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nd
2 Semester Algebra 2 Benchmark Toolkit
Benchmark PS 1.0 (Section 9-7) Probability of Independent & Dependent Events
1. There are 4 girls and 6 boys in the 2. On a certain day the chance of rain 3. There are 2 colors of large and
room. If two people are chosen, what is 40% in Visalia and 90% in Fresno. small marbles in a basket. You have an
is the probability that the first person Assume that the chance of rain in the 80% chance of drawing a large or red
chosen is a boy and the second person two cities is independent. What is the marble. If you knew you had a 30%
is a girl? (Without replacement) probability that it will not rain in both chance that it was red and a 90%
cities? chance it was small, then what is the
probability that it was a large red
marble?




(Will rain in both cities)
Benchmark PS 2.0 (Section 12-2) Conditional Probability
1. A football team has a 25% chance of winning when it 2. What is the probability of drawing a face card out of a
snows, but a 40% chance if it doesn’t snow. Suppose there deck of 52 cards, given that it is a diamond?
is a 60% chance of snow. What is the probability that they
will loss?
Benchmark 19.0 Probability Using Permutations & Combinations
1. Kim and Helen are competing with 3 other students to 2. Jason, Jose, Hans and 4 other students are left in a
get the highest grades in the class. What is the probability drawing for three ...

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nd 2 SemesterAlgebra 2 Benchmark Toolkit Benchmark PS 1.0(Section 97)Probability of Independent & Dependent Events 1. Thereare 4 girls and 6 boys in the2. Ona certain day the chance of rain3. Thereare 2 colors of large and room. If two people are chosen, whatis 40% in Visalia and 90% in Fresno.small marbles in a basket. You have an is the probability that the first personAssume that the chance of rain in the80% chance of drawing a large or red chosen is a boy and the second persontwo cities is independent. What is themarble. If you knew you had a 30% is a girl? (Without replacement)probability that it willnotrain in bothchance that it was red and a 90%  cities?chance it was small, then what is the  probabilitythat it was a large red  marble?(W illrain in both cities)
Benchmark PS 2.0(Section 122)1. Afootball team has a 25% chance of winning when it snows, but a 40% chance if it doesn’t snow.Suppose there is a 60% chance of snow. What is the probability that they will loss?
Conditional Probability 2. Whatis the probability of drawing a face card out of a deck of 52 cards, given that it is a diamond?
Benchmark 19.0Probability Using Permutations & Combinations 1. Kimand Helen are competing with 3 other students to2. Jason,Jose, Hans and 4 other students are left in a get the highest grades in the class.What is the probabilitydrawing for three DVDs.What is the probability that that Kim will get the highest grade and Helen the secondJason, Jose, and Hans will each win a DVD? highest grade?
Benchmark PS 7.0(Section 124)1. Whatis the standard deviation of the following set of data?8, 12, 20, 4
Variance & Standard Deviation 2. Whichof the following set of data3. Whatis the variance of the will probably have thelargest followingset of data?3, 2, 7, 8, 5 standard deviation and which will have thesmalleststandard deviation? a) 3, 20, 12, 5, 7, 12 b) 26, 21, 24, 33, 25, 17 c) 10, 15, 30, 41, 2, 1 d) 88, 90, 87, 91
Benchmark 12.0a(Sections 71 & 74)1. Simplifyand rewrite in radical 6/20 notation: x
2. Simplifyand rewrite in rational 4 6 exponent notation:x
Rational Exponents & Radicals3/2 3. Simplify: 25
Benchmark 12.0b(Sections 81 & 82)Exponential Growth and Decay Word Problems 1. Saraput $5,000 into the stock2. Jackbought a house for $700,000.3. Willborrowed $500 from his market and it is depreciating in valueOver the last 5 years, the values ofparents. Hetold his parents that he at an average of 6% per year.Write anhomes in his neighborhood havewould pay them back with 7% interest equation to find out how long it willincreased in value by 10% a year.and that he would compound interest take for her to loose half of her money.Write an equation to calculate thecontinuously. Writean equation that value of his house after those fivewill show how much he owes his years. parentsafter 3 months.
Benchmark 12.0c(Sections 81 & 82) 1. Forthe following exponential function, what is output when x = 6? x 3 1y= −2+3  3
Exponential Growth and Decay Functions2. Whatis the equation for the3. Bacteria in a culture are growing following exponential function?exponentially with time, as shown in  thetable below. What is an equation  thatexpresses the number of bacteria,  y,present at any time, t? Days0 1 2 Bacteria100 300 900
Benchmark 14.0a(Sections 83 & 84)2. Rewritethe 1. Evaluate: log464 following exponential equations as a logarithmic equation: x 7 =11
Properties of Logarithms3. Iflog 30.5andlog 70.8, then approximate the value oflog 63.
5 x log 4. Expand:64 7y
Benchmark 11.0a(Section 85)5x  43x – 1 1. Solve: 7= 49
Benchmark 14.0b(Section 86)3 1. Simplify:72 lne
Benchmark 11.0b(Section 86)1. Solve:3 ln(3x–1) = 21
Solving Logarithmic & Exponential Equationsx 2. Solve: 6(7)– 7= 113. Solve: 2log4(3x – 2) + 1 = 7
53 e x 2. Expand:ln4y
Properties of Natural Logarithms3. Condense:7 ln y+ 3ln x– ln8
Solving Natural Logarithmic & Exponential Equationsx 2. Solve: 6(e)– 7= 113. Which is the firstincorrectstep in solving the following equation? ln(x2)+ln(x+4)=ln 7Step 1:ln((x2)(x+4))=ln 7Step 2:(x2)(x+4)=72 Step 3:x+2x15=0Step 4:x=5and x= −3
Benchmark 7.0a(Section 94 and page 374)Various Operations with Rational Monomial Expressions2 525 3432 2 2a b2. Simplify:(2x y) (3xy)3x y9xy 3. Simplify:÷1. Simplify:35 73 16y4x 12ab c
Benchmark 7.0(Sections 94 & 95)2 2 2x2xy24y 1. Simplify: 2 2x+6xy
Benchmark 7.0c(Section 96)3 5 1. Solvefor x:=x+3 2x
Various Operations with Rational Polynomial Expressions2 2 x+2x3 2x86x2 2. Simplify:i3. Simplify:22x+6 1x 3x+9x3x18
3 25 2. Solvefor x:− =2x x6
Solving Rational Equationsx4 3. Solvefor x:=32 2x2x1
Benchmark 15.01. Ifx and y are real numbers, which value(s) for x make the following function true?y=3+x
Properties of Radical, Exponential, Logarithmic, and Rational Functions2. Ifx and y are real3. Ifx and y are real4. Ifx is a real number, numbers, what are thenumbers, which value(s) forwhat are the possible possible value(s) for y?x make the followingvalue(s) for x? 2 x function true? x3x28 y=3+2=x+4y=log (x+7)x7 2
Benchmark 22.0a(Sections 112 & 113)Arithmetic & Geometric Sequencesth th 1. Findthe common difference of the2. Write the rule for the nterm of the3. Writethe rule for the nterm of the arithmetic sequence where:following sequence:7, 3, 1, 5, …following sequence:3, 12, 48, …a4and a= 1012= 38.
Benchmark 22.0b(Sections 114 & 115)1. Findthe sum of the first 17 terms given the rule 2 – 3n.
2. Findthe sum of the first 4 terms of the geometric series in which: a1= 2 and r = 3
Arithmetic & Geometric Series3. Findthe sum of the infinite geometric series in which: a1= 5 and r = 1/3
Benchmark 16.0(Sections 102 thru 105)1. Whatis the focus of the2. Whatis the radius of the following parabola?following circle? 2 22 2y =24x x+ y= 4
Benchmark 17.0a(Sections 102 thru 106)1. Inwhich direction will2. Whatare the coordinates the following parabolaof the center of the open? followingconic? 2 22 5y =7x (x9)+ (y1)= 8
Benchmark 17.0b(Sections 102 thru 106)1. Thefollowing equation2. Whatis the equation for makes what type of graph?the graph? 2 2  6x 7y+ 7y + 4 = 0
Properties of Conic Sections at the Origin3. Whatare the vertices of4. Whatwould be the the following ellipse?equation of the asymptotes 2 2 4x +5y =40 ofthe following hyperbola? 2 2 6y –15x =30
Properties of Translated Conic Sections3. Whatwill be the4. Whatwill be the coordinates for the verticescoordinates for the foci of of the following conic?the following conic? 2 22 2 (y1) (x4)(x+2) (y5) + =11 =11 5 49 4
Translating Conic Sections3. Putthe following equation into standard form.What is 2 2 the center of the conic?9x –4y +36x – 24y – 36= 0