4. Find a, b, and c. 6. Find x and y.

Transcription

1 Grace Brethren Christian Schl Entering Trig/Analysis: Page f Summer Packet fr Students entering Trig/Analysis Review prblems frm Gemetry: Shw yur wrk!. Twice the cmplement f angle A is 35 less than the supplement f angle A. Find angle A.. The lengths f the sides f a triangle are 9cm, 3 cm and 5 cm. Is this triangle acute, right r btuse? 3. Given that triangle ABC and triangle DEF are similar. Slve fr and y. 4. Find a, b, and c. A D b y c B 9 C E 6 F a Find. 6. Find and y y 7. Find a, b, and h. 8. Which cngruency principle wuld yu use t prve that HIJ{ JKL if HI{ JK and IJ{ KL? (Recall: SSS, SAS, ASA, AAS, HL) a h b I K 3 9 H J L

2 Grace Brethren Christian Schl Entering Trig/Analysis: Page f 9. If m DE = and m BC = 78, find m<a. 0. Slve fr : D B A 4 6 E C. Find the value f if AB = 4, BC = 0, CD =.. An equilateral triangle has a perimeter f 4 3 m and an area f 48 3 m. Find the altitude f the triangle. D E C B A 3. In circle O, the radius is 3 meters. Find the area f the shaded sectrs. 4. Find the length f the diagnal AG in the slid right rectangular prism shwn belw: O 60 A B 4 C 8 E F H G 5. Find the area that is UNSHADED, if the circle is tangent t 3 sides f the rectangle: 6. Skip this prblem. This b is intentinally left blank. 8 4

3 Grace Brethren Christian Schl Entering Trig/Analysis: Page 3 f 7. Find the values f and y that will make this quadrilateral a parallelgram: 8. What values must and y have t make this quadrilateral a parallelgram? y y + 5 (5y + ) 9. What specific quadrilateral has diagnals that bisect each ther perpendicularly? 0. Write the fllwing sentence as an "if...then..." cnditinal; then write its cnverse and cntrapsitive sentences: All squares are rectangles. Identify which f the three sentences are true, and which are false.. Calculate the midpint, slpe and length f the segment determined by the pints (-3,-4) and (5,).. Graph the linear equatin y = Which is larger: <3 r <4? 4. Calculate the length f BC in simplest radical frm, then use this triangle t epress the fractins in simplest frm: B BC= SIN A = COS A = A C TAN A =

4 Grace Brethren Christian Schl Entering Trig/Analysis: Page 4 f Simplify the fllwing algebraic epressins: Eamples: E: 3 = 3 (3 ) = = (3) 4 E: i 3 5i + 6i 4 = 3 i 3 i + ( i) 5i + 6(+) = 9 i i 5i + 6 = 3 7i + 6 = 3 7i 5. i + 4i 3-3i 8-4 E : y + 3 = y y y + 3 = y y +3 = ( y y )( +3 ) = y y(+3) E: 5 y 0 = 5 () = y 6 y 4 y 6 (y) 4 7. e + g e 3 e g i i 3 i

5 Grace Brethren Christian Schl Entering Trig/Analysis: Page 5 f a hd d + a4 h e s u 4 s e u 7 3 u / 36. ( 7 )( + 7 ) i i + 4i 3 3i uv u v

6 Grace Brethren Christian Schl Entering Trig/Analysis: Page 6 f Use these reminders t cnvert measurements: Unit multipliers: km = 000 meters m = 00 cm in =.54 cm ft = inches yd = 3 feet min = 60 sec hr = 60 min mile = 580 ft Evaluate Functin Ntatin: Eample: f ( ) = f (3) =? f (3) = (3) + 4(3) 5 = = 5 Eamples: f ( ) = 4 g( ) = f g = f = f = = ( ()) ( ) (4) 4(4) 4 Eample: Change 30 mph t cm/sec 30miles hr min 580ft in.54cm hr 60 min 60 sec mile ft in = (30)(580)()(.54) (60)(60) cm sec g f = g = g = = ( ()) [4() ] (6) 6 36 g f = g = = + ( ( )) (4 ) (4 ) Cnvert 78 meters per hur t feet per secnd 4. f (6) =? f = + ( ) 3 4. Cnvert 6 feet per sec t miles per hur 43. f ( ) = 3 + g( ) = + 5 f ( g ()) =? 44. Cnvert 4 cm per min t inches per sec 45. Use f and g frm number 43 abve. g( f ()) =? 46.Use f and g frm number 43 abve. f () + g(0) =? 47. Use f and g frm number 43 abve. f ( g( )) =?

7 Grace Brethren Christian Schl Entering Trig/Analysis: Page 7 f Write apprpriate equatins and slve these prblems: 48. A ttal f 68 ducks and hrses were n the ranch. If tw times the number f ducks eceeded the number f hrses by seven, hw many f each were n the ranch? 49. A survey indicated that 3 ut f 4 dctrs used brand X aspirin. If 400 dctrs were surveyed, hw many used brand X? 50. In a randm selectin, 75% f the peple preferred t travel by car rather than fly. A ttal f 339 peple plled preferred flying. Hw many peple were plled? 5.Kaye has $.80 in nickels and dimes. She has three times as many dimes as nickels. Hw many nickels and hw many dimes des she have? 5. Find three cnsecutive dd integers such that fur times the sum f the first and secnd is 3 less than 7 times the third number. 53. The ally is 35% titanium. If there are 508 grams f ther elements in the ally, hw much titanium des it cntain? 54. LeAnn's test scres are 88, 00, 7 and 94. What scre des she need n the net test s that her verall average scre is 90? 55. Twice the number f reds eceeded 3 times the number f blues by 8. The rati f reds t the sum f reds and blues was 5 t 7. Hw many were red? Hw many were blue?

8 Grace Brethren Christian Schl Entering Trig/Analysis: Page 8 f Study the eamples and then slve the fllwing equatins: E: Using factring n 5 = 6 (Set equatin t zer, write plynmial in rder) = 0...e...( )( 3) = 0 = r = 3 E.Cmpleting the square 8 0 = 0 ( ) = 0 ( 4 + 4) = (-) =8 (-) = 9 -=!3 =5,- E: Slving radical equatins: (Islate radical n ne side; square bth sides) 3 = 4 3 = 5; -3=5; =8; =4 56. Slve by factring: 7 = 9 E.: Fractinal equatins: = 5(3)()( 4) 3 (3)()( 4) ( 4) 57. Slve by factring: 3 = 4 Multiply bylcd: (3)()(-4) = (3)()( 4) Reduce t: 5()( 4) (3)() = 3( 4) Distribute: = 3-7 =40 = 40 7 E. Slve linear systems by eliminatin/substitutin: - 3y = -6 u (-)[-3y =-6] + 5y = Add equatins tgether t - + 6y = eliminate ne variable + 5y = u y = 33uy=3 Substitute y = 3 int riginal equatin t btain = 3 Ans: (3,3) 58. Slve by factring: = Slve by cmpleting the square: + 7 = Slve by cmpleting the square: = Slve by cmpleting the square: - =

9 Grace Brethren Christian Schl Entering Trig/Analysis: Page 9 f 6. Slve fr : = Slve fr : 7 + = Slve fr : 7 + = 7 65.Slve this linear system: N R + N B = 70 N R + 3N B = Slve this system : N W + N G = 7 3N W 5N G = X 3 = = = 3 Cmplete the definitins f the basic trig ratis using ppsite leg, adjacent leg, hyptenuse, and supply the missing sides f the tw special right triangles 70. SIN =rati f 7. COS =rati f 7. TAN =rati f 45?? Leg = 74. Hyptenuse= 30?? Leg = 76. Hyptenuse =

10 Grace Brethren Christian Schl Entering Trig/Analysis: Page 0 f Draw a diagram,and set up an apprpriate trig rati t slve the fllwing prblems. Make sure that yur scientific calculatr is set t DEGREE MODE! 77. An airplane is flying at an altitude f 5000 feet abve the grund. The pilt sights an bject n the grund at an angle f depressin f 8. What is the slant range frm the airplane t the bject n the grund? (rund answer t nearest ft) 78. An issceles triangle has base angles f 70 and a base f 0 cm. Calculate the height f the triangle, and then determine the area f the triangle t the nearest cm. 79. A right triangle has legs f 0 cm and cm. Determine the degree measure in the angle ppsite the cm. leg. (Give answer t nearest degree). Analytic Gemetry Write equatins fr the lines r circles described: Linear equatins: y = m + b (slpe-intercept style) ( y y ) = m( ) (Pint-slpe frm) Circular equatins: ( h) + (y k) = r where center is (h,k), radius = r 80. Write an equatin f the line having slpe and y intercept (0, -3). 8. Write an equatin f the line passing thrugh the pints (,3) and (-4,5). 8. Write an equatin f the line parallel t 3y = 0, passing thrugh (,). 83. Write an equatin f the line that passes thrugh (,-) perpendicular t + 4y = Write an equatin f the circle centered at the rigin with radius Write an equatin f the circle centered at (,3) with radius 4.

11 Grace Brethren Christian Schl Entering Trig/Analysis: Page f E: Use the quadratic frmula 3 6 = 3 a = 3, b = 6, c = 6 ± = 6 ± = 6 + = 0 b ± = 6 ± = 6 6 ± = 6 b 4ac a ( 6) (3) = ± 4(3)() Slve using the quadratic frmula 8 = Slve using the quadratic frmula + 5 = Slve using the quadratic frmula = 0 Nw that yu ve finished, enjy the remaining summer days til schl begins this fall!!