Lyman Memorial High School. Honors Pre-Calculus Prerequisite Packet. Name:

Transcription

1 Lyma Memorial High School Hoors Pre-Calculus Prerequisite Packet 2018 Name:

2 Dear Hoors Pre-Calculus Studet, Withi this packet you will fid mathematical cocepts ad skills covered i Algebra I, II ad Geometry. These cocepts eed to be reviewed ad practiced throughout the summer. The completio of this review packet is very importat ad essetial for your success i Pre-Calculus. These skills are used frequetly throughout this course. Hoors Pre-Calculus is a rigorous ad fast-paced course. There will be etesive use of graphig calculators which is required for this course. A TI-84 Plus graphig calculator is recommeded. Ay other type of graphig calculator will have to be approved by the teacher. For this prerequisite packet, calculators should be used oly to check work. The Pre-Calculus prerequisite packet is due the first day of school. It will be graded ad it will cout as a test grade. Work must be show to support all aswers. Your test grade will reflect both, your effort (50%) which is based o attemptig all problems ad showig work for all problems, ad accuracy (50%). The packet is broke ito specific cocepts. Some sectios have worked out eamples followed by problems for you to complete. Be sure to complete each umbered eercise icluded i this packet. Below are a few websites you may wish to visit for additioal eamples ad support. Algebra1olie: Algebra 2 olie: Algebra Help: Geometry: Results from the summer prerequisite work will help guide skill ad cocept reiforcemet lessos that will take place the first few weeks of school. Have a ice summer, Lyma Math Departmet

3 Part 1 Lies ad Coordiate Geometry Algebra Cocepts Slope-itercept form of a lie y = m + b Stadard form of a lie A + By = C Poit-slope form of a lie y y 1 = m( 1 ) Slope of a lie m = y 2 y Midpoit formula ( Geometry Cocepts, y 1+y 2 ) 2 Distace formula d = ( 1 2 ) 2 + (y 1 y 2 ) 2 Perpedicular bisector a perpedicular lie passig through the midpoit of a segmet. Altitude of a triagle a segmet from a verte perpedicular to the opposite side. 1) Fid a equatio of the lie i slope-itercept form that passes through (2,1)ad (1,6). 2) Write the equatio of the lie parallel to the lie 4 6y = 1 i poit-slope form passig through the poit (-10,2). 3) Write the equatio of the lie i slope-itercept form passig through the poit (2, 4) ad perpedicular to the lie 2y = 7 4) Fid the value of a if a lie cotaiig the poit (a, 3a) has a y-itercept of 7 ad a slope of ) Fid the distace betwee the poits ad the fid the midpoit of the segmet that jois them. a) (0,8) ad (6,16) b) ( 2,5) ad (10,0)

4 Part 2 Epoets & Roots Properties of Epoets a m a = a m+ E: 5 2 = 7 a m a = am E: 8 5 = 3 a 0 = 1 a 0 (a m ) = a m E: ( 5 ) 2 = 10 ( a b )m = am b m E: (2 )3 = 8 3 a = 1 a 2 E: = (ab) m = a m b m E: (4y 2 ) 3 = 64 3 y 6 1 = a a E: 1 2 = 2 a Properties of th Roots = b meas b = a Defiitio of the th root: a 1 = a 1) ab 2) a b m 3) a 4) a 5) a = a = a b b 3 E: E: 16 m = a 81 3 E: = a if is odd E: ( 5) 3 4 = a if is eve E: ( 3) = 8 27 = 2(3) = 6 4 = 16 4 = = 729 = 5 = 3 = 3 = 3 Simplify the epressio. Elimiate ay egative epoets. 6) ( 3 2 y 4 ) 3 7) (33 ) ) ) ) ) (2 y 3 ) 4 (y 4 ) 3 2 y 4 12) ) (9st) 3 2 (27s 3 t 4 ) 2 3

5 Part 3 Factorig & Solvig Quadratic Equatios GCF Guess ad check Groupig Differece of two squares Factorig Methods Sum/differece of cubes Factor completely each epressio. 14) ) ) ) ) 28y 3 + 7y 2 19) ) ) ) 8a ab 3 Solve the equatio. 23) = 0 24) = 0 25) = 0

6 Part 4 Ratioal Epressios Multiplyig A B C D = AC BD Multiply umerators ad multiply deomiators Simplifyig AC BC = A B Factor both umerator ad deomiator ad cacel commo factors. Eample: Dividig A B C D = A B D C Keep the first fractio, flip the secod ad multiply Addig Like deomiators: A C + B A + B = C C Ulike deomiators: A C + B AD + BC = D CD Add = 3(+2)+( 1) = = +2 ( 1)(+2) ( 1)(+2) ( 1)(+2) Simplify the epressio. 26) 3(+2)( 1) 6( 1) 2 27) Perform the idicated operatio ad the simplify completely. 28) ) )

7 Part 5 Iequalities Solve each iequality. Graph the solutio. 31) ) ) ) 3 < Part 6 Fuctios & Graphs Determie if the graph represets a fuctio usig the vertical lie test. 34) 35) 36) 37) Sketch the graph of the each fuctio. If you eed a remider, use your graphig calculator to help remember trasformatios of fuctios. Keep i mid, you eed to be able to graph fuctios without a graphig calculator. 38) f() = ) f() = ( + 2) ) f() = + 3

8 41) f() = ) f() = ( + 1) Combiig Fuctios & Compositios of Fuctios Let f() = 1 ad g() = 2 Combiig Fuctios f() + g() E: (f + g) = 1 2 f() g() E: (f g) = 1 2 Give two fuctios f ad g, the composite fuctio, f g, (also called the compositio of f ad g) is defied by (f g)() = f(g()) Fid f + g ad f g 43) f() = 3, g() = 2 44) f() = 2, g() = ) Give f() = 6 5 ad g() = 2 fid: 46) Give f() = 2 ad g() = 3 fid: a) f g = f(g() = a) f g b) g f b) g f c) f f c) g g

9 Part 7 Polyomial Fuctios Polyomial Divisio Log Divisio EX: Sythetic Divisio Quotiet: Divide the polyomials usig log divisio 47) P() = ) P() = D() = D() = 2 3 Divide the polyomials usig sythetic divisio. 49) f() = , g() = ) h() = , j() = ) For the graph pictured at the right: a) Describe the ed behavior b) Determie whether it represets a odddegree fuctio or a eve-degree fuctio c) State the umber of real zeros

10 Part 8- Right Triagles & Trigoometry For the right triagle pictured: SOHCAHTOA Pythagorea Theorem si A = opp hyp c si 1 ( a ) = A c a 2 + b 2 = c 2 cos A = adj hyp = b c cos 1 ( b c ) = A ta A = opp adj = a b ta 1 ( a b ) = A Fid the value of the trig fuctio epressed as a fractio ad as decimal to the earest hudredth. Fid the value of the agle (θ) to the earest degree. Show all work for set up of ratios ad trig equatios. 52) 53) si θ = cos θ = ta θ = θ = si θ = cos θ = ta θ = θ = Solve for the value of. 54) 55) 56)