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1 Honors Pre-Calculus Unit 3 Review Sheet Name: Formulas that will be given on the test: a n = a1 + d(n 1) ; a n = a1(r) n 1 ; S n = n æ (a1 + a n) ; S n = 1- r n a1 ; S = 2 ö ç a1 è 1- r ø 1- r Matrices: Given the following matrices perform the indicated operations if possible: C Ss D ETI one CEE't fyi DNE I Cob 2644 DNE DNE æ 2 p 3 ö If A = ç and det A = 14 find the possible values è- 4 p pø of p. æa 2 ö Let M = ç where a Î. è 2-1ø (a) Find M 2 in terms of a. (b) If M 2 æ 5-4ö is equal to ç find the value of a. è- 4 5 ø (c) Using this value of a find M l and hence solve the system of equations: x + 2y = 3 2x y = 3 é5 2ù A and B are 2 2 matrices where A = ê ú and ë2 0û é11 2ù BA = ê ú. Find B. ë44 8û 2p2tl2p l4 2lpt7XpD 2p2tl2p 14 0 P lp2t6p 77 0 p Ea.IE E'II Eat La 2a 2

2 The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740 how many of each type of ticket were sold? Set up a matrix to solve. Student Adult 530 xty y 7 Rob has 40 coins all dimes and quarters worth $7.60. How many dimes and how many quarters does he have? Set up a matrix to solve. Xty 4O Binomial Expansion: Use binomial expansion to expand sit lb't b bscamtaibqaptybcaxt.cz b d3t3d2 3b t3dt3b5t1t3b r 3rd2 term of n 7 3 of 4th term n ycalb lb5C9 ll89b 5cg s fbuys vs F I 2nd term of n 21602T dBt5b 36174Sb d3 9d2bt27dbZ Mt Sequences: Describe the pattern in the sequence. Find the next three terms ADDing2eachtime to Arithmetic Given the formula terms of the sequence multiplyby2eachtimetgeometric General sequence ADDinetwotermsthenmultiplyby2ts Y Geometricto Multiplyby eachtime B d XY = 5 [ = An 12 yd Ane tbr sd t98 24 An 28. Geometric b r t7... Geometric Aye Write the explicit formula (rule) for the sequence. Then find the fifth term in the sequence. NocommonDifferanceorRatio Arithmetic T 31 Aj A O Ratio Neither b NOcommonDifferance or Neither A Find the first five Are the following Arithmetic Geometric or Neither? Explain your reasoning Arithmetic o Find the following terms of the binomial expansion N 8 r 4 gcy term of 5th term of (4x - 3y) g5 5s4f5v t1os3f5v5tlos2t5vpt5st5v5 t L i.ao.io oioxt.as y Edigmueakers XY = 1 [ = 6 An It Cn D un g As 243 Ag 23 As

3 Write the recursive formula for the sequences and find the next term Anti Ant2 a 18 Write the explicit formula (rule) for the sequence and find the indicated term find. An 7 5 n D 125h XYZ... find XY Ant 2An 4 Are n an A.geIztfTz fg5a ng The table shows the predicted growth of a particular bacteria after various numbers of hours. Write an explicit formula (a rule) for the sequence of the number of bacteria. Hours (n) Number of an attachd Bacteria rattan193 Suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor it rebounds to 85% of its previous height. How high will the ball rebound after its third bounce? Round to the nearest tenth. w.si fjounayia3 B2ouna Ha Ha Orlando is making a design for a logo. He begins with a square measuring 24 inches on a side. The second square has a side length of 19.2 inches and the third square has a side length of inches. Which square will be the first square with a side length of less than 12 inches? are are squure 5 square Series: Use summation notation (sigma) to write the following series: u Evaluate the following series: l9n for 14 terms n l 5h for 10 terms to l n i an for 5 terms. Ifs.sn a a n l to Does the infinite geometric series diverge or converge? Explain to. If1000K Evaluate the infinite geometric series. Round to the nearest hundredth if necessary. Converge sn z Diverge SF at

4 For the series find the first and the last term: Use the finite sequence. Write the related series. Then evaluate the series and and lt The sequence has 11 terms. q6nt9 4 an 45t6lmB 6nt93 n The sequence has 15 terms. an E5t5CnD3 5h103 f5n The sequence has 12 terms. An 2h Elan 1560 A large asteroid crashed into a moon of a planet causing several boulders from the moon to be propelled into space toward the planet. Astronomers were able to measure the speed of one of the projectiles. The distance (in feet) that the projectile traveled each second starting with the first second was given by the arithmetic sequence Find the total distance that the projectile traveled in seven seconds II Justine earned $17000 during the first year of her job at city hall. After each year she received a 4% raise. Find her total earnings during the first five years on the job A rubber ball dropped on a hard surface takes a sequence of bounces each one as high as the preceding one. If this ball is dropped from a height of 10 feet what is the total vertical distance it has traveled after it hits the surface the 5th time? Dante is making a necklace with 18 rows of tiny beads in which the number of beads per row is given by the series a. Use summation 3t7Cn notation to Dwrite 7h the series. 4 Explain what the numbers in the summation notation represent in this situation and how you found the expression used in the summation. 18 7h 4 nel b. Find the total number of beads in the necklace. Explain your method for finding the total number of beads. Cumulative Review: o i m ii E

5 2 FactorCancel x 3-2x Plugin x x x 2 x - 2 x + 10x + 25 fftf.ie I Y7sEtIx fiis E oo a z o w x FactorCancel Plugin 7ax ( x + h) ( 4x 7) 4 - h 0 h 3x - 5x -12 x 4 x - 3 4th h x 4 x 9 3 Z J J X An airplane travels 250 mph due south. There is a steady 35 mph wind with a bearing of 90. A) Write the component form of the velocity vector of the airplane (without wind). 1 LO 250 zoo B) Write the component form of the velocity vector of the airplane C) Write the component form of the actual velocity vector of the airplane D) What is the actual ground speed of the airplane? E) What is the actual compass bearing of the airplane? 6 Bearing_ tan 35 An airplane is flying at a direction angle of 40 at 350 mph. A wind is blowing west at 70 mph. A) Find the actual speed of the plane z 35ocos4assosinito B) Find the actual bearing of the plane ztany79s4yi Beanng 37I 4l C) Find the actual directional angle of the plane in L4mp.TT NFt224 si TL speect299 wind Identify the type of conic.change each to standard form and graph For a parabola find the a) Vertex b) Focus c) Directrix d) Focal Width

6 For an ellipse find the a) Center b) Vertices c) Foci d) Major Axis For a hyperbola find a) Center b) Vertices c) Foci d) Asymptotes 7. 4x 2 + 9y 2 16x 36y + 16 = 0 Name Ellipse a) yt4 g b) c) t9 y 25 C2 1 r52 d) MMMMM Cx g w a 3 ce9 4 5 b 2 c asf hperbola 8. 4x x 9y 2 36y 36 = 0 Name a) Cy2t4y b) O 2 c) 61 2 d) Cy2t4yt l 3 N3A C.gl yt2 Cx 3 A t b a c4 b I T xtg lyt42 c Fs Parabola 9. y 2 8x 6y 7 = 0 Name y2 6yt x a) 23 b) c) d) y x mmmm fly f o.ae