Bishop Kelley High School Summer Math Program Course: Trigonometry and Trigonometry with Pre-Calculus

Transcription

1 Summer Math Program Course: Trigonometr and Trigonometr with Pre-Calculus NAME: DIRECTIONS: Show all work on loose-leaf paper, which ou will turn in with the packet. (NO WORK IN PACKET!) Put final answer on the answer sheet. This material will be collected, graded, and points awarded at the discretion of each teacher on the first da of the math class. A test on this material will be administered during the first week of the class. An additional resource for help with this packet is It provides videos of about 10 minutes in length on hundreds of different math topics. Math Teachers will be available in C-1 the following dates/times if ou need help. Date Monda, Jul 7 th Thursda, Jul 30 th Monda, August 3rd Time 9-10:30am 9-10:30am 9-10:30am

2 1._Classif the angle as right, acute, or obtuse.._simplif the following comple fraction: (Leave Answer in simplified Radical Form) _Solve and simplif the following fraction: 5 7._Solve the right triangle: 30 and a 1; find, b, and c c a b, b, c 5._Rationalize the following radical: (Leave Answer in simplified Radical Form) 3. Solve the following rational equation. 7 15

3 7._ Line r is parallel to line t. Find m 5. The diagram is not to scale. r t 5 [A] 35 [B] 5 [C] 135 [D] 15._Simplif the following fraction to radical form: 3 9._ Rationalize the following denominator. Simplif an radicals Evaluate the following epressions without using a calculator. 1 log _Simplif the fraction: _ Use properties of logarithms to epand the logarithmic epression as much as possible. 3 log 3( )

4 13. Evaluate the following algebraic epression: ( ) ( 3 + ) for = -3 and = 1. Evaluate the following algebraic epression: + 5; when = and = 3 15._Which statement is true? [A] [B] [C] [D] are same-side angles. are same-side angles. are alternate interior angles. are alternate interior angles. 1._A baseball diamond is a square of side length 90 feet. How far is the throw, to one decimal place, from home plate to second base?

5 17._Find the value of and. (Leave Answers in Radical Form), 0 1._Find the value of and. (Leave Answers in Radical Form), _What is the length of the diagonal of a square with side lengths 7? 0._Find the values of and. The diagram is not to scale. 1 ( 3) ( + ) 7 [A] = 77, = 59 [C] = 57, = 77 [B] = 77, = 57 [D] = 1, = Write the equation of the line in slope- intercept form with a slope of 1/3 that passes through (5, -7).. Write the equation of the line in slope-intercept form that passes through (, -) and (3, ).

6 3._Find the length of the leg of this right triangle. Give an approimation to 3 decimal places. a._a 5.5 foot ladder rests against the side of a house at a point.1 feet above the ground. The foot of the ladder is feet from the house. Find the value of to one decimal place. (Circle Your Answer).1 ft 5.5 ft [A] 7.0 [B] 1.9 [C].3 [D] _Find the altitude of an isosceles triangle with base 10 and congruent sides of length 9. (Leave Answer in Radical Form)._A telephone pole breaks and falls as shown. 7 ft 10 ft To the nearest foot, what was the original height of the pole? (Circle Your Answer) [A] 19 ft [B] 0 ft [C] 1 ft [D] 1 ft

7 7._The cit commission wants to construct a new street that connects Main Street and North Boulevard as shown in the diagram below. The construction cost has been estimated at $110 per linear foot. Find the estimated cost for constructing the street. (1 mile = 50 ft) North Blvd. (new street) 9 mi W 5 mi Main St. S E (Circle Your Answer) [A] $1133 [B] $5,31 [C] $50,00 [D] $5,979,70._How long is a string reaching from the top of a 1-ft pole to a point 1 ft out from the bottom of the pole? Give an eact answer and an approimation to 3 decimal places. 9._Solve the proportion: [A] [B] [C] [D] 3 30._Solve the perimeter formula for an isosceles triangle,, for b. [A] [B] [C] [D]

8 31._The complement of an angle is 5. What is the measure of the angle? [A] 75 [B] 155 [C] 5 [D] 15 3._Solve the area formula for a trapezoid,, for. [A] [B] [C] [D] 33._Solve: 3 1 (Leave answer as an improper fraction) 5 3._A worker in an assembl line takes 7 hours to produce parts. At that rate, how man parts can she produce in 1 hours? (Circle Your Answer) [A] parts [B] 13 parts [C] parts [D] parts _Solve the proportion Solve the following sstem of equations _ 37._Two sides of a triangle have lengths 1 and. The length of the third side must be greater than and less than., 3._Two sides of a triangle have lengths 1 and 10. What are the possible lengths of the third side? < < 39. Simplif using the laws of eponents:

9 0._Identif the shortest side of ABC. C A 5 B 1. Simplif using the laws of eponents. Do not leave an zero or negative eponents. (- -3 )( -7 ) _. Solve the quadratic equation using the quadratic formula. 3 3 = 0 3._ Find 70 Q R The diagram is not to scale. 50 [A] 0 [B] 10 [C] 110 [D] 70

10 ._Find the missing side lengths for and. (Leave answers in Radical Form) 30 9, 5._ Find the values of,, and z. The diagram is not to scale z [A] [B] [C] [D]._Write the standard form of the equation of the circle that passes through the point (3, ) with its center at the origin. 7._Find the distance between the points (5, ) and ( 3, 0).._Solve the equation

11 9._ If and, then what is the measure of The diagram is not to scale. [A] [B] 1 [C] 5 [D] 7 50._ and are supplementar angles., and. Find the measure of each angle. [A] [B] [C] [D] 51._Identif all horizontal and vertical asmptotes of the graph of the function. f ( ) 5._Sketch the graph of the function. f ( ) 3 (Use Graph Provided) H.A., V.A.

12 53._The price per person of renting a bus varies inversel with the number of people renting the bus. It costs $1 per person if people rent the bus. How much will it cost per person if 31 people rent the bus? (Circle Your Answer) [A] $1.5 [B] $15.50 [C] $.00 [D] $ _Solve: 1 3 (Leave answer as a fraction) _A certain gas will escape from a storage tank according to the formula p, where e represents the amount escaping per minute in gallons, and p represents the pressure in pounds per square inch. What is the pressure on the gas when about 50 gallons per minute are escaping? (Circle Your Answer) e 10 [A] 0. lb/in. [B] 3. lb/in. [C] 1. lb/in. [D] 19.7 lb/in. 5._Graph: f() = (Use Graph Provided)

13 57_ Find the value of the variable if and The diagram is not to scale. 1 3 l 5 7 m [A] 1 [B] [C] 3 [D] 5._ If and are supplementar angles and, find and [A] 7, 1 [B] 1, 3 [C] 1, 7 [D] 3, 1 59._Write the polnomial as a product of linear factors _Find all real zeros of the function. 3 g( ) _ Find the value of. Round the length to the nearest tenth. (Leave Answers in Radical Form),, 1 d Not drawn to scale [A] 15. d [B] 10. d [C] 9 d [D] 31. d._factor completel:

14 Perform the indicated operations. 3._ b 1g( 1)( 3)._ ( 7 3) ( 1) 5._Graph: f() = 3 9 (Use Graph Provided) Use compass directions to describe the direction of the Ra. (Not drawn to scale)._ N W S E [A] 10 west of south [B] 10 east of north 7._ Evaluate the logarithm. [C] 10 east of south [D] 10 west of north [A] 3 [B] 5 [C] [D]._A rock is thrown from the top of a tall building. The distance, in feet, between the rock and the ground t seconds after it is thrown is given b d 1t t 505. How long after the rock is thrown is it 500 feet from the ground?

15 9._Solve b the quadratic formula: 3 0 = 0, 70._A bulldozer operator considered the following pricing strateg for contract jobs: $30 base charge, plus a variable cost that is a function of the number of hours worked. The cost would be $ 3. 05, where is the number of hours. The total cost of a contract job would be given b the function C( ) $ Graph the function. For what value of will this function be maimized? Round to the nearest tenth of an hour. (Circle Your Answer) [A] = 7.0 [B] =.0 C() C() [C] = 3.0 [D] =.0 C() C() _Write the epression as a comple number in standard form. ( 3 7i)( 1 i) 7._Solve the equation. 0 0 (Leave Answers in Radical Form), 73._Solve for : = 150, 7._Factor the epression: 1

16 Use compass directions to describe the direction of the Ra. (Not drawn to scale) 75._ N W S E [A] 3 east of north [C] 3 west of south [B] 3 east of south [D] 3 west of north Use compass directions to describe the direction of the Ra. (Not drawn to scale) 7._ N W E S [A] 7 north of west [C] 7 north of east [B] 7 south of west [D] 7 south of east 77._Simplif the following comple fraction. (Leave Your Answer as a Proper Fraction) _ Write the equation in logarithmic form. [A] [B] [C] [D]

17 79._Simplif the following Fraction: 3( 1) 5 In which quadrant does the point lie? Write the coordinates of the point. A O C B 0._ Point A [A] quadrant II; (, ) [C] quadrant III; (, ) [B] quadrant I; (, ) [D] quadrant I; (, ) 1._ Point B [A] quadrant II; (, ) [C] quadrant III; (, ) [B] quadrant III; (, ) [D] quadrant IV; (, )._ Point C [A] quadrant IV; (, ) [C] quadrant III; (, ) [B] quadrant III; (, ) [D] quadrant IV; (, )

18 #3-, Perform the indicated operation and simplif if possible _Write the slope-intercept form of the line that passes through the point 1. (Circle Your Answer) (, 5) and is parallel to the line 1 1 [A] = 3 [B] = 17 [C] = [D] = 17 3._Write the equation in slope-intercept form. Then identif the slope and -intercept slope-intercept form, slope, -intercept 1 9._Graph the line. 1 3 (Use Graph Provided) 90._Find the slope of the line passing through (3, 1) and (, ).

19 91._Solve the inequalit. Then graph our solution. 3( 1 ) 15 (Use Graph Provided) 9._Solve for z: z 7z 93._Solve the equation _Find the arc length of AB to two decimal places. 95._Find the length of a 0 arc in a circle with a radius of. (Circle Your Answer) [A] [B] [C] [D] _The circumference of a circle is cm. Find the diameter, the radius, and the length of an arc of 110. (Leave Answers in terms of π) 9 diameter, radius, length of arc 97._A circle has a circumference of meters. Find its radius. (Circle Your Answer) [A] 15. m [B] 7. m [C] 1 m [D] m 9._Find the circumference of a circle with radius mm. Use _Find the equation of the circle with center (5, ) and radius of.

20 100._Find the equation of the circle of radius with its center at the origin Determine whether the following function is even, odd, or neither. f() = 5 Solve the proportion. 10._ [A] 3 [B] [C] [D] _ [A] [B] [C] [D] 10._Evaluate the logarithm. log 0.01 [A] 10 [B] [C] [D] _Simplif the epression. [A] [B] [B] [D]

21 Answer Sheet Graph Below Graph Below Graph Below Graph Below Graph Below

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23 Answer Sheet