To all students entering 11th grade Math SL & HL class.

In order to keep our current math skills sharp, please complete this summer review packet. Use your previous class notes and work, websites

such as Khan Academy and IXL and other math reference books for guides. Please complete before the first day of school in August 2019. You

will be tested on this material when you return to school.

Show all work, graphs and solutions clearly on a separate sheet of paper. Your work should be numbered and organized so it is easy to read.

Solutions are not provided with this packet.

Have a good summer!

CDS Mathematics Department

Name:_________________________________

11th grade Math SL & HL Summer Packet 2019 DUE on the FIRST day of SCHOOL 2019

Formulas:

Topic Extra Help on Khan Academy

Factoring https://www.khanacademy.org/math/algebra/polynomial-factorization/factoring-quadratics-strategy/v/strategy-in-factoring-quadratics-1

Index Laws https://www.khanacademy.org/math/algebra2/exponential-growth-and-decay-alg-2/equivalent-forms-of-exponential-expressions/v/simplifying-an-exponential-expression

Radical Operations

https://www.khanacademy.org/math/algebra-home/alg-exp-and-log/miscellaneous-radicals/v/adding-and-simplifying-radicals

Complex https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/multiplying-complex-

numbers numbers/a/multiplying-complex-numbers

Solving Quadratics

https://www.khanacademy.org/math/algebra/quadratics

Solving Rational Equations

https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/solving-rational-equations/v/equations-with-two-rational-expressions

Systems of Equations

https://www.khanacademy.org/math/algebra/systems-of-linear-equations

Graph Transformations

https://www.khanacademy.org/math/algebra2/manipulating-functions/stretching-functions/v/shifting-and-reflecting-functions

Exponential Functions

https://www.khanacademy.org/math/algebra2/exponential-and-logarithmic-functions/graphs-of-exponential-functions/v/transforming-exponential-graphs

Right Triangle Trig

https://www.khanacademy.org/math/trigonometry/trigonometry-right-triangles

Non-Right Triangle Trig

https://www.khanacademy.org/math/trigonometry/trig-with-general-triangles

Solving Trig Equations

https://www.khanacademy.org/math/precalculus/trig-equations-and-identities-precalc/solving-sinusoidal-models-precalc/a/trigonometric-equations-review

Trig Identities https://www.khanacademy.org/math/in-in-grade-10-ncert/in-in-chapter-8-introduction-to-trigonometrics/in-in-trigonometric-identities/v/example-1-proving-trigonometric-identities

Set Notation https://www.khanacademy.org/math/statistics-probability/probability-library#basic-set-ops

Venn Diagrams

https://www.khanacademy.org/math/statistics-probability/analyzing-categorical-data/two-way-tables-for-categorical-data/v/two-way-frequency-tables-and-venn-diagrams

Statistics BoxPlot

https://www.khanacademy.org/math/ap-statistics/summarizing-quantitative-data-ap/stats-box-whisker-plots/v/interpreting-box-plots

Statisicis Standard Deviation

https://www.khanacademy.org/math/probability/data-distributions-a1/summarizing-spread-distributions/a/calculating-standard-deviation-step-by-step

Statistics Cumulative Graphs

https://www.khanacademy.org/math/ap-statistics/density-curves-normal-distribution-ap/percentiles-cumulative-relative-frequency/v/analyzing-a-cumulative-relative-frequency-graph

I.BASICS:1.Simplifytheexpression: 2− 20i( )+ 14−7i( ) .2.Simplifytheexpression: 7+9i( ) 8−10i( ) .

3.Simplifytheexpression: 36+7i

.

4.Simplify 25x20 y14 .5.Inanalternating-currentcircuit,thevoltageEisgivenbyE=IZ,whereIisthecurrent(inA)andZistheimpedance(inΩ ).Eachofthesecanberepresentedbycomplexnumbers.FindthecomplexnumberrepresentationforIif E = 62+32i voltsand Z =1200−560i ohms.

6.Simplifytheexpression 24332

5 .

7.Find f t +7( ) for f x( ) = 2x2 −9x +8 .8.Divideusinglongdivision: 6x6 −3x5 +15x4 − 21x3 +15x2 −3x −5( )÷ −3x +3( ) .9.Find x3 +5x2 −16x −80( )÷ x + 4( ) byusingsyntheticdivision.

10.Expandandsimplify 2x −3y( ) x +5y( )− x − y( )2.

11.Simplifyx2 −9

x3 +7x2 +12x.

12.If 2x −5yx −6y

=34,findthevalueof x

y.

13.Makeythesubjectoftheformula 1x+1y=1z.

14.Giventhat ax −5y5a− 2x

=23,expressaintermsofxandy.

15.Simplify 2 +1+ 11+ 2

II.SOLVE:1.Solve x2 − 2x = 24 bycompletingthesquare.2.Findtheexactsolution x2 −5x = 36 byusingtheQuadraticFormula.3.Solvethesystemofequationsbyusingsubstitution.

6r +7s = −12r + 4s = −12

4.Solvethesystemofequationsbyusingelimination.

−3p−9q = −63−8p−6q = −60

5.Solveforx: 9x −3+1= 20 .

6.Solveforx: 4x +1+ 2 = 8x +7 .7.Solveforx:5x3 −7x2 −19x −15= 0 .

8.Solveforx:4x − 4

−7x +5

=66

x2 + x − 20.

9.Solveforx: 2x +3( ) x +8( ) ≥ 0 .

10.Solveforx: 2y +15

−2+7y15

>23.

11.Solvefory.Roundtothenearesthundredth: y +5 ≥ 3 .

12.Giventhat x = 12+ y4− y

,solvethefollowing:

a)Ify=-2,calculatethevalueofx,givingyouranswerasafractioninitslowestterms. b)Expressyintermsofx.13.Solvethefollowingequations:

a)3x2 +3=10x b) 5x − 2( )2−9x2 = 0

14.Thesidesofanequilateraltriangleare 2y +3( ) cm, x + 2( ) cm,and x + y −1( ) cm.Findtheperimeterofthetriangle.

III.GRAPH:1.Usethegraphofftodescribethetransformationthatresultsinthegraphofg.Thensketchthegraphsofgandf.

f x( ) = ex ; g x( ) = −5ex+4 + 2 2.Graph y = log2 x − 2( ) .3.Sketchandanalyzethegraphof f x( ) = 6x −5 .Describeitsdomain,range,intercepts,andasymptotes.

4.Writeanequationofthecosinefunctionwithamplitude2andperiod6π .5.Forthefollowing,identifytheparentfunctionandthengraphusingtransformations.Statethedomain,range,andasymptotesifapplicable.

a)y=!!x–3

b) y = −3 x −1( )2

c) y =1x + 2

−3

d) y = x +1+ 2

e) y = −12x3

f) y = −x +1

g) y = − x − 23

h)y=-sin(2x-π)

IV.EXPONENTIALANDLOGARITHMICFUNCTIONS:

1. Evaluatetheexpression log5125 .

2. Evaluatetheexpression log3 243 .

3. Evaluatetheexpression6log61.5 .4. Evaluatetheexpression log75 .

5. Solvetheequationforx:32x−1 =16x+4 .

6. Solvetheequationforx: log7 x2 +11( ) = log715 .

7. Solvetheequationfory: ln −y + 4( )− ln y +3( ) = ln −3y +1( ) .

8. Solve log6 x = 2 .

9. Expandtheexpression: log62x +6

3−3x5 .

10.Solvetheequationforx: 2.9x = 9.7 . V.TRIGONOMETRICFUNCTIONSANDEQUATIONS:

1. Find the values of the six trigonometric functions for angle θ , when AC = 26 and BC = 24.

2. If g = 35.4 and F = 34° , find h. Round to the nearest tenth.

3. Find one positive and one negative angle coterminal with an angle of 166° .

4. Find the area of a sector with a central angle of 170° and a radius of 17 millimeters. Round to the

nearest tenth.

5. For a circle of radius 3 feet, find the arc length s subtended by a central angle of 21° .

6. Find the values of the six trigonometric functions of an angle in standard position if the point with coordinates (40, 9) lies on its terminal side.

7. Find the exact value of sin135° .

8. Find the exact value of cos −5π4

⎛

⎝⎜

⎞

⎠⎟ .

9. Find the reference angle for 342° .

10. Solve ΔABC if c =10, B = 35°,C = 65° .

11. Solve ΔPQR , if Q = 53°, p =14, q =14.6 .

12. Find the area of a triangle with a = 3 feet, b = 4 feet, and c = 6 feet. Round to the nearest tenth.

13. If cosθ = 47

and cscθ < 0 , find sinθ and tanθ .

14. Simplify sec x − tan xcsc x .

15. If sinθ = 725

and tanθ > 0 , find cotθ and cscθ .

16. Verify the following: 1− 2sin xcos x = sin x − cos x( )2.

17. Verify the following: sin2 x = cos2 xsec2 x − cos2 x .

18. Solve 7−6sin x = 3+ 2sin x for 0° ≤ x ≤180° .

19. Find all solutions of the equation on the interval 0, 2π⎡⎣ ) : sin2 xcos2 x − 2sin2 x = 0

VI.SEQUENCES:1. Find the next four terms of the arithmetic sequence: 46.25, 45, 43.75, … 2. Find the next term of the geometric sequence: 9, -45, 225, -1125,… 3. Find the specified nth term of the geometric sequence: a4 =10, r = 2, n = 9 . 4. Find the general term of the sequence: 17, 14, 11, 8, 5, 2, -1, -4 5. Find the general term of the sequence: 12, 18, 27, 81/2, . . .

VII.STATISTICS:1. LetU = 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18{ } , A= 2,4,9,13,14{ } ,andB = 9,10,13,18{ } .Find A∪B and A∩B .

2. UsetheVenndiagrambelowtofind A∪B ,C∩D ,and A∪C( )∪D .

3.Jeffreysurveyed50randomlyselectedworkersatafactory.Hecollecteddataabouttheindividualoutputofaworkeronanaverageday.Theresultsareshownusingthebox-and-whiskerplot.

a.Whatpercentofworkershaveoutputmorethan70units?b.Whatistheinterquartilerangeofthebox-and-whiskerplotshown?c.Findtherangeofthedatashowinthebox-and-whiskerplotshow

4.TheIBgradesattainedbyagroupofstudentsarelistedasfollows.

a.Findthemediangrade.

b.Calculatetheinterquartilerange.

c.Findtheprobabilitythatastudentchosenatrandomfromthegroupscoredatleastagrade .

5.Thecumulativefrequencygraphshowsthespeed, ,in ,of vehiclespassingahospitalgate.

a.Estimatetheminimumpossiblespeedofoneofthesevehiclespassingthehospitalgate.

b.Findthemedianspeedofthevehicles.

c.Writedownthe percentile.

d.Calculatetheinterquartilerange.

e.Thespeedlimitpastthehospitalgateis Findthenumberofthesevehiclesthatexceedthe

speedlimit.

f.Thetableshowsthespeedsofthesevehiclestravellingpastthehospitalgate.

Findthevalueof andof .

6.Danielgrowsapplesandchoosesatrandomasampleof100applesfromhisharvest.

Hemeasuresthediametersoftheapplestothenearestcm.Thefollowingtableshowsthedistributionof

thediameters.

Usingyourgraphicdisplaycalculator,writedownthevalueof

a)themeanofthediametersinthissample;

b)thestandarddeviationofthediametersinthissample.7.Theamountoftimethatasampleofstudentsatacollegespendsstudyingphysicseachweekisshownbelow.Constructaboxplot.

Time Spent Studying Physics (hours) 12 30 27 23 13 19 27 33 39 20 31 26