A cell phone plan costs20dollars each month, plus5cents pertext message sent, plus10cents for each minute used over30hours. In January Michelle sent100text messages and talkedfor30.5hours. How much did she have to pay?(A)$24.00(B)$24.50(C)$25.50(D)$28.00(E)$30.002011 AMC 10A, Problem #1—2011 AMC 12A, Problem #1—“How many minutes of excess chatting are there, and what dothey cost?”Diﬃculty:EasyCCSS-M:N-Q.1.Use units as a way to understand problems and to guide the solution of multi-stepproblems; choose and interpret units consistently in formulas.1
A small bottle of shampoo can hold35milliliters of shampoo,whereas a large bottle can hold500milliliters of shampoo.Jasmine wants to buy the minimum number of small bottlesnecessary to completely fill a large bottle. How many bottlesmust she buy?2011 AMC 10A, Problem #2—2011 AMC 12A, Problem #3—“The quantity 35 goes into 500 how many times?”needs to buy is 15.Diﬃculty:EasyCCSS-M:N-Q.3. Choose a level of accuracy appropriate to limitations on measurement when reportingquantities.2
Suppose[a b]denotes the average ofaandb, and{a b c}denotes the average ofa,b, andc. What is{{1 1 0}[0 1] 0}?(A)29(B)518(C)13(D)718(E)2Answer (D):First note that{1 1 0}=23and[0 1] =2. Therefore{{1 1 0}[0 1] 0}={23120}=23+12+ 03=718.Diﬃculty:Medium EasyCCSS-M:A-SSE.1.Interpret expressions that represent a quantity in terms of its context.Interpretcomplicated expressions by viewing one or more of their parts as a single entity.32011 AMC 10A, Problem #3—“Pay attention to the order of substitutions.”Solution13
LetXandYbe the following sums of arithmetic sequences:X= 10 + 12 + 14 +· · ·+ 100,Y= 12 + 14 + 16 +· · ·+ 102.What is the value ofY-X?2011 AMC 10A, Problem #4—“What are the elements inYbut not inX, and vice versa?”Diﬃculty:MediumCCSS-M:A-SSE.2. Use the structure of an expression to identify ways to rewrite it.4