1 added to three times the number.Find the number.(b) <strong>The</strong> new governor of California makes $27,500 more than the governor of New York, and$120,724 more than the governor of Alaska. If the sum of these 3 salaries is $471,276, findthe salary of each governor.(c) A premedical student <strong>at</strong> a local college was complaining th<strong>at</strong> she had just paid $86.<strong>11</strong> for heralgebra book, including tax. Find the price of the book before taxes if the tax r<strong>at</strong>e <strong>at</strong> thiscollege is 9%.(d) Find the measures of the angles of a triangle whose two base angles are equal and whosethird angle is 12° less than twice the base angle.(e) <strong>The</strong> length of a rectangular playing field is 5 meter less than twice its width. If 230 meters offencing goes around the field, find the dimensions of the field.(f) <strong>The</strong> sum of the second and fourth of four consecutive integers is 186. Find the four integers.(g) A car rental company charges $19.95 per day for a compact car plus 12 cents per mile forevery mile over 100 miles driven per day. If Mr. Woo’s bill for 2 days’ use is $46.86, findhow many miles he drove.Revised <strong>05</strong>/<strong>11</strong> 2
Can you cre<strong>at</strong>e tables and use tables to solve problems? (1.7)(4) A local gas st<strong>at</strong>ion has 1000 gallons of premium gasoline and has been selling it <strong>at</strong> a r<strong>at</strong>e of 1.5gallons per minute.(a) Write an algebraic represent<strong>at</strong>ion for the number of gallons, y1, in terms of the numbers ofminutes th<strong>at</strong> have passed, x . (Assume no gasoline is delivered.)(b) Complete the table for the gallons of gasoline remaining given the number of minutes th<strong>at</strong>have elapsed.Minutes Elapsed 0 60 120 180 240 300 360Gallons Remaining(c) If the st<strong>at</strong>ion does not get a gasoline delivery, when will the st<strong>at</strong>ion run out of premium gas?(5) Judy Martinez has been shopping for school clothes and has picked out several outfits. Sheknows th<strong>at</strong> the following Thursday there will be a Super Thursday sale and everything in thestore will be discounted 35%.(a) Write an algebraic represent<strong>at</strong>ion for the sale price, y1, in terms of the price, x , on the pricetag. (Without tax.)(b) Complete the table and find the cost of each item on sale given the price on the price tag(Without tax.) Round to the nearest cent.Item Shirt Dress Shorts Shoes Purse Earrings BackpackPrice Tag $29.95 $35.95 $19.25 $39.95 $17.95 $9.95 $25.75Sale Price(c) If she purchases all the items when on sale, wh<strong>at</strong> will her total bill be before taxes?(d) Wh<strong>at</strong> is the total after taxes if a 7% tax is added to the bill?(e) How much did she save before taxes by waiting for the sale?Revised <strong>05</strong>/<strong>11</strong> 3
Answers:(1) (a) All real numbers16(b) t = −943(c) m =17(d) No solutions or ∅(2) (a) All real numbers. Both sides of the equ<strong>at</strong>ions form the same line.y987654321x−9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10−1−2−3−4−5−6−7−8−9−10(b) <strong>The</strong> lines intersect <strong>at</strong> x = − 9.16 or1x = − 9 6y4321x−14 −13 −12 −<strong>11</strong> −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5−1(c) <strong>The</strong> lines intersect <strong>at</strong> x = 6.14286 or98765432y−2−3−4−5−6−7−8−9−10−<strong>11</strong>−12−13−14−15x =4371x−9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10−1−2−3−4−5−6−7−8−9−10(d) <strong>The</strong> lines do not intersect. Thus there is no solution or ∅y987654321x−9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10−1−2−3−4−5−6−7−8−9−10Revised <strong>05</strong>/<strong>11</strong> 4
(3) (a) <strong>The</strong> number is -7(b) <strong>The</strong> California governor makes $206, 500, New York makes $179,000, and Alaska $85,776.(c) <strong>The</strong> book cost $79 before taxes.(d) <strong>The</strong> angles measure 48˚, 48˚, and 84˚.(e) <strong>The</strong> width is 40 m and the length is 75 m.(f) <strong>The</strong> integers are 91, 92, 93, and 94.(g) 258 miles(4) (a) y1 = 1000 − 1.5x(b)Minutes Elapsed 0 60 120 180 240 300 360Gallons Remaining 1000 910 820 730 640 550 4602(c) <strong>The</strong> st<strong>at</strong>ion will run out of gas in 666 minutes; or 666 minutes 40 seconds, or <strong>11</strong> hours 63minutes 40 seconds.(5) (a) since the discount is 35%, the percentage of the price x th<strong>at</strong> we WILL pay is100% - 35% = 65%. Thus the equ<strong>at</strong>ion for the price should be y1 = 0.65x(b)Item Shirt Dress Shorts Shoes Purse Earrings BackpackPrice Tag $29.95 $35.95 $19.25 $39.95 $17.95 $9.95 $25.75Sale Price $19.47 $23.37 $12.51 $25.97 $<strong>11</strong>.67 $6.47 $16.74(c) $<strong>11</strong>6.20(d) $124.33(e) $62.55Revised <strong>05</strong>/<strong>11</strong> 5