25) x x + 30 x2 + 15x ) x Graph the equation. 30) y = - x - 1

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1 Pre-AP Algebra Final Eam Review Solve. ) A stone is dropped from a tower that is feet high. The formula h = - t describes the stoneʹs height above the ground, h, in feet, t seconds after it was dropped. What is the stoneʹs height seconds after it is released? Simplif the algebraic epression. ) -( - 9) - + Simplif the eponential epression. Assume that variables represent nonzero real numbers. --z - ) -z- ) (--)(-) Rationalize the denominator. ) - ) Use the product rule to simplif the epression. ) 0 Add or subtract terms whenever possible. ) Name Simplif b reducing the inde of the radical. ) Find the product. ) ( - )( + ) ) ( + )( - + ) ) (9 + ) Factor b grouping. Assume an variable eponents represent whole numbers. ) Factor the trinomial, or state that the trinomial is prime. 9) + - 0) Factor the difference of two squares. ) ( - ) ) Find the formula for the volume of the region outside the smaller rectangular solid and inside the larger rectangular solid. Epress the volume in factored form. Factor and simplif the algebraic epression. ) ( + )/ + ( + )/ Simplif the rational epression. Find all numbers that must be ecluded from the domain of the simplified rational epression. ) Multipl or divide as indicated. ) + - Add or subtract as indicated. + ) ) Doctors use the rational epression DA A + to determine the dosage of a drug prescribed for children. In this epression, A = childʹs age and D = adult dosage. What is the difference in the childʹs dosage for an -ear-old child and a -ear-old child? Epress the answer as a single rational epression in terms of D. Simplif the comple rational epression. + 9) - ) = - + ) = Solve and check the linear equation. ) [- + + ( + )] = - - Solve the equation. ) = + 9) - Evaluate the epression without using a calculator. ) / ) -/ a b a b a Graph the equation. 0) = - - ) = - Perform the indicated operations and write the result in standard form. ) ( + i)( - i) - ( - i)( + i) Simplif using properties of eponents. ) (/)(9/) ) / / Factor using the formula for the sum or difference of two cubes. ) Divide and epress the result in standard form. ) - i + i

2 Perform the indicated operations and write the result in standard form. ) ( -)( -) Solve the absolute value equation or indicate that the equation has no solution. 0) = For the given functions f and g, find the indicated composition. ) f() = - +, g() = + (g f)() Evaluate or simplif the epression without using a calculator. ) ln e Solve the equation b factoring. 9) - - = ( + ) Solve the equation b the square root propert. 0) ( + ) = 9 Solve the equation b completing the square. ) = 0 ) A rain gutter is made from sheets of aluminum that are inches wide. The edges are turned up to form right angles. Determine the depth of the gutter that will allow a cross-sectional area of square inches. There are two solutions to this problem. Round to the nearest tenth of an inch. Solve the absolute value inequalit. Other than, use interval notation to epress the solution set and graph the solution set on a number line. ) - < 0 ) Begin b graphing the standard quadratic function f() =. Then use transformations of this graph to graph the given function. ) h() = ( + ) - Find the domain of the composite function f g. 9) f() = +, g() = + Find the inverse of the one-to-one function. 0) f() = - Solve the polnomial equation. In order to obtain the first root, use snthetic division to test the possible rational roots. ) = 0 ) = 0 Graph the functions in the same rectangular coordinate sstem. ) log Use properties of logarithms to condense the logarithmic epression. Write the epression as a single logarithm whose coefficient is. Where possible, evaluate logarithmic epressions. 9) (log (r - ) - log r) Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places 0) log. Solve the logarithmic equation. Be sure to reject an value that is not in the domain of the original logarithmic epressions. Give the eact answer. ) log - log = log 9 Solve the polnomial equation b factoring and then using the zero product principle. ) = 0 Solve the radical equation, and check all proposed solutions. ) 0-0 = + ) = ) Solve the formula r = Solve and check the equation. ) ( + )/ = - V for V. πh Solve the equation b making an appropriate substitution. ) = 0 9) / - / - = Find the domain of the function. ) g() = - Given functions f and g, perform the indicated operations. ) f() = -, g() = - - Find f g. ) f() = -, g() = - Find f - g. Find the domain of the composite function f g. ) f() = ; g() = + ) f() = and g() = log / Evaluate the epression without using a calculator. ) log ) log 9 ) log ) ln () = 9 ) log ( + ) + log ( - ) = Use properties of logarithms to epand the logarithmic epression as much as possible. Where possible, evaluate logarithmic epressions without using a calculator. ) loga + ( -) Solve the equation b epressing each side as a power of the same base and then equating eponents. ) = Solve the eponential equation. Epress the solution set in terms of natural logarithms. ) + =

3 ) Two cars leave a cit and head in the same direction. After hours, the faster car is miles ahead of the slower car. The slower car has traveled miles. Find the speeds of the two cars. ) In Miguelʹs home town, the percentage of women who smoke is increasing while the percentage of men who smoke is decreasing. The function = models the percentage,, of women in this cit who smoke ears after 990. The function 0. + = 9. models the percentage,, of men in this cit who smoke ears after 990. Use these models to determine when the percentage of women who smoke will be the same as the percentage of men who smoke. Round to the nearest ear. What percentage of women and what percentage of men (to the nearest whole percent) will smoke at that time? Solve the sstem b the addition method. 9) = -9 - = Solve the sstem of equations. 0) + + z = - - z = z = Use the formula for the general term (the nth term) of an arithmetic sequence to find the indicated term of the sequence with the given first term, a, and common difference, d. ) Find a when a = -, d = -. Write a formula for the general term (the nth term) of the arithmetic sequence. Then use the formula for an to find a0, the 0th term of the sequence. ) -, -, -, -,... Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence. ) (-)i i = Find the sum of the infinite geometric series, if it eists. ) ) A radio transmission tower is 0 feet tall. How long should a gu wire be if it is to be attached feet from the top and is to make an angle of with the ground? Give our answer to the nearest tenth of a foot. Use the Pthagorean Theorem to find the length of the missing side.then find the indicated trigonometric function of the given angle. Give an eact answer with a rational denominator. ) Find csc θ. Find the eact value of the epression. ) sin- - Use a sketch to find the eact value of the epression. 9) csc tan- Find the eact value of the epression, if possible. Do not use a calculator. 90) tan- tan π Solve the right triangle shown in the figure. Round lengths to one decimal place and epress angles to the nearest tenth of a degree. 9) a =. m, B = 9. An object is attached to a coiled spring. The object is pulled down (negative direction from the rest position) and then released. Write an equation for the distance of the object from its rest position after t seconds. 9) amplitude = cm; period = π seconds Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round lengths to the nearest tenth and angle measures to the nearest degree. 9) B =, b =, c = Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. 9) b =, c =, A = 0 Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. Round lengths to the nearest tenth and angle measures to the nearest degree. 9) B =, b =., a =. Solve the equation on the interval [0, π). 9) csc - csc = 0 9) The output voltage for an AC generator is approimated b v = cos (πt - π ). Find the smallest positive value of t for which the output is 0 volts. Epress the sum or difference as a product. 0) sin 9 + sin Use a half-angle formula to find the eact value of the epression. ) sin π Use the given information to find the eact value of the trigonometric function. ) sec θ = -, θ lies in quadrant II Find sin θ. Complete the identit. tan ) + tan =? ) sec + sec tan - tan =? ) sin + tan + cot =? Use reference angles to find the eact value of the epression. Do not use a calculator. ) csc π ) cot -π ) sin Find the indicated sum. ) Find the sum of the first terms of the arithmetic sequence:,,,,... Use a right triangle to write the epression as an algebraic epression. Assume that is positive and in the domain of the given inverse trigonometric function. 9) tan(sec- + 9 ) Solve the equation on the interval [0, π). 99) cot cos = cot

4 Answer Ke Testname: PRE AP ALGEBRA WITH TRIGONOMETRY FINAL EXAM REVIEW Answer Ke Testname: PRE AP ALGEBRA WITH TRIGONOMETRY FINAL EXAM REVIEW ) ft ) ) z ) - ) 0 + ) ) ) + 9) ) ) ) / ) / ) ) - - ) + ) + + ) ( + )( + ) 9) ( + )( - ) 0) ( + )( - ) ) (9 + )( + )( - ) ) a(a + b)(a - b) ) ( - )( + + ) ) ( + )/ ( + ( + )/) ) +, -9, ) - ) + + ( + )( + )( - ) ) 0 D 9) + - 0) ) ) ) ) ) {-} ) + i ) i )

5 Answer Ke Testname: PRE AP ALGEBRA WITH TRIGONOMETRY FINAL EXAM REVIEW Answer Ke Testname: PRE AP ALGEBRA WITH TRIGONOMETRY FINAL EXAM REVIEW 9) -, - 0) {-, } - - ), - + ). in. and. in. ) {0, -, -} ) {} ) {-} ) V = πr h ) - ) {-,, -i, i } 9) {-, } 0) -, - ) (, ) 0 ) (-, -] [, ) ) ) (-, -) (-, ) (, ) - ) - - ) + ) [-, ) ) - + 9) (-, -) or (-, ) 0) f-() = + ) {-, -, } ) {-,, + i, - i} 9 ) ) - ) 9 ) 0 ) ) 9) log r - r 0). ) {} e ) ) {} ) loga + log a ( + ) - loga ( - ) ) - ) ln ln - ) mph and mph ) 0; % 9) {(, )} 0) {(-,, )} ) - ) an = -n - 9; a0 = -99 ) ) - ) ) 9. feet 9 ) ) - π

6 Answer Ke Testname: PRE AP ALGEBRA WITH TRIGONOMETRY FINAL EXAM REVIEW 9) 90) - π 9) 9) A = 0., b =. m, c =. m 9) d = - cos t 9) no triangle 9) a =., B =, C = 9) A = 0, C =, c = ; A =, C = 0, c =. 9) π, π, π, π 9) 0.00 second 99) π, π 0) sin cos ) + ) ) sin ) sec - ) sec ) - ) )

AP Calculus AB Summer Assignment Mrs. Berkson

AP Calculus AB Summer Assignment Mrs. Berkson The purpose of the summer assignment is to prepare ou with the necessar Pre- Calculus skills required for AP Calculus AB. Net ear we will be starting off the